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Variations of the H and K emission lines of singly ionized calcium in the eclipsing binary star system AR Lacertae

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Title:
Variations of the H and K emission lines of singly ionized calcium in the eclipsing binary star system AR Lacertae
Creator:
Hoffmann, Sara Witherow
Publication Date:
Language:
English
Physical Description:
xv, 200 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Eclipses ( jstor )
Emission spectra ( jstor )
Latitude ( jstor )
Light curves ( jstor )
Spectroscopy ( jstor )
Starspots ( jstor )
Stellar evolution ( jstor )
Stellar rotation ( jstor )
Stellar spectra ( jstor )
Wavelengths ( jstor )
Astronomical spectroscopy ( lcsh )
Eclipsing binaries -- Spectra ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1983.
Bibliography:
Includes bibliographical references (leaves 188-196).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Sara Witherow Hoffman.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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ACK1490 ( NOTIS )
11272217 ( OCLC )

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VARIATIONS OF THE H AND K EMISSION LINES
OF SINGLY IONIZED CALCIUM
IN THE ECLIPSING BINARY STAR SYSTEM AR LACERTAE










BY

SARA WITHEROW HOFFMAN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY








UNIVERSITY OF FLORIDA


1983




























Copyright 1983

by

Sara Witherow Hoffman






























For


Stardust


Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation


http://www.archive.org/details/variationsofhkem00hoff














ACKNOWLEDGMENTS


To all those who aided me during my work on this

dissertation I would like to express my appreciation.

I would like to thank the members of my committee:

Dr. Frank Bradshaw Wood, Dr. John P. Oliver, Dr. Howard L.

Cohen, Dr. Alex G. Smith, and Dr. Charles F. Hooper, Jr.

I would like to offer my thanks to Dr. Wood for serving

as chairman of my committee and escorting me at commence-

ment. In addition, I greatly appreciated his assistance in

my attempts to find rare references and his lending to me

his personal copies of papers. I would also like to express

my deepest gratitude to him for making possible the

replacement of the University of Florida spectrograph with

the University of South Florida spectrograph when the former

instrument was sent to Mt. John Observatory. I am also

greatly appreciative of his relating to me those fascinating

details of astronomical- history which could be recounted

only by one who had actually experienced them.

To Dr. Oliver I would like to express my greatest

appreciation for acting as my research adviser and acting as

co-chairman of my committee. His most generous expenditure

of his time, his lending of his support, and his

contribution of his expertise with photometric and








electronic equipment were invaluable aids to me in pursuing

the objective of completing a project of great interest to

both of us.

I am very grateful Dr. Cohen for his support, advice,

and guidance.

To both Dr. Smith and Dr. Hooper I would like to offer

my sincerest thanks for the very helpful information they

conveyed to me, but primarily I would like to thank them for

their recognition and support at critical points in my

career.

For his precision construction of the slit-viewing

optics from my drawings I would like to express my great

appreciation to Mr. Eli Graves.

To Marty deGeorge I would like to state again how very

grateful I was that he provided the transportation for the

spectrograph back and forth between Gainesville and Tampa on

so many weekends.

I would like to thank Roger L. Scott for so willingly

providing on request sensitometry and astrophotography

information gained from his own experience.

To Paul Gombola I would like to express my gratitude

for his accurate renderings of the figures in this

dissertation.

For his exacting performance in the painstaking typing

and printing of this dissertation, I would like to express

my extreme gratitude to Mr. Dan R. Rich. His patience,








endurance, and support during the very tedious production of

this document are most greatly appreciated.

I would like to offer my utmost thanks to Mr. Jean G.

Klein, Chairman of Natural Sciences, Santa Fe Community

College, for granting me a flexible teaching schedule and

spring terms with no teaching load so that my research could

be continued.

Thanks go also to Marinell Brown, who made the final

word processor corrections and printed the final copies of

this dissertation.

On a personal level my appreciation goes to my friends

who were supportive and understood that this project was

important enough for me to have to decline their social

invitations for a total time of years. For his steadfast

support during the early years of this project, I would so

very gratefully like to acknowledge Nelson L. Mathis--I'm

just sorry that this Christmas present is so belated. .

To my fellow graduate students who honored me with that

sinfully original committee at the first BLACK HOLE I would

like to say: Thanks, guys, maybe I should've been in

microwave astronomy with Penzias and Wilson (get it,

guys?)! And of course, I will be forever indebted to RLS

(?) and JTP (?) for the spectrophotometer I used to obtain

sensitometry spots. .

I would also like to express my special thanks to my

family (human and fuzzy alike) for their much appreciated

support, both emotional and monetary, while I saw this








project through. My great appreciation goes to my father,

Richard Thompson Hoffman, for answering my childhood

questions about stars, planets, calculus, and other math,

and to my brother, Richard Thompson Hoffman, Jr., for being

my childhood companion in adventures of scientific

discovery. My ultimate thanks go to my mother, Marguerite

Kinser Hoffman, for helping me with some of the tedium of

this work, for doing all the things she did to make this

zenith of educational achievement possible--among them

stimulating my mind from birth, showing me the excitement of

discovery, teaching me things far beyond my years,

enthusiastically allowing me the freedom to pursue my

dreams, and then sticking by me while I pursued them.


vii















TABLE OF CONTENTS


ACKNOWLEDGMENTS ......................................

LIST OF TABLES ...... ...................................

LIST OF FIGURES ....... ...............................

ABSTRACT ............................................. .


SECTION I


A HISTORY OF OBSERVATIONS OF H AND K
EMISSION AND THE AR LACERTAE SYSTEM


Prologue .............................................
Introduction .........................................
Early Observations of H and K Emission ...............
Early Observations of AR Lacertae ....................
Early Photometry ...................................
Early Spectroscopy .................................
Correlation of Photometry and Spectroscopy .........
Early Polarimetry ..................................
The "AR Lac Group" and Other Stars with Ca II
Emission ........................................
Further Observations of AR Lacertae ..................
System Elements ....................................
Spectroscopy and Photometry ........................
Radio Measurements .................................
Polarimetry and Other Measurements .................
Summary ..............................................


SECTION II


INSTRUMENTATION AND OBSERVATIONS ........


Instrumentation ..............................
Telescope ..................................
Spectrograph ...............................
Plates .....................................
Sensitometer ...............................
Densitometers ..............................
Calculator .................................
Observing Program ............................


viii


iv

xii

xiii

xiv








SECTION III DATA REDUCTION .......................... 40

Procedure and Theory ................................. 40
Plate-Tracing ...................................... 40
Conversion of Deflections to Relative Intensities .. 43
Density-deflection relations: D(d) .............. 43
Characteristic curves (D-log E curves): D(log E)
and D(E) ................................... 44
Relative-exposure-deflection relations
and relative-intensity-deflection
relations: E (d) and I(d).................. 45
Relative plate speeds ............................ 46
Photographic normalization of relative
intensities ................................. 46
Calculation of Equivalent Widths ................... 47
Actual (absorption-plus-emission) line profiles .. 47
Emissionless profiles ............................ 49
The emissionless profile for the K star ......... 49
Photometric scaling ................. ........... 54
The emissionless profile for both stars
in combination ................. ........... 55
Further photometric scaling .................... 56
The emissionless profile for the G star ......... 56
Synthesized emissionless profiles ............... 57
Profiles of the K-line emission ................... 62
The equivalent widths of the K-line emission ..... 62
Determination of error in the equivalent widths of
the K-line emission ......................... 66

SECTION IV DISPLAY AND ANALYSIS OF REDUCED DATA .... 70

Data Display: The Graphical Relation .................. 70
General Description ................................ 70
Eclipses of the Emission ........................... 73
Primary eclipse ................................. 73
Secondary eclipse ................................ 75
Comparison of primary and secondary eclipses ..... 76
Extra-Eclipse Behavior ............................. 76
Interpretation of the Graphical Relation ............ 77
Variability of the Emission ....................... 77
Relative Strengths of the Emission ................. 77
Observed Surface Distribution of the Emission ...... 79
Model for the Surface Distribution of the Emission 81
Model for the Generation of the Observed Behavior
of the Emission with Phase .................... 83
Primary eclipse .................................. 83
Secondary eclipse ................................ 84
Extra-eclipse behavior ........................... 86
Anisotropic model .............................. 86








Temporal model .............. .................. 87
Spatial model ................................ 90
Conclusion .................................. ... 96
Correlations of Spectroscopy and Photometry ........ 96
Eclipse correlation .............................. 97
Pre- and post-eclipse depressions ................ 97
Distortion-wave-minimum--emission-maximum--
period-change relation ...................... 99
Period changes ........................ ...... 99
Distortion wave minimum and Ca II emission
maximum ................................... 102
Conclusion .................................... 108
Summary .... ........... ..... ....................... 108

SECTION V GENERAL MODEL .......................... 111

Introduction ...................................... .. 1il
Spectroscopic Characteristics ....................... 111
Ca II Emission ..................................... ill
Site of the emission ............................. 111
The chromosphere .............................. 112
An extended envelope .......................... 114
Gas streams ................................... 114
The tidal bulges ........................ ... .... 114
The entire stellar surface ..................... 115
Patches ........................................ 116
Mechanism for and motion of the Ca II emission ... 117
Eruptive activity ............................... 118
Collisions and thermal gradients .............. 118
Gas streams .................................... 123
Binary character ............................... 124
Conclusion ..................................... 125
Depressions in emission .......................... 126
Magnetic fields ................ ... .... ..... .... 126
Other Spectroscopic Features ....................... 127
Hydrogen, cerium, iron and other metals .......... 127
Radio emission .................. ................... 128
Photometric Characteristics ......................... 129
Introduction ..................................... .. 129
Depressions in the light curve ..................... 129
Irregular Light-Curve Variations and the
Photometric Distortion Wave .................. 129
Pulsation as the agent .......................... 131
Ring, shell, or envelope as the agent ............ 131
Gas streams as the agent ......................... 132
Starspots as the agent .......................... 132
Existence and observability of starspots ....... 145
Conclusion ........ ............................. 148
Period Changes ....................................... 148
Introduction .................................... 148
Mass Loss as the Mechanism ........................ 149
Component Interaction as the Mechanism ............. 152
Other Effects as the Mechanism ..................... 152








Correlations of Phenomena .......................... 153
Introduction ...................................... 153
Spectroscopic-Photometric Correlation .............. 153
Photometric-Infrared Correlation ................... 155
Photometric-Radio Correlation ...................... 155
Luminosity Correlations ............................ 156
Conclusion ......................................... 156
Evolution of Stars with Ca II Emission ............... 156
Introduction ........................................ 156
Stage of Evolution ................................ 157
Pre-main sequence ................................ 157
Post-main sequence ............................... 158
Circumstellar matter, component masses, and
population count .......................... 160
Ca II emission and Li absorption ................ 165
Ages of the RS CVn Systems ......................... 168
Other Evolutional Effects .......................... 169
Summary .............................................. 170

SECTION VI FUTURE INVESTIGATIONS ................... 176
Introduction ......................................... 176
Spectral Analysis ...................................... 176
Equipment ............................................ 177
Observations .............................. ........... 182
Epilogue ............................................. 187

REFERENCES ........................................... 188

BIOGRAPHICAL SKETCH ................................... 197















LIST OF TABLES


Table 1 GENERAL CHARACTERISTICS OF RS CVn BINARY STAR
SYSTEMS AND PARTICULAR CHARACTERISTICS
OF AR Lac .................................. 23

Table 2 RS CVn BINARY STAR SYSTEMS ................. 29

Table 3 RELATIVE EQUIVALENT WIDTHS OF THE Ca II
K-LINE EMISSION IN AR Lac .................. 71

Table 4 PHASE OF AR Lac AT DISTORTION WAVE MINIMUM,
EMISSION MAXIMUM, AND PERIOD CHANGE ........ 105


xii















LIST OF FIGURES


Figure 1

Figure 2


Figure 3



Figure 4


PROFILES OF THE Ca II K LINE IN AR Lac ...

CONSTRUCTION OF EMISSIONLESS PROFILES FOR
THE Ca II K LINE IN AR Lac ...............

VARIATION OF THE RELATIVE EQUIVALENT
WIDTH OF THE Ca II K-LINE EMISSION WITH
ORBITAL PHASE IN AR Lac ..................

THE ENHANCED MIGRATION CURVE FOR AR Lac ..


xiii


51


52



72

107














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


VARIATIONS OF THE H AND K EMISSION LINES
OF SINGLY IONIZED CALCIUM
IN THE ECLIPSING BINARY STAR SYSTEM AR LACERTAE

by

Sara Witherow Hoffman

August, 1983


Chairman: Frank Bradshaw Wood
Cochairman: John P. Oliver
Major Department: Astronomy


The variability of the Ca II emission and the associa-

tion of any such variation with the photometric behavior and

with other characteristics of AR Lac were the primary

questions considered in this investigation. In pursuit of

these objectives a series of spectrographic plates spanning

the entire orbital cycle of AR Lac was obtained by the

author during 1976-1977.

Reduction of the K-line emission data by photographic,

photometric, and spectroscopic scaling revealed emission

throughout the cycle and emission eclipses well-correlated

in phase with the photometric eclipses. Also observed were

(1) pre- and post-primary eclipse emission depressions fol-

lowed and preceded, respectively, by pre- and post-primary

eclipse emission increases, (2) pre- and post-secondary


xiv








eclipse emission increases, and (3) an extra-eclipse local

emission maximum at phase 0.384.

The model constructed to account for these phenomena

consisted of (1) permanent emission distributed over the

entire stellar surfaces, (2) permanent emission regions

located at the tidal bulges of the stellar components, (3)

Ca II-absorbing circum-secondary material and (4) an

isolated emission region temporary in surface or temporal

location (a moving spot group or a flare, respectively).

The extra-eclipse emission maximum at phase 0.384 was

discovered to be congruent with the migration curve for the

photometric distortion wave minimum of AR Lac, as was

another apparent extra-eclipse emission maximum recorded at

a different epoch by a different observer. Data from yet

another source revealed that at a still different epoch an

extra-eclipse Ca II emission maximum coincided in phase with

the photometric distortion wave minimum at that epoch. On

the basis of these limited data an interrelationship of the

Ca II emission, the distortion wave, and the period changes

in AR Lac was therefore tentatively demonstrated.

A re-evaluation of contradictory reports regarding the

visibility of individual starspots led to the conclusion

that large spots would indeed be observable with equipment

of high precision.

A comprehensive physical and evolutional model for the

cumulative spectroscopic and photometric behavior of AR Lac

was constructed by augmentation of other models and

incorporation of the results of the present investigation.














SECTION I
A HISTORY OF OBSERVATIONS OF H AND K EMISSION
AND THE AR LACERTAE SYSTEM


Prologue

The history presented herein is an approximate

chronology of the observations which are pertinent to the

present investigation. Because it is intended merely as a

chronicle of observations, no extensive interpretation or

discussion by the observers is presented; and only brief,

bracketed comments are offered by the author. Detailed

discussions are included in Sections IV, V, and VI.

Introduction

H and K emission, which is observed in the spectra of

numerous late-type stars and stellar systems, has confounded

astronomers for over a century. Prominent H and K emission

is exhibited by the eclipsing binary system AR Lacertae,

which has manifested itself as a puzzle of considerable

complexity not only because of its strong emission but also

because of its many other unusual characteristics. The

history of astronomical observation of H and K emission

began over a third of a century before AR Lacertae was

detected as a variable and more than half a century before

AR Lacertae was discovered to exhibit H and K emission.







Early Observation of H and K Emission

The H and K spectral lines are two of the solar lines

which were alphabetically designated by Fraunhofer in

1814-1815 (Abell, 1964) when he rediscovered the myriad of

dark (absorption) lines crossing the solar spectrum. The H

and K lines are resonance lines of singly ionized calcium

(Ca II).The H line, at wavelength 3968.47 A, is produced by

the 4p 2pi/20 4s 2S1/2 transition; whereas the K line, at

3933.67 A, arises from the 4p 2P3/20 4s 2S1/2 transition

(Shore and Menzel, 1968). The H line is usually blended

with the H-epsilon line (3970.07 A) of the Balmer series of

hydrogen.

The discovery of H and K emission in the spectrum of an

astronomical object was made by Young (1872), who visually

detected emission reversals at the centers of Ca II

absorption lines in the sun (St. John, 1910). According to

Young, the lines were observed to be "regularly reversed on

the body of the sun itself, in the penumbra and the

immediate neighborhood of every important spot" (St. John,

1910, pp. 36, 37). Four years later, Draper made the first

photograph of the solar spectrum (Smithsonian, 1978). The

first photographic plates of the spectra of sunspots,

obtained in 1883 by Lockyer, revealed H and K emission

reversals over the spots. Subsequent plates obtained in

1886 and 1887 by Rowland exhibited both single and double

reversals. Hale's plates taken in 1891 demonstrated that

the reversals are not confined to the vicinity of sunspots,








but are instead found "in regions irregularly distributed

over the entire disk of the sun" (St. John, 1910, p. 37).

Hale's plates showed the double reversal of the H and K

lines reported by Rowland: a broad absorption feature

(which Hale termed HI or Kl) upon which is superposed an

emission line (H2 or K2) with a narrow absorption line (H3

or K3) at its center.

Emission reversals at the centers of absorption lines

of stellar spectra were first observed in 1900 by Eberhard

and Ludendorff, who detected an emission core in the Ca II K

line on a "very strongly overexposed" (Eberhard and

Schwarzschild, 1913, p. 292) spectrum of Arcturus. Engaging

in further investigation of the phenomenon, Schwarzschild

recorded H and K emission reversals on spectral plates of

Arcturus, Aldebaran, and sigma Geminorum in 1913. By

comparison of the strength of the stellar emission to that

of the average spectrum of the sun, Eberhard and

Schwarzschild concluded that "the emission is much stronger

in these stars than in the sun" (Eberhard and Schwarzschild,

1913, p. 294). They stated further that "reversals of lines

in stellar spectra are not rare" (Eberhard and Schwarz-

schild, 1913, p. 294).

By 1929 a veritable multitude of other stars, such as

Capella and epsilon Pegasi, had been discovered to exhibit H

and K emission superposed on absorption. Others, such as

Arcturus, Antares, and Betelgeuse, were discovered to have a

complex double reversal of the H and K lines similar to that








found in the sun (Adams and Joy, 1929a,b). A correlation

between emission strength and absolute magnitude was

discovered by Deslandres and Burson (1921, 1922), "the more

luminous giants having stronger emission lines" (Adams and

Joy, 1929b, p. 373).

Early Observations of AR Lacertae

Early Photometry

AR Lacertae was discovered to be variable by Leavitt

(Leavitt, 1903; Pickering, 1907a; Sahade and Wood, 1978).

For the next twenty years, though, its variability seemed

questionable, being confirmed by some observers (Pickering,

1907b; Munch, 1909; Wendell, 1913) and denied by others

(Hoffmeister, 1919; Zinner, 1922).

By obtaining a visual light curve from analysis of his

observations made in 1927 and 1928, Loreta (1929) first

recognized AR Lac as an Algol-type system with a period of

1998. By his own observations and by analysis of Loreta's

(1929) and Wendell's (1913) observations, Jacchia (1929)

confirmed Loreta's analysis of AR Lac as an eclipsing

binary.

The first photographic light curve of AR Lac was

published in 1931 by Rugemer (1931). In the following year

Schneller and Plaut (1932) published a second light curve.

These three investigators calculated the apparent visual

magnitudes and the relative sizes and luminosities of the

components, the orbital inclination, and a more precise

value for the period of the system. Their data also








established that the cooler star eclipses the hotter one at

primary eclipse, which is total. In addition, the depths of

the minima at both eclipses were determined. Application of

their photometric results to the HD Catalogue spectral

classification (G5), which they suspected might be a

composite, allowed rough determinations of the spectral

classes of the components as either G5 and K5 or GO and KO

for the smaller and the larger stars, respectively

(Schneller and Plaut, 1932; Harper, 1933).

From his photometric observations Himpel (1936)

classified AR Lac's components as G5 and gK5, the luminosity

class of the cooler star having been determined from its

surface brightness. In the light curve he noted a bump

during totality (primary minimum).

The first photoelectric observations of AR Lac (Sahade

and Wood, 1978), made in 1938 and 1939 by Wood (1946),

enabled him to complete his solution of the orbit in 1941.

(Publication of his dissertation was delayed until 1946

because there was "a small war on then": Wood, 1983.)

He determined that between the time of earlier observations

by Dugan and Wright and the time of his own observations,

the period of the system had undergone an abrupt change,

thereby necessitating the calculation of new orbital

elements. From light-curve variations which occurred only

outside primary minimum, Wood (1946) inferred that the

brighter (G5) component is variable. Although it was later

discovered (Blanco and Catalano, 1970) that Wood's








comparison star, HD 209813 (HK Lac), is a variable, Wood's

observations were not invalidated, because he had compen-

sated in his data reductions for what he termed "large night

errors" (Wood, 1946, p.13). His results are therefore quite

harmonious with more recent observations using nonvariable

comparison stars.

While attempting to measure the limb darkening coef-

ficient of the KO component of AR Lac, Kron serendipitously

discovered "small abrupt irregularities" (Kron, 1947, p.

264) in the light level during primary minimum ingress and

egress, thereby complementing Wood's (1946) observations of

anomalous photometric variations only outside primary

minimum. Kron interpreted his observations as Wood had

interpreted his: viz., that the primary star (G5 star) is

intrinsically variable. Kron also reported several

observations of strong asymmetry between minima. Comparison

of data from several epochs showed variability of the

asymmetry and variability of the skewness of secondary

minimum. Prominent ellipticity and reflection effects were

evident, as was a "very high degree" (Kron, 1947, p. 264) of

limb darkening for the KO star.

Early Spectroscopy

Spectrograms obtained in 1932 by Harper revealed AR Lac

to be a double-line spectroscopic binary. He made an

attempt to classify the spectral types of the components

more precisely, but was not entirely successful because

clouds precluded his obtaining any plates at primary








minimum, when the spectrum of the cooler component alone

would have been visible. He did, however, publish the first

radial velocity curves for the system and was able to

establish the spectroscopic elements within "reasonable

agreement" (Harper, 1933, p. 148) with the previous

photometric elements determined by the three Germans. His

analysis determined that the masses of the components are

very nearly equal, the larger star (1.42Me) being only

O.01Me more massive than the smaller more luminous one. He

found the lines of the primary to be sharper than those of

the secondary. The three-to-one disparity in the relative

luminosities of these components of almost equal masses and

very similar spectral types (G5 and G2, respectively, by his

spectrograms) caused Harper to express some puzzlement.

The discovery of H and K emission reversals in AR Lac

was announced by Wyse (1934). He had detected sharp

emission cores in the broad H and K absorption lines in the

spectrum of the cooler component. He classified the spectra

of the components as G5 for the brighter and KO for the

fainter. The luminosity class of the primary (brighter) was

ascertained to probably be main sequence, whereas the

luminosity and the density of the secondary placed it

intermediately between the main sequence and the giants.

Joy and Wilson (1949) tabulated previously unpublished

data obtained by Sanford (1951), who had discovered in 1945

that Ca II emission is present not only in the AR Lac

secondary but also in its primary. They listed the








spectral-luminosity classifications of the components as

sgG5 and sgKO, the luminosity class of the primary

heretofore having not been explicitly specified except for

Wyse's (1934) tentative main-sequence classification.

New spectroscopic elements for AR Lac were published in

1951 by Sanford (1951), whose data indicated that the orbit

is circular. The spectra showed the absorption lines to be

very broad and shallow for such late-type stars, a

characteristic which he ascribed to the lines' being

appreciably broadened by synchronous rotation. Measurements

of the equivalent widths of the Ca II emission (H2 and K2)

and the underlying absorption (Hi and KI) for each component

showed the emission contributions from both stars to be

variable with phase. Additionally, the ratio of the

primary's to the secondary's emission increased from phase

0.0 to 0.5 and decreased from phase 0.5 to 1.0. Radial

velocities computed from the emission lines were 6.4 km/sec

less than those from the absorption.lines. Assuming that the

breadth of the Ca II emission indicates that it emanates

from all parts of the stellar surfaces or from complete

equatorial zones, Sanford calculated the radii of the

components to be about 85% of the value determined by Wood,

who had included a large coefficient of limb darkening.

Sanford's measurements indicated the masses to be 1.3 Me and

1.31 Me for the primary and the secondary, respectively.








Using spectra obtained in 1954, Roman (1956) noted the

presence of H and K emission and classified the spectrum of

AR Lac as K2 III at primary eclipse and K2 III + F8 at

secondary eclipse, her results confirming yet again that no

two observers obtain exactly the same results for AR Lac.

Correlation of Photometry and Spectroscopy

From the photometric elements of AR Lac and Sanford's

(1951) spectroscopic data, Eggen (1955) derived the absolute

visual magnitudes, the masses, and the radii of the

components.

While analyzing several systems with light-curve

variations not explainable by tidal effects, the reflection

effect, or eclipse, Kron (1952) noted a rotational

periodicity of these photometric variations in AR Lac, RT

And, RS CVn, and YY Gem. He further observed that all four

systems exhibit emission lines. In YY Gem, changes in the

Ca II emission strength were observed to show a pattern of

amplitude and period behavior similar to that of the

light-curve variations.

Early Polarimetry

Seeking to measure the polarization of the H and K

emission in AR Lac, Struve (1948) obtained null results; but

he was able to establish an upper polarization limit of 10%

for the system.

The "AR Lac Group" and Other Stars with Ca II Emission

In his study of spectra of eclipsing binaries, some

displaying Ca II emission, Wyse noted an "unexpected








tendency" (Wyse, 1934, p. 41) for late-type secondaries to

exhibit hydrogen emission.

Swings and Struve (1941) and Struve (1945) investigated

stars which exhibit late-type absorption features combined

with bright lines of high excitation. Struve (1945)

observed that "in single stars emission lines are rare for

these types [A through K]" (Struve, 1945, p. 79); whereas

"binaries of types G and K very often exhibit bright lines

of Ca II, and the number of these cases is also considerably

in excess of what might have been expected from the

frequency of occurrence of these lines in single stars"

(Struve, 1945, p. 79).

Upon surveying emission-line stars again, Struve (1946)

recognized a fledgling group of binaries characterized

primarily by bright lines of Ca II. Additional identifying

features of this grouping were (1) spectral type usually

later than F5, (2) resemblance of the emission lines to

those of normal single K-type dwarfs, (3) usually single or

slightly broadened lines, which are (4) superposed on deep,

broad Ca II absorption, and are (5) usually visible

throughout the cycle, but in some systems are strengthened

at primary minimum or weakened at secondary minimum.

A list of 445 stars and star systems known to exhibit

Ca II emission, published by Joy and Wilson (1949), verified

Eberhard and Schwarzschild's (1913) suspicion that H and

K emission is not a rare phenomenon in stars. Joy and

Wilson's comparison of intensity levels at various parts of









each spectrum showed that although the emission is usually

much weaker than the local continuum, the broad H and K

absorption is so strong that it provides a low-intensity

background against which the faint emission is easily

observed. Visual comparison of emission in stars of the

same spectral-luminosity type produced no correlation

between emission strength and any other physical

characteristics. At the dispersions used they noted no H3

or K3 in subgiants or dwarfs. In the sun, giants, and

supergiants, they observed the red component of the emission

(the red component of H2 and K2) to be more intense than the

violet. Further, they stated that the emission intensity is

probably variable in many stars.

A new decade dawned with Gratton's review of

characteristics of stars which exhibit Ca II emission. He

opened his discussion by stating that for late-G or early-K

binaries "these emission lines are much stronger than those

observed in single late-type stars such as alpha Boo

[spectral class K2 (Abell, 1964)], being real emission lines

rather than a reversal of the absorption lines" (Gratton,

1950, p. 31). [However, the author can find no previous

statement of this assertion, or any reports of observations

substantiating this statement, not even in the very

references from which Gratton purportedly obtained this

information. Perhaps he misread or misunderstood Struve's

(1945) statement regarding the frequency of occurrence of

the emission, not the strength of the emission.] Gratton








discovered a period-luminosity relation for binaries with

Ca II emission.

Tables of quantities for 426 stars whose spectra

exhibit H and K emission lines were published in 1954 by

Bidelman, who repeated Gratton's (1950) assertion, though

not quite so positively: "The Ca II emission lines are

probably stronger in binaries than in single stars"

(Bidelman, 1954, p. 178). [Perhaps his compendium of

references would offer supporting evidence; however Gratton

(1950) is among them .] Bidelman also noted from his

survey the likelihood that all late-type giants exhibit

some, "usually self-reversed" (Bidelman, 1954, p. 178), Ca II

emission and that there exist some "surprising variations

in intensity" (Bidelman, 1954, p. 178) among stars of the

same spectral class.

Spectrograms of the Fraunhofer lines obtained by McMath

et al. revealed that in the solar H and K lines (1) the line

intensity was similar between the disc and the chromospheric

bulge, and (2) the line cores were observed to "merge

smoothly with the chromospheric emission bulge" (McMath et

al., 1956, p. 7) as the limb was approached. In addition,

asymmetry of the emission profile persisted to the limb; and

the K emission was enhanced over plages.

Measurements of the H and K emission lines in the sun

by Wilson and Bappu (1957) showed them to be of nearly equal

width and of intensity ratio 1:2. Stellar evidence, though

not conclusive, seemed to indicate a similar picture.









Enlarging upon the work of Adams and Joy (1929a,b), Wilson

and Bappu discovered a relationship between emission-line

width and absolute magnitude. In G, K, and M stars the

K-line emission width varies as the one-sixth power of the

absolute luminosity, the emission-line width being

independent of spectral class and emission-line intensity.

This relationship has become known as the Wilson-Bappu

effect.

While investigating single stars, visual binaries, and

galactic clusters with H and K emission, Wilson (1963)

observed that the spectroscopic binary component in each of

two visual binaries (ADS 2644 and ADS 8119) exhibits a

preponderance of Ca II emission compared to its single

visual companion. In addition, he noted that in the sun a

strong correlation exists between the local chromospheric

magnetic field and the intensity of the Ca II emission, a

condition which he inferred could obtain in other stars

also.

At Lick Observatory, spectroscopy by Preston and

simultaneous UBV photometry by Kilston showed that the

Cepheid-like variable BL Her exhibited "well-marked emission

lines of hydrogen and Ca II for about 2h during rising

light" (Lick, 1966, p. 779) and that "the emission and the

atmospheric velocity reversal occur during a still-stand on

the light curve" (Lick, 1966, p. 779).

Oliver (1971, 1974) tendered the suggestion that AR Lac

and similar systems belong to a group characterized by (1)








Ca II emission, (2) a KO subgiant secondary which does not

fill its Roche limiting surface, (3) a mass ratio near 1.0,

and (4) light-curve variations which are attributable to the

cooler component. He proposed that this group be designated

the RS Canum Venaticorum binary systems. In his

investigations he discovered that several members of the

group exhibit (1) asymmetries in their light-curve minima

and shoulders and (2) a photometric "quasi-sinusoidal

distortion wave" (Oliver, 1974, p. 252), comprising nearly

sinusoidal extra-eclipse variations which migrate epoch by

epoch toward earlier phase.

The discovery of "significant variations" (Weiler,

1975, p. 1) in the H and K emission-line intensities of

several RS- CVn systems was announced by Weiler (1975,

1978). For three of the systems (UX Ari, RS CVn, Z Her) he

further determined that the maximum of emission intensity

and the minimum of the photometric distortion wave coincide

in orbital phase. In AR Lac he found the emission

variations to be basically random.

In an extensive review of the observational properties

of the RS CVn binary systems (and other related systems),

Hall (1976) proposed a working definition [reminiscent

of Oliver, 1971, 19741 composed of those observational

characteristics exhibited by all twenty-four systems so far

identified as belonging to the group. [For a list of these

characteristics as they apply to AR Lac, see Table 1.]

Members of one of the related groups of stars exhibit flare








activity, which Hall proposed may occur in RS CVn stars

also, but go unobserved because of their greater intrinsic

luminosities.

Late in the following year, Young and Koniges (1977)

published the results of their study of the Ca II emission

and other spectral characteristics of late-type binaries [AR

Lac was not included]. They found that systems with periods

near 20 days typically have the strongest Ca II emission.

Popper's evidence (1977) had shown that the emission is

strongest when one of the components is evolved. Young and

Koniges determined that both the strength of chromospheric

emission and the strength of tidal coupling are directly

related to the ratio of the radius of the star to its Roche

lobe. As for other spectral characteristics, their

spectrograms showed no emission in the Na D lines and no

strong Li I (6708 A) line for any of the systems. [The

latter characteristic is of interest because it is

apparently an age discriminator. See Section V.]

Complementing the findings of Young and Koniges, Naftilan

and Drake (1977) observed no evidence of Li 6708 in AR Lac

either.

Further Observations of AR Lacertae

System Elements

In attempts to improve mass determinations in binary

systems Popper (1967) acknowledged AR Lac as being the only

subgiant system with well-determined masses, which he

calculated as 1.32 0.06Me and 1.31 0.07 M for the








primary and the secondary, respectively. He quoted the

radii as 1.8 Re and 3.0 Re, respectively, adding that they

are less well-determined than those of the components of

other systems.

V R photometry of AR Lac (and other binaries) by Lacy

(1979) allowed a new determination of its mass, radius,

absolute magnitude, and distance. He determined that the

primary of the system is underluminous compared to his

theoretical zero-age main sequence.

Spectroscopy and Photometry

Three-color photometry of AR Lac in 1972, 1973, and

1974 by Chambliss (1976) produced a new set of photometric

elements, from which the effective temperatures of the

primary and the secondary were calculated to be compatible

with spectral-luminosity classes G2 IV and KO IV,

respectively. In the light curve Chambliss observed an

0.04-mag intrinsic photometric variation (Chambliss,

1975a,b; 1976) which shifted in phase from season to season

(Chambliss, 1976), behavior which constituted a photometric

distortion wave (Chambliss, 1975b; Hall, Richardson, and

Chambliss, 1976). The wave was later discovered to be

varying in amplitude (0.04-0.1 mag) and migrating toward

decreasing orbital phase (Hall, Richardson, and Chambliss,

1976). Chambliss' (1976) data also indicated that the

coefficient of limb darkening is low for the primary and

high for the secondary. Attempts to correlate optical

variability with radio outbursts yielded null results.








Babaev (1974a,b,c,d; 1975a,b; 1976) published seven

papers dealing with spectroscopy and photometry of AR Lac.

From his radial velocity curves he derived revised

spectroscopic elements. His profiles for the H and K lines

exhibited changes in the emission reversals during ingress,

egress, and eclipse. Measurements of the equivalent widths

of the H and K lines showed variation throughout the orbital

cycle and a pronounced absorption maximum at phase 0.6489.

His three-color light curves exhibited irregularities within

as well as outside of eclipse.

Supplementing Babaev's work, Weiler (1975, 1978)

further investigated AR Lac's migrating photometric

distortion wave and its emission-line intensity variation

with phase. He could discern no correlation between the two

phenomena, and his observations showed "basically random"

(Weiler, 1978, p. 77) emission intensity variation.

Hall, Richardson, and Chambliss (1976) discovered by

reviewing data obtained by previous observers that the

photometric distortion wave of AR Lac migrates toward

decreasing orbital phase and that the migration rate is not

constant, but instead has varied smoothly from one cycle

every 50 or 60 years to one cycle every 10 or 15 years. The

grand climax of their work was the discovery of a

relationship which could be used to predict the epochs of

future period changes in AR Lac. Graphs of (1) orbital

phase of the migrating photometric distortion wave minimum

versus epoch and of (2) orbital phase of the photometric







distortion wave minimum at which period changes have

occurred versus epoch appeared to coincide. Period

decreases occurred when the wave minimum was at phase 0.25;

increases, at 0.75.

Moderate metal underabundances in both components of AR

Lac were measured by Miner (1966), who reported that all

eclipsing binaries so far measured had been found to be

metal poor.

Naftilan and Drake (1977) determined that the

displacements of the emission cores from the centers of the

Balmer lines of the AR Lac secondary component are

symmetrical about the absorption-line centers. Rapid

changes in the emission profiles over very short time

intervals were also observed. Their spectra showed further

that the emission-line broadening for both stars is

consistent with that of synchronous rotation, and that for

all the stronger emission lines the emission of the

secondary is much stronger than that of the primary. The

secondary was found to be moderately metal-deficient;

whereas the primary was found to have normal solar

abundances, Miner (1966) notwithstanding. In addition, the

microturbulence velocity for the secondary was found to be

anomalously high for a subgiant, being more in keeping with

values usually observed in supergiants. That for the

primary was relatively high also.








Radio Measurements

Hjellming and Blankenship (1973) announced their

discovery of variable radio emission from AR Lac at 2695 MHz

and 8085 MHz.

Further radio observations of AR Lac by Owen and

Spangler established an upper angular limit of about 1" on

the size of the radio emitting region and a lower volume

limit of "much larger than the stars in the system" (Owen

and Spangler, 1977, p. L43), the latter being determined by

the failure of a clearly defined eclipse to appear in the

radio emission. Their data exhibited no evidence of the

previously deduced circular polarization of the radio

emission.

In 1978 Feldman (1978) reported the observation of a

large radio flare in AR Lac.

Polarimetry and Other Measurements

Measurements of V- and R-band polarization in binary

systems by Pfeiffer and Koch (1977) indicated that AR Lac

displays polarization which is constant and no different

from that of the interstellar medium. No results were

available for tests to determine (1) the shape of AR Lac's

polarization spectrum compared to that of the interstellar

medium or (2) the variability of AR Lac's electric vector

with wavelength.

An infrared excess was measured for AR Lac by Atkins

and Hall (1972), and an ultraviolet excess which increases

with decreasing wavelength below 4600 A was discovered by

Rhombs and Fix (1977).








Continuing to demonstrate that it is no ordinary

system, AR Lac apparently underwent further period changes

in 1975 as evinced by observations of minima from 1973-1976

by Scarfe and Barlow (1978) and in 1977 by observations of

minima from 1960-1982 by Nha et al. (1982). [Neither

observation is included in Table 4 or in Figure 4.] Soft

x-rays were detected emanating from AR Lac by Walter

(1978). Observations by Nha and Kang (1982) indicated that

the KO star may exhibit long-term light variations. The

amplitude of AR Lac's migrating photometric distortion wave

increased to 0.1 between 1978 and 1979 (Hall, 1980). During

this period of time the wave also migrated extremely

quickly, changing position by 0.4 phase units (Hall, 1980).

The minimum of the photometric distortion wave was at about

phase 0.9 in 1979, and the amplitude of the distortion wave

was very low--less than 0.01 mag (Caton, 1981).

Summary

The presence of H and K emission occurs with great

frequency in late-type (G, K, and M) stars. It is

apparently observed in all types of binaries more frequently

than in single stars. In some close binaries the emission

is much stronger than in single stars, but whether this

holds as a general rule has not been verified.

In the sun the ratio of the strength of H to K emission

is 1:2, a condition which evidence suggests may exist in

other stars also. H3 and K3 are observed only in the sun,

giants, and supergiants. In these stars the red component








of H2 and K2 is more intense than the violet. A correlation

was reported between emission strength and absolute

magnitude, the more luminous giants having stronger emission

lines. This discovery has been superseded by the more

recent discovery of a more accurate relationship--that

between Ca II emission-line width and absolute magnitude in

G, K, and M stars. This relation is expressed by the

Wilson-Bappu effect: viz., that the K-line emission width

varies as the one-sixth power of the absolute luminosity.

The emission-line width is independent of both spectral type

and emission-line strength. There appears to be no

correlation between emission strength and any other physical

characteristics of stars of the same spectral-luminosity

class.

In many stars the emission intensity is variable

outside eclipse, and the emission undergoes eclipse as the

stars revolve. In some cases there is an enhancement of

emission at primary minimum and a diminution of emission at

secondary minimum.

Evidence indicates that the solar correlation between

chromospheric magnetic field strength, Ca II emission

intensity, and plages and sunspots may obtain in other stars

also. In binary systems there seem to be direct

relationships between the strength of chromospheric

emission, strength of tidal coupling, and the ratio of the

radius of the star to its Roche lobe, and between the

strength of chromospheric emission and the evolutional stage








of the star. Stronger emission correlates with a more

advanced evolutional stage.

Many of the binary systems which exhibit H and K

emission also exhibit asymmetry and irregular fluctuations

in their light curves.

Virtually all the eclipsing binaries for which

abundances have been measured exhibit metal deficiencies.

AR Lacertae is a typical RS Canum Venaticorum binary

star system. In excess of 25 such systems have been

discovered; all but three are eclipsing binaries. Table 1

lists the characteristics of RS CVn systems in general and

of AR Lac in particular. Table 2 lists the currently known

RS CVn systems and some of their vital statistics.







Table 1
GENERAL CHARACTERISTICS OF RS CVn BINARY STAR SYSTEMS
AND PARTICULAR CHARACTERISTICS OF AR Lac


The RS CVn systems form a class of spectroscopic
binaries which are distinguished by three characteristics
(Oliver, 1974; Hall, 1976):
(1) The orbital period is between Id and 14d.
(2) The hotter component is of spectral class F or G
and of luminosity class IV or V.
(3) Spectra at phases outside eclipse exhibit strong
Ca II H and K emission. ("Strong" is defined to
mean stronger than the normal H and K emission
reversals in late-type single stars of the same
spectral class.)
AR Lac fulfills these three defining criteria for
membership in the RS CVn classification:
(1) It has an orbital period of 1983 (Loreta, 1929).
(2) The spectral-luminosity class of its hotter
component is G2 IV (Chambliss, 1974).
(3) The system exhibits strong H and K emission at
phases outside eclipse (Wyse, 1934; Sanford,
1951).
There are a number of other characteristics which AR
Lac has in common with varying numbers of the other RS CVn
systems (Hall, 1976). Spectral characteristics shared with
many of the other systems are:
(1) The system is a double-line spectroscopic
eclipsing binary (Harper, 1933).
(2) The H and K emission is from the cooler star or
from both stars. The latter is the case for AR
Lac (Sanford, 1951).
(3) The spectral-luminosity class of the cooler
component is close to KO IV. The secondary of AR
Lac is classified KO IV (Wyse, 1934).
(4) The system exhibits H-alpha emission outside
eclipse (Weiler, 1975, 1978).
(5) The system exhibits an infrared excess in one or
both components. It is observed in both
components of AR Lac (Atkins and Hall, 1972).
(6) The system exhibits an ultraviolet excess. In the
ultraviolet AR Lac is too bright by an amount
which increases with decreasing wavelength below
4600 A (Rhombs and Fix, 1977).
(7) The system exhibits radio emission (Hjellming and
Blankenship, 1973).
Photometric characteristics which AR Lac has in common
with one-third to one-half of the other RS CVn systems are:
(1) The light curve of the system exhibits an
extra-eclipse quasi-sinusoidal wave-like
distortion (Chambliss, 1975b) which migrates
toward decreasing phase (Chambliss, Hall, and
Richardson, 1975).







Table 1 continued

(2) The depth of primary minimum is variable. This is
a natural consequence of the distortion wave
(Hall, 1976).
(3) The displacement of secondary minimum (asymmetry)
is variable. This is a natural consequence of the
distortion wave (Hall, 1976).
(a) no asymmetry observed (Taylor, 1941)
(b) strong asymmetry (Wood, 1946)
(c) variable asymmetry (Kron, 1947; Hall, 1976;
Theokas, 1977).
(4) The light curve exhibits irregular variations
(Wood, 1946; Kron, 1947; Babaev, 1971; Chambliss,
1975b; Hall, Richardson, and Chambliss, 1976;
Hall, 1976).
Physical characteristics which AR Lac has in common
with one-third to one-half of the other RS CVn systems are
(Oliver, 1974; Hall, 1976):
(1) The mass ratio of the components of the system is
near unity. For AR Lac it has been computed
between 0.987 and 1.008 (Harper, 1933; Sanford,
1951; Wood, 1946; Kopal, 1958; Popper, 1967;
Oliver, 1974; Babaev, 1975; Popper, 1976;
Chambliss, 1976; Hall, 1976; Popper and Ulrich,
1977; Weiler, 1978).
(2) The system is detached; that is, neither component
fills its Roche lobe (Wood, 1950; Kopal, 1958;
Plavec and Grygar, 1965; Oliver, 1974; Chambliss,
1976; Morgan and Eggleton, 1979)
Orbital characteristics which AR Lac and a few of the
other RS CVn have in common are:
(1) The system has a varying orbital period. Between
1932 and 1982 AR Lac appears to have undergone
several abrupt period changes, one almost as much
as 3s (Wood, 1946; Chambliss, 1976), another of
about 20m (Nha et al., 1982).
(2) Period changes are correlated with the migration
of the photometric distortion wave. For AR Lac,
period increases have occurred at epochs when the
orbital phase of the minimum of the distortion
wave was 0.75; decreases, when it was 0.25
(Chambliss, Hall, and Richardson, 1975).
Other observed characteristics of AR Lac are:
1. Photometric Characteristics:
(a) magnitudes (Chambliss, 1976):
(1) apparent magnitudes:
my primary = 6.75
my secondary = 6.41
my system max = 6.09
(2) absolute magnitudes:
My primary = 4.01
My secondary = 3.64
My system = 3.06







Table 1 continued

(b) coefficient of limb darkening:
(1) 0.8 from spectral classes (Wood, 1946)
(2) secondary has very high value (Kron, 1947)
(3) 0.7-0.8 for primary: from Wood's (1946)
data (Kopal and Shapley, 1952)
(4) secondary high: 1.0 in U; primary low: 0.6
in U (Chambliss, 1976)
(c) secondary more uniformly bright than primary
(Wood, 1946; Chambliss, 1976)
(d) nearly central total primary eclipse, annular
secondary eclipse (Schneller and Plaut, 1932)
(e) duration of totality = 2hl0m 15m (Hall, Rich-
ardson, and Chambliss, 1976)
(f) variable skewness of secondary minimum (Kron,
1947)
(g) ellipticity and reflectivity effects prominent
(Kron, 1947)
(h) depressions preceding first contact and following
fourth contact of primary eclipse:
(1) observed (Kron, 1947)
(2) 0.05 mag (Catalano, 1973, 1975)
(3) flanking primary eclipse (Naftilan and Drake,
1977)
(i) variable amplitude of the quasi-sinusoidal
wave-like distortion:
(1) variable throughout cycle, peak at phase
0.6293 in V,B (Babaev, 1974d)
(2) probably variable, ranging from 0.04 mag to
0.1 mag in blue (Hall, Richardson, and
Chambliss, 1976)
(3) large 0.1-mag amplitude in 1978-1979 after
decades of erratic fluctuations (Hall, 1980)
(4) very low amplitude in 1979 (less than 0.01
mag) (Caton, 1981)
(j) smoothly varying rate of migration of the quasi-
sinusoidal wave-like distortion:
(1) varied smoothly from 1 cycle/50-60 yrs to 1
cycle/10-15 yrs during a 40-yr time period
(Hall, Richardson, and Chambliss, 1976)
(2) rate increased to. 0.4 phase units during
1978-1979 (Hall, 1980)
(3) phase of distortion wave approximately 0.9 in
1979 (Caton, 1981)
(k) smoothly decreasing period of migration of the
photometric distortion wave from 1900-1980 = 45-15
yrs (Chambliss, Hall, and Richardson, 1975)
2. Spectroscopic Characteristics:
a. General
(1) the lines of the primary are sharper than
those of the secondary (Harper, 1933;
Sanford, 1951; Struve, 1952; Naftilan and
Drake, 1977)






Table 1 continued

(2) absorption lines of primary deeper than those
of secondary except from phase 01289-01637
(Sanford, 1951)
(3) absorption lines of primary strongest when
primary receding fastest, weakest when
primary approaching fastest (Sanford, 1951)
(4) flat shallow absorption profiles of the
secondary (observed in the lines of Ce)
characterize the intervals preceding and
following primary minimum (Sanford, 1951)
(5) variable changes in line profiles on the
ascending and descending branches of the
radial velocity curve of the secondary
(Struve, 1952)
(6) on the ascending branch of the secondary's
radial velocity curve its strong absorption
lines (such as Fe I 4045) are strikingly
narrow (Struve, 1952)
(7) when the secondary's lines are narrow, it is
conspicuous only in the stronger lines (like
Fe I 4045), even for lines in the same
multiple (Struve, 1952)
(8) when the secondary's absorption lines are
narrow, the corresponding emission lines
remain broad (Struve, 1952)
(9) Na I D lines of the secondary show the same
structure as other strong lines in the blue;
their overall strength is normal for stars of
this spectral class, rotation accounted for
(Naftilan and Drake, 1977)
(10) equivalent width of Ca II lines variable
throughout cycle, pronounced Ca II absorption
maximum at phase 0.6489 (Babaev, 1974c)
(11) the absorption lines of the Ca II triplet in
the infrared are weak (Hiltner, 1947)
(12) no evidence of Li I 6708 (Naftilan and Drake,
1977; Young and Koniges, 1977)
(13) metal abundances:
(a) both components underabundant (Miner,
1966)
(b) primary has solar abundances, secondary
moderately underabundant (Naftilan and
Drake, 1977; Young and Koniges, 1977)
(14) polarization:
(a) none detected (Struve, 1948)
(b) no evidence for circular polarization at
radio wavelengths (Owen and Spangler,
1977)
(c) polarization in V band constant, same as
that of interstellar medium (Pfeiffer
and Koch, 1977)







Table 1 continued

(15) no spectral evidence for a third body ever
found (Hall, Richardson, and Chambliss, 1976)
b. Emission
(1) all emission lines of the secondary are much
stronger than those of the primary:
(a) ratio of 5:1 for the Ca II emission
iines (Joy and Wilson, 1949)
(b) holds for all lines examined (Naftilan
and Drake, 1977)
(2) the Ca II emission lines are present within
as well as outside eclipse:
(a) observed from his own plates (Sanford,
1951)
(b) from Wyse's 1934 plates: H and K bright
at primary minimum totality (Sanford,
1951)
(3) the radial velocity of the H and K emission
is 6.4 km/sec less than the radial velocity
of all absorption lines in each component
(Sanford, 1951)
(4) the equivalent width of the Ca II emission is
variable with phase:
(a) the ratio of the primary's to the
secondary's emission increases from
phase 0.0-0.5 and decreases from 0.5-1.0
(Sanford, 1951)
(b) variability observed on Wyse's plates
(Kron, 1952)
(c) basically random, no correlation with
phase (Weiler, 1975, 1978)
(5) possible short-term variation of Ca II
emission intensity:
weak self-reversal of K line not seen on
all plates; sharp red-displaced
absorption seen on one plate; plates
from phases 0.983 0.003 (Naftilan and
Drake, 1977)
(6) no Na I D-line emission has been detected
(Young and Koniges, 1977)
(7) emission features in hydrogen lines:
(a) H-alpha: during primary eclipse and at
phase 0.30 there are a possible central
emission feature and two weak emission
features on both sides of line center
and symmetric about line center in and
out of eclipse (Naftilan and Drake,
1977); line intensity variable (Weiler,
1975, 1978)
(b) H-beta: emission during totality
(Naftilan, 1975)
(c) H-gamma and H-delta: during primary
eclipse two emission features on each







Table 1 continued

side of line center (Naftilan and Drake,
1977)
(8) Fe I emission is variable with phase: it is
weaker from phase 0.0-0.5 and stronger from
phase 0.5-1.0, has a minimum at phase 0.25
and a maximum at phase 0.76 (Sanford, 1951)
(9) soft x-rays detected (Walter, 1978)
(10) variable radio emission:
(a) observed (Hjellming and Blankenship,
1973)
(b) variable on a scale of greater than a
few hours; during secondary eclipse
there was a small increase in flux
density; at phase 0.98 there was a
depression of about 25% superposed on a
longer-time-scale rise (Owen and
Spangler, 1977)
(c) radio flare (Feldman, 1978)
3. Correlation of Optical and Radio Behavior
(a) no correlation of optical variations and radio
outbursts (Chambliss, 1976)
(b) no strong eclipse-like radio feature occurred
during optical eclipses (Owen and Spangler, 1977)
4. Physical Characteristics
(a) radii (Chambliss, 1976):
(1) Rprimary = 1.54 Re
(2) Rsecondary = 2.81 Re
(b) masses (Popper, 1967):
(1) Mprimary = 1.32 0.06 Me
(2) Msecondary = 1.31 0.07 Me
(c) system is detached (Kopal, 1958)
(d) temperatures:
(1) 5600K for G2 IV, 4700K for KO IV (Chambliss,
1976)
(2) very nearly the same for U, B, V
light curves (Chambliss, 1976)
(e) microturbulence velocity:
secondary has an anomalously high value for a
subgiant (10 km/s); primary is not far behind (8
km/s) (Naftilan and Drake, 1977).
5. Orbital Characteristics
(a) i = 860 (Rugemer, 1931; Schneller and Plaut, 1932)
(b) P = 1983 (Rugemer, 1931; Schneller and Plaut,
1932)
(c) a = 8.92 Re = 0.0429 AU (Chambliss, 1976)
(d) d = 40 pc (Chambliss, 1976)
(e) e = 0 (Sanford, 1951; Chambliss, 1976)







Table 2
RS CVn BINARY STAR SYSTEMS

Orbital Distortion
Namea Vmaxa Perioda Spectral Typea H and K Wave
(mag) (days) (hot + cool) Emissionb,k Amplitudea
(mag)


UX Ari
CO Aur
SS Boo
SS Cam
AD Cap
RU Cnc
UX Comn
RS CVn
RT CrB
WW Dra
Z Her
AW Her
MM Her
PW Her
GK Hya
AR Lac
RT Lac
RV Lib
VV Mon
LX Per
SZ Psc
TY Pyx
V711 Tau
RW UMa
RS UMi
HR 5110
HD 5303
HD 175742
HD 178450
HD 224085


6.5
9.0
10.3
10.0
9.8
10.1
10.0
8.4
10.2
8.8
7.3
9.7
9.5
9.9
9.4
6.9
9.0
9.0
9.4
8.1
7.3
6.9
5.9
10.2
10.1
5.0
7.8
8.41i
8.1J
7.6


6.438
10.621
7.606
4.824
6.118
10.173
3.642
4.498
5.117
4.630
3.993
8.801
7.960
2.881
3.587
1.983
5.074
10.722
6.051
8.038
3.966
3.199
2.8
7.328
6.2
2.613
1.840
2.879
2.185
6.724


G5 V + KO IV
GO + ?
G5 V + G8 V
F5 V + Gl V
G5 + G5
F9 V + G9 V
G5-9
F4 V-IV + KO IV
GO
G2 IV + KO IV
F4 V-IV + KO IV
G2 IV + K2 IV
G8 IV
GO
G4
G2 IV + KO IV
G9 IV + Kl IV
G5 + K5
GO
GO V + KO IV
F8 V + Kl V-IV
G5 + G5
G5
F9 V + KI IV
F8
F2 IV + K IV
G2 V + FO
KO V + K5 V-M2 V
G6 V
K2-3 IV-V


Sd
P(S?e)
S
S
P+S
S
Se
S
Sd
S
S
S
S

Sd
P+S
P+S
p+Se
S
S
S
P+S
P+S9
S
Se
Sc
ph
?f
?f
?f


0.03-0.10
0.06-0.12
0.05-0.19
0.11
??
0.02-0.09
0.10
0.05-0.20
0.04
0.06
0.03
??
0.06-0.12
0.12

0.04
0.01-0.17
0.06
0.01-0.09
0.01-0.05
0.02-0.15
0.04
0.07-0.21
0.11
??
0.00
0.3
0.079
0.033
??


? Detected, but not yet measured
?? Unknown
a Hall (1981), except where otherwise indicated
b Oliver (1974), except where otherwise indicated
c Conti (1967)
d Hall (1976)
e Popper (1976)
f Joy and Wilson (1949)
g Weiler (1976)
h Hearnshaw and Oliver (1977)
i Henry (1981a)
j Henry (1981b)
k P = emission in hotter star (primary);
S = emission in cooler star (secondary);
P+S = emission in both components














SECTION II
INSTRUMENTATION AND OBSERVATIONS


Instrumentation

Telescope

The telescope which was used in this investigation is

the Tinsley Newtonian-Cassegrain 76-cm instrument at

Rosemary Hill Observatory. The telescope was operated in

the f/16 Cassegrain mode. (See Wheeler, 1973, for the

equations used to calculate the parameters cited below.)

Spectrograph

The spectrograph which was used is a Boller and Chivens

Model 26767 f/13.5 Cassegrain spectrograph equipped with a

corrector lens for the conversion of the incoming telescope

beam from f/16 to f/13.5, thereby providing a reciprocal

scale of 20"/mm in the slit plane. The focal ratio of the

spectrograph camera is f/3. The aluminized glass slit plate

has fixed slit widths of 28, 40, 56, 80, 112, and 160

microns. The 56-micron slit corresponds to an angular image

size of 1" at the slit plane. The decker plate has fixed

slit lengths (deckers) of 1.5, 3, 6, 13, and 25 mm. Two

holes of 0.5 and 0.75 mm were drilled into the decker plate

to be used as shorter slit lengths to allow shorter exposure

times.








The spectrograph is equipped with a variable-focus

collimator and an adjustable grating tilt. (The

spectrograph is worked at negative grating angles.) There

are two interchangeable 64mm X 64mm gratings. Grating I,

ruled at 150 lines/mm, produces a linear reciprocal

dispersion of 128 A/mm at 3933 A in the third order.

Grating II, ruled at 300 lines/mm, produces a linear

reciprocal dispersion of 60 A/mm at 3933 A in the third

order. Both gratings are blazed at a wavelength of 1.25

microns, and the wavelength of maximum energy in the third

order is 3776 A. The resolution limit of grating I is 0.14

A, and that of grating II is 0.068 A, both at 3933 A in the

third order.

The comparison source is a helium-argon glow lamp.

Positions are provided for the insertion of filters into

the comparison source beam as well as into the incoming

stellar beam.

The manufacturer-supplied slit-viewing eyepiece was

inadequate for observation of stars fainter than sixth

magnitude. (The small aperture of the exit pupil allowed

only about two-thirds of the beam of starlight reflected

from the slit edges to emerge from the system.) This

eyepiece was replaced with an improved design (devised by

Hoffman and Oliver) featuring an enlarged exit pupil and

increased magnification (15X rather than the previous 10X)

so that the slits and the deckers could be viewed in greater

detail.








An image tube was used for some spectra in attempts to

(1) reduce exposure times and (2) obtain spectra of the

sodium D lines in the second-order yellow.

An exposure meter (designed by Oliver) which employed

an end-window S20 EMI 9558A photomultiplier tube was

constructed. Although excellent for bright stars or a dark

sky, the meter was unable to discriminate between a faint

star and a bright sky background, thereby grossly

undercounting the stellar photons and rendering erroneously

lengthy exposure times. It was abandoned in favor of

directly timed exposures until a more suitable tube could be

obtained. (See Section VI.)

Plates

The spectroscopic plates used were backed plates of

emulsion type IIa-O, which were cut to 2-in x 2-in squares

from larger plates and then hypersensitized (both done by

the author). The hypersensitization/storage procedure for

the plates (Smith, 1975) consisted of (1) evacuation of the

plate-filled thick-walled aluminum plate-storage box, (2)

back-filling with anhydrous hydrogen, (3) storage of the

plates in the hydrogen for 2h, (4) flushing with anhydrous

nitrogen and (5) subsequent refrigerated storage of the

plates in the nitrogen at greater than 1 atm of pressure.

In addition, the plate box was sealed within a deflated

zip-lock bag containing a canister of silica gel desiccant,

the addition of the desiccant being an innovation suggested

by the author.








The IIa-O emulsion has a linear resolution limit of 16

microns. At the dispersion of grating I at 3933 A in the

third order, the wavelength resolution limit of this

emulsion is 2.3 A. The corresponding wavelength resolution

limit for this emulsion in combination with grating II is

1.2 A.

Sensitometer

The Florida-Smithsonian Plate Sensitometer was used to

record spots of standard emulsion density on a sample plate

from each hypersensitization batch. Designed in 1969 by

Smith (1977a), this instrument is a variable-illumination-

constant-exposure-time tube sensitometer, which produces an

intensity scale of graduated emulsion densities (Jones,

1931, 1934). In order to minimize errors due to reciprocity

failure, (1) the sensitometry spots were exposed for times

as close as possible to those of the stellar exposures, and

(2) the sensitometry plates were developed by the same

procedure as that for the stellar plates (Wright, 1962).

Densitometers

A Model 520-A Photovolt transmission densitometer was

used to measure the densities of the spots on the standard

sensitometry plates and the densities of the unexposed areas

on the stellar plates.

A Joyce, Loebl and Co. Ltd. Model MK III CS double-beam

recording (scanning) microdensitometer with a Honeywell

strip-chart recorder was used to obtain tracings of the

lines on the spectrograms and of the spots on the








sensitometry plates. The controlled adjustments on the

recording (scanning) microdensitometer are the gain settings

for the level of the sample light beam relative to the

standard reference light beam, the heights and widths of the

upper and lower slits, the focusing of the image of the

lower slit onto the plane of the upper slit, and the

focusing of the image of the plate onto the plane of the

upper slit. Inadequacies in the microdensitometer system

necessitated its modification by Oliver, Parise, and

Hoffman: (1) The non-functioning logarithmic amplifier was

eliminated from the circuitry, thereby converting the

strip-chart deflection readout from emulsion-density units

to units which are a function of emulsion-transmission.(2)

The scanning speed of the microdensitometer and the chart

speed of the chart recorder were reduced in order to achieve

greater spectral resolution on the chart and to minimize

distortion of the line profiles. No attempt was made to

determine the instrumental profile for the reason that broad

lines (like H, Cr, and Ca II H and K) are virtually free of

instrumental effects (Wright, 1962). (3) The vertical range

("transmission" scale) of the chart recorder was extended by

the incorporation of a zero-level-maximum-level

potentiometer, which enabled the entire width of the chart

paper to be used. This modification also effected

enhancement of the visibility of small changes in

transmission level.








Calculator

A Hewlett-Packard Model 9810A calculator was

programmed to perform a linear regression to determine the

functional relationship between "transmission" level and

intensity at each wavelength.

Observing Program

Between 1971 and 1978, 153 spectra of single stars,

stellar systems, and planets were obtained. This series of

spectrographic observations marked the inception of

astronomical spectroscopy at the University of Florida.

The spectra of single stars were used to establish

(1) a relationship between apparent visual

magnitude and exposure time as a function of

spectral type and varying sky conditions, and

(2) an atlas of spectra of MK standard stars

(Johnson and Morgan, 1953) for the purpose of

spectral classification.

The primary portion of the program consisted of the

observation of the RS Canum Venaticorum binary star systems.

In order to determine which of the RS CVn systems are

observable and analyzable with the available optical

systems, selection criteria were established according to

the capabilities of the telescope-spectrograph system, the

scanning microdensitometer system, and the stars themselves.

Two exposure requirements imposed by the telescope-

spectrograph system and the physical parameters of the








star systems provided the basis for selection of observable

stars:

(1) It was necessary to obtain the shortest possible

exposure time in order to achieve adequate time

resolution to allow observation of detailed

changes in the H and K emission as a function of

phase, particularly at the phases at or near the

relatively short (about 2h) eclipses.

(2) The spectra had to be overexposed in order to

reveal the emission reversal. This requirement

resulted in exposure times approximately

25% greater than those necessary to produce a

density of 0.6 in the local continuum. Additional

exposure time was needed to compensate for haze,

enlarged discs, and large air mass.

These constraints restricted the observations to

systems of average visual magnitude brighter than 7.5.

Imposing this condition narrowed to only six the field of RS

CVn systems which could feasibly be observed. The six

systems which fulfill the observational criteria are UX

Arietis, HR 1099 (V711 Tauri), TY Pyxidis, Z Herculis, RZ

Eridani, and AR Lacertae. (RS CVn itself, however, was

observed on a few occasions for purposes of comparison.)

Although TY Pyx is one of the brightest of the RS CVn

systems, its extremely large zenith angle (580. minimum) at

this latitude (30 N) forced observation through a large air

mass, which rendered the necessary exposure time too long to








allow sufficient time resolution. Seasonal burning of

undergrowth by nearby landowners required an additional

increase in exposure time (if the star could be seen at

all). The weakness of the emission in TY Pyx further

compounded the problem to the extent that the system was

eliminated from the observing program.

RZ Eri was subsequently deleted from the membership of

the RS CVn group for failure to satisfy the period

requirement (ld-14d) established by Hall (1976).

The four remaining systems which satisfy the magnitude

requirements are the stars which were regularly observed in

the program.

An additional system, HR 5110, was observed because it

was suspected of being an RS CVn system. No strong H and K

emission was observed; therefore it was deleted from the

program. Hall et al. (1978), however, list it as an RS CVn

system.

The inability of the scanning microdensitometer to

analyze plates of poor quality dictated the remaining

criterion for selection among the plates of systems which

fulfill the observational criteria.

Of the 67 plates of RS CVn systems, 3 were made using

the image tube in conjunction with the spectrograph in

attempts to (1) enhance time resolution by reducing exposure

times and (2) record data on the sodium D lines in the

second order yellow. The image tube, however, was abandoned

because it yielded plates of very poor spectral resolution








and very high fog levels. These effects were encountered

primarily because of arcing between the plate and the face

of the image tube due to the extremely high humidity. The

problem persisted despite the installation of a heating ring

to dissipate moisture.

Of the remaining 64 plates of RS CVn stars, 51 were of

sufficient quality to be analyzed. The 13 which could not

be analyzed were rendered unusable for one or more of the

following reasons:

(1) high fog level produced by long exposure to high

humidity,

(2) lines too thin due to inadequate exposure time

because of haze, clouds, etc., and/or

(3) lines insufficiently widened by use of short

deckers in attempts to reduce exposure times

(short deckers rendered the spectra so narrow that

too little information was recorded for analysis

with the available equipment).

The usable plates of the stars fulfilling the

observation criteria tallied 11 for UX Ari, 10 for HR 1099,

4 for Z Her, and 19 for AR Lac. (See Section VI for plans

for analysis of the first three systems listed.) The other

7 usable plates were of RS CVn stars which did not fulfill

the observation criteria.

AR Lac was the system chosen for analysis because for

this system the amount of data obtained was greater than for

any of the others and because the need for additional data








analysis was greater than for all of the others. Also, the

spectrograms of the other three aforementioned systems did

not offer enough coverage of their entire cycles to allow

any definitive conclusion to be drawn regarding the behavior

of their Ca II emission. The 19 spectrograms of AR Lac span

the entire orbital cycle of the system, an achievement which

required more than one epoch of observation. AR Lac's

nearly integral period (11983) produces a rate of phase

change of only 0.004 phase unit per day (placing the system

at approximately the same phase at the same time on

successive nights), a circumstance which necessitates an

extended program of observation to obtain spectra at all

phases.

All of the spectra of AR Lac were recorded on IIa-O

spectrographic plates at a linear reciprocal dispersion of

128 A/mm with grating I (150 lines/mm). A slit width of 80

microns was used because it (1) corresponds almost exactly

to the diameter of the usual seeing disc (about 1'5) at

Rosemary Hill Observatory and (2) provides the minimum

resolution required to observe the desired detail in the

spectra. The spectra were widened by trailing along a slit

length (decker) of 1.5 mm. Exposure times ranged from 40m

on clear nights of good seeing to 90m on hazy nights or

nights of poor seeing.














SECTION III
DATA REDUCTION


Procedure and Theory

The following procedure was used to obtain and reduce

the data. Any theory necessary to the data reduction has

been incorporated into the discussion.

There does exist a problem of disparate nomenclature

among the five disciplines--astrophysics, optics, spectro-

scopy, photography, and photometry--which enter into this

investigation. Each field has its own definition for items

such as intensity and brightness, and a term widely used in

one field may be unacceptable in another. Clarifications

are parenthetically included where two conflicting

nomenclatural systems are simultaneously encountered. If,

however, the discussion is confined to a single discipline

or to non-conflicting disciplines, no alternative terms are

listed; but archaic terminology has been replaced, where

necessary, by the proper modern term in the parlance of that

field.

Plate-Tracing

Three tracings of each stellar spectrogram were

obtained using the recording (scanning) microdensitometer.

The plates were scanned from 3889 A to 4026 A. On each

spectrum scan, tracings of the sensitometry plates were

recorded across the full range of the chart paper at the








same gain setting, slit width, and slit height as was the

spectrogram tracing.

Minimum deflection on the chart paper, indicating

maximum emission intensity recorded by the emulsion at a

given wavelength (maximum flux density received at the earth

at a given wavelength), was scaled to correspond to an

emulsion transmission of zero by adjustment of the

chart-recorder zero-level potentiometer while the sample

beam was passed through the densest (blackest) part of the

continuum in the vicinity of the H and K lines. The densest

part of the local continuum at H and K was determined by

microscopic examination to be at 4026 A.

Maximum deflection on the chart paper, indicating

minimum emission intensity recorded by the emulsion at a

given wavelength (minimum flux density received at the earth

at that wavelength), was scaled to correspond to an emulsion

transmission of 100% by equalization of the sample- and

reference-beam levels and adjustment of the chart recorder

maximum-level potentiometer while the sample beam was passed

through the plate fog (the "clear" area on the plate).

It was determined experimentally that a slit width

setting of 30 is optimum for obtaining the maximum amount of

light possible while still preserving the resolution of

detail in the line tracing. The focus of the plate image

onto the upper slit is critical to resolution.

As was stated in Densitometers, Section II, the

instrumental profile was not measured, a step which would be








necessary in order to determine the true line profile. This

step was unnecessary not only for the (previously stated)

reason that there is virtually no distortion in broad lines

(Wright, 1962) but also for the reason that the calculation

of equivalent width circumvents the problem because

equivalent width is independent of instrumental profile

(Aller, 1951; Stromgren, 1951; Thackeray, 1961).

In order to reduce noise introduced by the recording

microdensitometer and the chart recorder, point-by-point

averages of the three tracings of each stellar spectrogram

and its accompanying sensitometry spots were graphically

computed. The chart paper which must be used on the chart

recorder has a grid size too large to render a faithful

reproduction of the precision attained by the tracing system

and the plates; therefore the averaged tracings were

transferred point-by-point to 0.1-inch chart paper for

greater precision of deflection-reading. The resulting

tracings displayed deflection ordinatee) as a function of

wavelength interval abscissaa).

In order to convert the wavelength intervals to

Angstroms the wavelength scale factor for the chart paper

was calculated (1.18 0.06 A/div) and applied.

The recorded deflection at each point in a line tracing

is a measure of the emulsion transmission (T), where T is

defined as the ratio of the measured photographic intensity

at a given wavelength to a standard photographic intensity.

In this case the standard was chosen to be the continuum at








4026 A, so that T = I/ICONT. The electronics of the

scanning microdensitometer, however, could not be calibrated

so that deflection would be a direct readout of either

emulsion transmission or emulsion density (D = log 1/T).

Further conversion was therefore required.

Conversion of Deflections to Relative Intensities

Because the relationship between deflection and

intensity was unknown, it was necessary to determine that

correspondence through the application of the characteristic

curve for the emulsion. The deflections were converted to

relative intensity units by the following procedure.

Density-deflection relations: D(d)

The transmission densitometer was used to measure the

densities of the sensitometry spots on each sensitometry

plate and the densities of the clear areas on the stellar

plates. The correspondence of each spot-density to its

measured deflection on the scanning microdensitometer

tracing for each stellar plate established a relationship

between density and deflection at the gain setting used for

each tracing. A graph of deflection abscissaa) versus

density ordinatee) was plotted for each stellar plate.

Because the transmission densitometer is designed to

measure diffuse density and the scanning microdensitometer

is designed to measure specular density, a question might

arise regarding the possibility of encountering errors due

to the procedure employed herein. A comparison of densities

measured by the two instruments might yield a difference as








great as 50%, which would be equivalently expressed as a

ratio of 2:1 by the Callier factor, the ratio of specular to

diffuse density (Neblette, 1970). In the present

calibration, however, there were no such comparisons made.

Instead, emulsion densities measured with the transmission

densitometer were correlated with the deflections measured

by the scanning microdensitometer in order to establish a

scale of relative densities for the spectra traced by the

latter instrument. This procedure was necessitated by the

lack of an available density calibration for the scanning

microdensitometer. Because this procedure did not involve a

comparison of densities measured by the two different

methods, there was no additional error other than the usual

amount incurred by reading data from a strip chart.

Through the use of sensitometry spots to calibrate a

stellar spectrum (Wright, 1962), an unknown, but probably

small, error was encountered.

Both of the errors cited above are included in the

discussion in the segment entitled Determination of Error in

the equivalent width of the K-line emission.

Characteristic curves (D-log E curves): D(log E) and D(E)

By use of the sensitometer correlation established by

Smith (1977b) between sensitometry spot number and logarithm

of relative exposure, a characteristic curve, D(log E), was

plotted for each stellar plate. Spot number, representing

the logarithm of relative exposure abscissaa), was plotted

versus density ordinatee) for each stellar plate. The








characteristic curves were transferred data-point-by-data-

point to semilog paper in order to facilitate the reading of

the density-relative exposure coordinates. Relative

exposure abscissaa) was plotted on the logarithmic scale;

and density ordinatee), on the linear scale, in order to

obtain the functional relation D(E).

Relative exposure-deflection relations and relative
intensity-deflection relations: E(d) and I(d)

Correlation of relative exposures with deflections

through the use of the data points on the density-deflection

graphs and on the density-relative exposure curves allowed

the construction of a relative exposure-deflection curve,

E(d), for each stellar plate. Plotted on semilog paper,

relative exposure ordinatee, on the logarithmic scale) was

expressed as a function of deflection abscissaa, on the

linear scale).

Because these graphs appeared to be very nearly linear,

a Hewlett-Packard 9810A linear regression program was used

to derive empirically an equation, E(d), for relative

exposure as a function of deflection for each stellar plate.

(The linearity correlation for each resulting equation was

greater than 0.99.) This step greatly facilitated the

process of determining the relative exposure resulting from

a given deflection recorded on the stellar plate tracings.

Without an available equation the relative exposure-

deflection graphs would have had to have been used to read

the relative exposure for each deflection-data-point on each








stellar plate. This procedure would have entailed hundreds

of individual correlations and would have taken considerably

longer to complete.

Upon establishment of the relative exposure-deflection

function, E(d), for each plate, the relative intensity-

deflection function, I(d), for each plate was immediately

known because relative intensity is directly proportional to

relative exposure for a plate of given exposure time.

Relative plate speeds

The relative plate speed of two plates is the ratio of

the inverses of their relative exposures at a given

density. In order to compare on the same scale the relative

intensities of plates of different relative speeds, the

stellar plates would be standardized relative to the speed

of an arbitrarily selected sensitometry plate by simply

dividing the speed of each plate by the speed of the

sensitometry plate. In this investigation, however, only

ratios of relative photographic intensities of a given plate

were used; consequently the determination of relative speeds

was not necessary.

Photographic normalization of relative intensities

At each 0.1-inch grid-line of the wavelength axis of

each stellar plate tracing, deflection (in number of

0.1-inch intervals along the intensity axis) was read.

Substitution of each deflection into the Hewlett-Packard

9810A relative intensity-deflection equation for that

stellar plate and subsequent division of the calculated








relative intensity at each wavelength by the relative

intensity of the local continuum for each stellar plate

resulted in a printout of tabulated relative intensities

photographically normalized to the intensity of the local

continuum for each plate.

Calculation of Equivalent Widths

The equivalent width of the K emission was determined

by the following procedure.

Actual (absorption-plus-emission) line profiles

In keeping with standard spectroscopic methods (Keenan

and Morgan, 1951) the line profile for the K line was

constructed for each stellar plate by plotting the tabulated

relative intensities normalized to the intensity of the

local continuum ordinatee) as a function of wavelength

abscissaa) on 0.1-inch graph paper. These line profiles,

constructed from the original data, are superpositions of

the K absorption and the K emission for both stellar

components of the system at the orbital phase of the

spectrogram. The linear reciprocal dispersion of 128 A/mm

is too low by a factor of two to resolve the K-line

components of the individual stars at any phase. (See

Figure 1.)

At every phase the scaled line profile exhibits a

small, narrow emission core of variable strength and

position superposed on deep (except at primary minimum),

broad absorption about 30 A wide at the continuum level.

(See primary minimum, below.) Unidentified narrow








absorption lines flank and are blended with the major

absorption core of the K line. (See Figure 1.) The

profiles in this investigation are virtually identical to

those observed at corresponding phases by Babaev (1974a).

The emission core broadening has variously been

attributed to turbulence in an optically thin layer (Wilson

and Bappu, 1957) and abundance in an optically thick layer

(Goldberg, 1964; Linsky and Avrett, 1970).

The absorption core is broadened by thermal motions,

microturbulence (Naftilan and Drake, 1977) and turbulence

(Abell, 1982), and rotation (Sanford, 1951). The

microturbulent and turbulent broadening is evident in the

anomalously broad bell-shaped Gaussian (Doppler) core, whose

width far exceeds that of normal thermal broadening. The

rotational effects add to the core profile, rendering the

core broader and shallower. The characteristic broad,

shallow shape of a rotationally broadened line is most

apparent at phases during primary eclipse, when only the

large, rapidly rotating K star is visible. (See Sanford,

1951.)

The true extent of any absorption wings is difficult to

discern in the profiles in this investigation and in general

because of the lack of a true continuum level in this

wavelength region so dense in spectral lines (Wright,

1962). Linsky and Avrett (1970) determined that for

wavelengths shorter than 4000 A in the sun there is no true

continuum level except for an interval 0.08 A wide at








3999.89 A. Comparisons can be made to the profiles of other

observers, however. Line profiles published by Struve

(1948) exhibited broad absorption wings in the H and K lines

of AR Lac. Joy and Wilson spoke of the "great absorption

wings" (Joy and Wilson, 1949, p. 231) of the H and K lines

in late-type stars, and Weiler (1978) mentioned the overlap

of the wings of the H and K lines of RS CVn stars. Other

observers mentioned only that the H and K lines are

characterized by broad absorption and sharp emission. The

wings could be generated by rotational broadening alone or

by rotation plus abundance effects (collision, radiation,

and/or pressure broadening). These observers did not

attribute the wings to any particular process, but those in

Struve's (1948) paper match fairly well with a superposed

Lorentzian curve, the shape of which would be produced by

abundance broadening.

Emissionless profiles

By the following procedure an emissionless profile for

the K line of the system was constructed empirically for the

phase of each stellar plate.

The emissionless profile for the K star. Because the

primary eclipse of AR Lac is total (Scheller and Plaut,

1932), the actual (absorption-plus-emission) profile for the

K star alone could be determined by taking the graphical

mean of all the profiles during totality. (Only one

spectrogram was obtained at this phase.) The emissionless

profile for the K star alone was determined by visually








estimating by the following procedure what the appearance of

this line profile would be without the emission peaks. (See

Figure 2.)

The fact that the profile at totality was quite

evidently degraded considerably by emission and broadened

and shallowed by rotation were great hindrances; however, by

modeling the emissionless profile after the general

characteristics of the K line and after the general

appearance of the K line in the sun and in other late-type

stars, a reasonable picture, internally consistent with all

the data, was developed.

The great depth selected for the constructed

emissionless profile is justified by the fact that the K

line is a resonance line. The line centers of such lines

are characterized by an extremely low residual intensity,

which can be attributed to the apparent characteristic

tendency for resonance lines to be formed by the mechanism

of scattering rather than absorption. There are two

scattering processes: coherent and non-coherent.

In the coherent scattering process the probability of a

quantum's reaching the stellar surface from great depths is

very low because it is absorbed and re-emitted in no

preferred direction; consequently the line center is

virtually black (less than 1% of the continuum: Linsky and

Avrett, 1970). In actuality no line center is truly black,

though; for there is some probability of a quantum's

emergence.








































































0 0 0 0 0 0 0 0 0
SN3 3A 3 S NI 3A 3
: (%) AIlSNILNI IAI73H () AIISNILNI 3ALlV731















100 *

-80




40 -



2
0






z
o .-







40



20 3
c 0


a. Primary Eclipse b. Secondary Eclipse
Profiles Profiles
( K star ) ( G star plus
annulus of K star )
( plate 34 ) ( plate 38 )
I scaled profile ( absorption plus emission )
2 empirically constructed theoretical emissionless
3 emission profile ( I minus 2 )


c. Extra-eclipse
Profiles
( G star plus
K star )
( plate 18 )

profile ( absorption )


d. Construction of the Absorption Profile for the G Star
4 same as c2
5 some as a2
6 empirically constructed theoretical emissionless profile for the
G star ( 4 minus 5 )







Figure 2
CONSTRUCTION OF EMISSIONLESS PROFILES
FOR THE Ca II K LINE IN AR Lac








For the cores of the H and K lines in the sun, however,

and probably in all other stars also, non-coherent

scattering is the process which renders the central

intensity non-zero (Linsky and Avrett, 1970). Non-coherent

scattering arises because lines are not perfectly sharp;

therefore a quantum absorbed in one part of the line is not

guaranteed to be re-emitted from the same part of the line.

This process results in a redistribution of the energy

across the line profile, transferring energy from the wings

to the core, thereby producing a greater central intensity

than does coherent scattering. In the observed solar K-line

absorption profile, smooth extrapolation of the sigmoid

curve of the Doppler core to the line center yields a

central residual intensity of only a few percent (4% at

most; i.e., I/ICONT = 0.04: Aller, 1963). Theoretical

absorption profiles for the solar K line present a similar

picture (Aller, 1963).

Modeling the emissionless line profiles after those of

the sun constituted an empirical method which produced

inexact results; consequently any calculated differences or

ratios between the emissionless profiles and the actual

profiles could be only relative values. Determination of

the absolute values of (rather than the relative changes in)

the line profiles would require the precise calculation of a

theoretical line profile. This procedure would involve the

calculation of a model atmosphere, which would include








(1) the determination of the line absorption coefficient

dictated by the chosen model atmosphere and (2) the

assumption of a line-forming mechanism (Aller, 1963). There

are apparently no completed model atmosphere calculations

for the AR Lac system or a similar one.

Other observers (e.g., Weiler, 1978) have constructed

emissionless profiles by utilizing the Ca II line shapes

observed in spectra of single stars of the same spectral or

spectral-luminosity class as the stars in the AR Lac

system. Because there is some emission in these single

stars, employment of this method did not avoid the problem

of deciding the depth of the line empirically, but merely

Doppler-narrowed it slightly because single stars of these

spectral classes display much less rotational broadening

than do stars of the same classes in binaries.

Photometric scaling. Each of the ten spectra obtained

at phases outside eclipse exhibits a superposition of the

spectra from the entire discs of both stars. As a

preliminary step to determining the emissionless profiles

for these combination spectra, their actual (absorption-

plus-emission) profiles were photometrically scaled on the

assumption that the U light level (the ultraviolet light

level as measured in the standard UBV photometric system)

outside eclipse is constant. This practice is equivalent to

assuming that the U light output of each star is (1)

isotropic over its surface and (2) invariant with respect to

time.








This assumption is not strictly true for AR Lac because

there are small irregular variations in the light curve out

of eclipse and additional periodic variations due to the

photometric wave-like distortion. The small irregular

variations amount to only 0.025 mag (Chambliss, 1976), and

the amplitude of the distortion wave during the epochs of

this investigation (1976-1978) was only 0.04 mag. The

combination of these two effects resulted in a total U

intensity variation of only 0.3%, which is negligible. The

extra-eclipse U light level therefore provides a virtually

constant level to be used as a reference standard by which

to (1) scale light levels at all phases and (2) make

absolute comparisons among data of various observers. All

extra-eclipse profiles were therefore photometrically scaled

to the same U light level, selected to be equal to the

maximum U light level (the extra-eclipse U light level) of

the system.

The emissionless profile for both stars in combina-

tion. By alignment of the short-wavelength continuum edges

of all the extra-eclipse photometrically scaled actual

profiles, a composite was constructed to synthesize the

appearance of the actual combination spectrum of both

stars. Use of a composite rather than a spectrum at a

single phase tended to smooth any variations due to possible

differences in amounts of emission at different phases and

any Doppler shifting in position of emission peaks across

the absorption profiles at different phases.








To obtain the emissionless profile for the sum of the

K-lines of both stars, a smooth deep envelope was

constructed on the composite, which already exhibited a

center-line residual intensity of only about 8%. This

envelope was employed in the data analysis as the

representation of the combination emissionless profile at

all phases. (See Figure 2.)

Further photometric scaling. As a preliminary step to

determining the emissionless profile for the G star alone,

the K star's emissionless profile was photometrically scaled

so that it could be graphically subtracted from the

combination emissionless profile. On the assumptions that

(1) each star's photographically normalized U continuum is

equal to that star's fractional contribution to the total

extra-eclipse U light of the system and that (2) the

intensity at each wavelength in the line profile of each

star is proportional to that star's fractional contribution

to the total extra-eclipse U light level of the system (see

Binnendijk, 1960, pp. 180ff, 264ff), Chambliss' (1976)

photometric data were used to scale the K star's

extra-eclipse U continuum level to 44% of the total

extra-eclipse U continuum level of the system. (The value

used for the G star was, then, of course, 56%.)

The emissionless profile for the G star. With the K

star's extra-eclipse U continuum level scaled at 0.44 and

the extra-eclipse combination continuum level scaled at

1.00, the K star's emissionless profile was centered on the








combination emissionless profile and subtracted from it

point by point. The resulting emissionless profile for the

G star exhibited an extra-eclipse U continuum level of 0.56

with respect to the total extra-eclipse U continuum level of

the system. (See Figure 2.)

Synthesized emissionless profiles. After obtaining an

emissionless profile for each star, combination

emissionless profiles were synthesized for the phase of each

spectrogram by graphically adding the K- and G-star

emissionless profiles after they had been (1)

photometrically scaled to the proper proportion for that

phase and (2) Doppler-shifted relative to each other

according to their relative radial velocity at that phase.

Basing the emissionless profiles (i.e., the absorption

profiles) for all phases on the emissionless profiles for

one phase is tantamount to assuming that (1) any changes in

the actual (absorption-plus-emission) profiles are caused by

variations in emission rather than in absorption or in

both--(Weiler (1978) assumed this--and that (2) the

absorption profile of each star is the same shape for all

phases and for all time (i.e., that the absorption profile

is uniform over the surface of the star at all times). The

following procedure was employed to generate the syntheses.

The combination emissionless profile for each phase

outside eclipse was formed simply by graphically adding the

Doppler-shifted emissionless profile of the G star at a

given phase (its continuum photometrically scaled to 0.56)








and of the K star at that phase (its continuum photo-

metrically scaled to 0.44). All of the extra-eclipse

combination emissionless profiles were therefore scaled to a

U continuum level of 1.00.

Synthesis of emissionless profiles for eclipse phases

required additional photometric scaling. During phases

of partial eclipse of stars with uniform luminances, the

fractional U contribution from each star relative to the

total U light of the system at that phase is equal to the

unocculted fraction of the star's disc area. As previously

stated, the U continuum contribution of each star is also

this fraction; and the intensity at each wavelength in the

absorption line profile is assumed to be proportional to

this fraction.

The components of AR Lac, however, are not of uniform

luminance. The limb darkening in the K star is high; that

for the G star is relatively low (Chambliss, 1976).

Chambliss calculated the limb darkening coefficient for each

star by determining the values which yielded photometric

solutions consistent with his data. By this process he was

forced to one extreme with the K star--obtaining 1.0 as its

limb darkening coefficient in the U. The U limb darkening

coefficient for the G star was calculated to be 0.6. In the

present investigation, the value for the K star was assumed

to be 0.8 (thereby softening somewhat Chambliss' extreme

value), but the value for the G star was placed at the other

extreme--it was assumed to be 0.0.








Because the G star was assumed to be of uniform

luminance, the disc-fraction rule was applicable during the

partial and total phases of primary minimum, when the K star

is occulting part or all of the G star, respectively. For

example, at one of the partial phases of primary minimum the

total U light from the system was 0.89 of the total

extra-eclipse U light level of the system. Relative to the

total extra-eclipse level of the system, the K star's

contribution at this phase was 0.44, because the entire disc

of the K star was visible and it was contributing its

maximum amount possible: 0.44 of the total extra-eclipse U

level. Relative to the total extra-eclipse U light level

0.45 remained for the G star to contribute. For the

emissionless profile at this phase, the G star's U continuum

level was therefore scaled at 0.45; and the K star's, at

0.44. The sum of their continuum levels then equalled 0.89,

the total U continuum level visible at that phase relative

to the total extra-eclipse U continuum of the system. The

intensity at each wavelength in each emissionless profile

for each star was proportionately scaled to the U continuum

contribution from that star.

The disc-fraction rule does not obtain during secondary

minimum, when the G star is occulting part of the

non-uniform K-star's disc and the K-star's limb darkening

therefore comes into play. During ingress and egress of

secondary minimum, the U continuum of the system is at a

higher level than it would be if the luminance of the K star








were uniform (because the light lost by occultation of the K

star's limb is only 20% of what would have been lost if the

star were uniform). Conversely, during mid-secondary

eclipse, the U continuum of the system is at a lower level

than it would be if the K star were uniform in luminance

(because the bright center of the K star is being occulted,

leaving visible only the limb, which is 80 less luminous

than the disc-center).

Even though the disc-fraction rule does not obtain in

these instances, once the proper proportions of light are

determined for each star, the intensity at each wavelength

in the absorption profile of each star is, as usual,

proportional to that star's fractional U continuum

contribution normalized to the total extra-eclipse U

continuum of the system. In this case it would be each

star's fractional "limb-darkened U continuum contribution."

If the limb darkening of the K star had been ignored, errors

from negligible to approximately 3% for ingress and egress

of secondary minimum and of approximately 3% for phases

within secondary minimum would have been incurred in the

equivalent widths of the K emission, the magnitude of the

error depending on the amount of surface area occulted

(i.e., on phase) and on the value selected for the limb

darkening coefficient.

The value determined by Chambliss for the K star's limb

darkening and that used in the present investigation for the

G star's limb darkening are admittedly somewhat unrealistic.








Inclusion of a (probably reasonable) G star limb darkening

factor of 0.5 in the present calculations would only lower

somewhat the values of the K-line emission calculated for

the partial phases of primary eclipse, a consequence which

would have no effect on the general behavior of the emission

during primary eclipse, on the general conclusion reached,

or on the model formulated. Omission of the G star's limb

darkening generates errors ranging from negligible to almost

30% in the equivalent width of the emission for the partial

phases of primary eclipse, the error depending, as

previously stated, upon the phase and upon the value

selected for the limb darkening coefficient.

Chambliss (1976) also acknowledged a general problem

encountered with limb darkening and gravity brightening in

the G star of AR Lac. The assumption of the standard cosine

law of limb darkening and of a uniform variation of flux

with gravity does not represent the actual fall-off in

luminance at the limb of that star or the gravity-variation

of luminance over the surface of that star because the star

has large dark spots--discontinuous concentrated areas of

light-diminution rather than a continuous decrease in light

level as the limb is approached. The proper functional

dependence for limb darkening is unknown. Gravity

brightening was ignored in the present calculations.

In summary, the appropriate photometric scaling

criteria for each phase were used to scale the emissionless

profiles for each star at each phase. The two scaled








emissionless profiles were then centered on each other,

Doppler-shifted by the proper amount to account for the

relative radial velocity at that phase, and finally

graphically added to obtain the combination emissionless

profile due to the contributions of both stars at that

phase. Radial velocity curves obtained by Harper (1933)

were used to determine the Doppler shift of the K star

relative to the G star at each phase. Harper's curves were

selected because they appeared to be the more reliable of

the two sets of curves available, the others being those of

Sanford (1951).

Profiles of the K-line emission

The profile of the K-line emission at each phase was

determined by graphically subtracting the properly scaled

combination emissionless profile from the properly scaled

actual (absorption-plus-emission) profile at that phase.

(See Figure 2.) Somewhat similar Ca II emission profiles

are found in Greenstein (1960).

The equivalent widths of the K-line emission

As previously stated and applied, the profile of a

spectral line is the graph of the ratio of the line

intensity at each wavelength in the line to the intensity of

the nearby continuum; i.e., the spectral intensities are

normalized to the continuum intensity.

A measure of the strength of a spectral absorption line

is its total absorption relative to the level of the nearby

continuum. Graphically speaking, it is the area which the







line profile subtracts from the nearby continuum. In order

to express line strengths independent of instrumental

effects such as diffraction and finite resolving power, the

artifice of the equivalent width was devised (Aller, 1951;

Stromgren, 1951; Thackeray, 1961).

The equivalent width (W) of a spectral line is the

width (in wavelength units) of a rectangular line of zero

residual intensity relative to the local continuum and of

the same area as the actual line. In other words, the line

of equivalent width W absorbs the same amount of intensity

from the continuum as does the actual line profile. The

graphical representation of the equivalent width of a line

is a perfectly black rectangular profile extending from zero

intensity to the level of the local continuum and of the

same area as the line profile (Stromgren, 1951; Aller,

1951). In equational form,


W ICONT IX dX IX N d ,
ICONT ICONT



where

W = equivalent width of the spectral line (A),

ICONT = intensity of the local continuum (ergs/cm2/sec)

(Jones, 1931, 1934),

IX = intensity at wavelength X (ergs/cm2/sec),

Xl1 ,2 = short- and long-wavelength extremities of the line

profile at the level of the local continuum (A).








Investigation of the strengths of the emission

reversals in absorption lines necessitated the determination

of the equivalent widths of the emission alone. The

equivalent width of the emission profile (We) at each phase

was calculated by subtracting the equivalent width of the

scaled combined emissionless profile (W-) for that phase

from the equivalent width of the scaled actual

(absorption-plus-emission) profile (W+) for that phase:




We = W+ W~,



where W+ = f I-- )
ICONT)



w- = 1 X




therefore We = +--T
ICONT ICONT



From this expression for We it can be seen that it was not

necessary to actually calculate W+ and W-, but only to

subtract the relative intensities of the absorption-plus-

emission profile and the emission profile, a method which

greatly simplified the calculations.








Because no equation was known for relative line

intensity as a function of wavelength, the integration was

performed numerically by the rectangular method:




n In
wrICONT






= intensity at wavelength Arelative to
SCONT .
local U continuum dimensionlesss),



A ? = wavelength increment between wavelengths at

which relative intensities are measured; AN=

1.2 A = chart resolution limit.





Because the chosen integration step-size (1.2 A) was

smaller than the resolution limit of the IIa-O plates at

128 A/mm (2.3 A), a more exact numerical method (e.g.,

Simpson's one-third rule) was unwarranted because it would

have produced more precision in the result than was inherent

in the data.

The equivalent width of the K-line emission at each

phase is tabulated in Table 3, Section IV.








Determination of error in the equivalent widths of the
K-line emission

Sources of error in the calculations of the equivalent

widths of the K-line emission were

(1) photographic errors, including emulsion grain clumps,

non-uniform emulsion density, and sensitometry methods

(2) electronic noise in

(a) the recording microdensitometer

(b) the chart recorder

(c) the transmission densitometer

(3) the plotting of points for graphs and the reading of

points from graphs

(4) variations in light curves and scatter of photometric

data points

(5) the photometric distortion wave

(6) the wavelength scale for the recorder chart

(7) the radial velocity curves.

Errors incurred due to photographic grain clumps or

non-uniform density were minimized by tracing the

spectrograms with a slit of the greatest height and width

possible without incurring degradation of resolution within

the line profile. Errors from these sources were therefore

rendered negligible. Sensitometry errors were of unknown,

but probably small, magnitude.

Electronic noise was smoothed by averaging multiple

tracings of each spectrogram. All of the tracings of any

one spectrogram were virtually identical. Use of their

average therefore generated negligible error.








Plotting of points and construction of smooth curves

through those points was performed with very fine-pointed

writing instruments on graph paper of a scale large enough

to represent the precision of the raw data. Readings of

points from graphs were made to the same precision as that

to which the points were plotted.

The error ultimately calculated for the equivalent

widths is an internal error only, generated by the method

employed to obtain and analyze the data; i.e., it is not an

error relative to any absolute standard.

Error analysis was carried out by two methods:

(a) "Data analysis method": The mathematical rules for

error analysis were applied to the values computed in

successive intermediate calculations leading to equivalent

width, a procedure which incurred compound errors propagated

by the mathematical operations on the inexact values which

were employed in the calculations. The error for each

spectrogram depended upon the particular values used in the

calculation of its equivalent width. In order to

demonstrate which changes in equivalent width with phase

exceeded the normal computational error (i.e., were "real"

changes in equivalent width), it was sufficient in this

investigation to calculate only a maximum error for all

spectrograms. If this calculation had proved insufficient

for the determination of the validity of a particular

equivalent width, the necessary individual error would have

been computed. The itemized list of the errors computed by








this method is as follows:

(1) The calculation of the photographically normalized

values of the relative intensities resulted in a maximum

error of 2.0%. This value includes the errors incurred by

plotting and reading data points on graphs.

(2) The combined photometric errors (due to individual

variations in light curves, scatter, and the distortion

wave) in the U light curves used to photometrically

normalize the U continue of the spectrograms contributed a

maximum error of 0.3% in the relative photometric

intensities of the spectrograms.

(3) The error in the calculated value of the wavelength

scale for the recorder chart was 4.7%.

(4) The error in the radial velocities contributed

negligible error to the calculated Doppler shifts.

(5) Because all of the quantities containing these

errors were multiplied or divided to obtain the equivalent

width, the combined error was their sum: 7.0%.

(b) "Noise-lobe" method: By assuming that all lobes on the

actual profiles were noise, maximum and minimum values for

the K-line emission equivalent width were calculated. The

maximum profile was constructed by inscribing on the

photometrically scaled actual profile a smooth inner

envelope which eliminated all intruding lobes. The minimum

profile was constructed by circumscribing a smooth outer

envelope which eliminated all extruding lobes. Subtraction

of the areas subtended by these two profiles and division of








this difference by two yielded for each plate a sort of

average equivalent-width error (in A). In general, this

method produced errors far greater than the maximum 7.0%

computed by the data analysis method. Because the lobes of

the actual profiles appear in virtually every spectrogram,

regardless of phase, it seems rather unlikely that they are

noise. (They are, in fact, merely some of the many

unidentified lines which are at wavelengths in the vicinity

of the H and K lines and which are blended with them. No

correction for them was applied, and no attempt was made to

subtract them from the line profile; therefore they, too,

contribute to the We measurements' being relative rather

than absolute.) This method is deemed, therefore, to

provide, for the most part, a gross exaggeration of the

errors incurred in this investigation. For purposes of

comparison of changes in equivalent width from phase to

phase, however, and in order to demonstrate beyond any

reasonable doubt the mathematical significance of the

differences in the calculated values for the equivalent

widths at different phases, this method is useful. Where

any question might arise regarding the mathematical validity

of stating that a difference exists between two equivalent

widths, this extreme method can be used to demonstrate

unequivocally that the difference is well above any

reasonably assumed value for a noise level.

The results of the equivalent-width calculations for AR

Lac are summarized in Table 3, Section IV.













SECTION IV
DISPLAY AND ANALYSIS OF REDUCED DATA


Data Display: The Graphical Relation

General Description

A graph (Figure 3) was constructed to display the

relation between the relative K emission-line equivalent

width and the orbital phase of the AR Lac system (data in

Table 3). Data points were connected in order of phase by

dotted lines merely to illustrate the general contour of the

relation and to facilitate the visual scanning of the

emission changes, rather than to imply the graphical

representation of a function W(phase). There are too few

data points over large spans of the domain to be able to

graphically or equationally represent a true functional

dependence. Line-terminated error bars indicate for all

data points the 7.0% variation in K emission-line

equivalent width as computed by the data-analysis method.

Circle-terminated error bars indicate the non-constant

variation as computed by the noise-lobe error method, which

was employed only when necessary to establish beyond any

reasonable doubt whether a particular data point lay within

data noise or was instead indicative of a real departure

from the general trend of equivalent widths in that phase

region.








RELATIVE


Table 3
EQUIVALENT WIDTHS OF THE Ca II K-LINE EMISSION
IN AR Lac


Phase Plate Epoch We (A) 7.0%
(year) Error (A)

.002 34 1976.6130 5.49 0.38
.060 56 1977.6989 15.20 1.06
.115 57 1977.7318 8.26 0.58
.130 58 1977.7536 11.10 0.78
.377 60 1977.9071 12.20 0.85
.384 45 1976.9402 17.35 1.21
.385 24 1976.5663 11.78 0.82
.406 18 1976.5555 14.59 1.02
.415 46 1976.9403 19.69 1.38
.456 41 1976.6209 16.79 1.17
.458 37 1976.6155 17.27 1.21
.498 38 1976.6157 14.71 1.03
.504 42 1976.6211 15.28 1.07
.560 50 1977.0605 20.19 1.41
.724 59 1977.7895 12.15 0.85
.857 61 1977.9097 13.19 0.92
.902 21 1976.5637 12.36 0.87
.923 28 1976.6017 17.34 1.21
.939 33 1976.6127 12.01 0.84


Phase:


Plate:


Epoch:



We:


+7.0% Error:



See Figure 3.


fraction of the period
system


of revolution of the


the ordinal number of the plate, indicating
the temporal order in which it was obtained

the epoch of the observation, listed as the
year and the day + month + hour of the
observation as a decimal fraction of a year

the relative equivalent width of the K-line
emission at the corresponding phase, in A

7% of We, the error determined by the "data
analysis method," in A



















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A cursory comparison of the error bars for all the data

points indicates that the emission exhibits prominent

eclipse features (local relative minima in the emission) and

some extra-eclipse variations.

Eclipses of the Emission

Well-defined eclipse minima in the emission and

pronounced near-symmetry about the mid-eclipse phase

characterize both primary and secondary eclipses. Phases

were computed using the ephemeris in Hall, Richardson, and

Chambliss (1976).

Primary eclipse

From the graph it is seen that as primary eclipse is

approached, the emission level dips slightly just prior to

first contact, then rises to a local maximum at first

contact. This maximum is followed by a sharp decline to a

mid-eclipse local minimum, which lies well below the

pre-eclipse emission level. Following mid-eclipse is a rise

to a local maximum just prior to fourth contact, a

subsequent decline to a local minimum lying above the

mid-eclipse level, and a sharp rise to a post-eclipse level

slightly below the pre-eclipse level. The existence of the

pre-ingress depression in the emission is somewhat doubtful

because the error bars of the two adjacent data points (#61

and #21) share some common ground. The post-egress

depression may be a real phenomenon rather than noise,

because there is a lack of commonality in the error bars of

the three data points (#56, #57, and #58) which define it.








The data exhibit a lack of perfect symmetry about

mid-eclipse. The existence of near-symmetry strongly

suggests that symmetry does exist, but is in some manner

veiled. The veiling agent is probably a selection effect:

namely, that data were obtained only at certain phases,

which were not chosen for their symmetry about mid-eclipse.

The presence of additional data points at phases symmetrical

relative to mid-eclipse would probably reveal the suspected

symmetry. In further support of this suggestion it is noted

that there is a large span (0.04 phase unit) between the two

points defining pre-ingress depression (#61 and #21),

whereas there is only 0.015 phase unit between the two

post-egress plates (#57 and #58). If it can indeed be

contended that the depressions are symmetrical (and there is

nothing in these data or in those of others to preclude

symmetry), then between #61 and #21 there could be a much

lower value of equivalent width (at about phase 0.885)

similar to that of #57.

The lack of symmetry between the levels of pre- and

post-depression emission levels can also probably be

attributed to the paucity of data points at symmetrical

phases relative to primary mid-eclipse. A data point at

phase 0.14 (just beyond #58) might well have returned to the

pre-ingress level. No concrete conclusion can be drawn

regarding perfect symmetry without additional data at the

required phases.








Within primary eclipse the ratio of maximum emission to

minimum emission is 3.7, maximum occurring at first contact

and minimum at mid-eclipse. The ratio of maximum emission

to the average extra-eclipse level (at the shoulders of the

pre- and post-eclipse depressions) is 1.4. The ratio of the

average extra-eclipse level to the minimum emission level is

2.4. The minimum emission level at mid-eclipse is the

absolute minimum for the entire orbital cycle.

Secondary eclipse

As secondary eclipse is approached on the graph, the

emission rises to a local maximum prior to first contact (at

phase 0.384). (See Extra-eclipse Behavior.) The emission

then declines to the previous level before rising to a

slightly higher local maximum at first contact. Following

first contact is a decline to a mid-eclipse local minimum,

which lies slightly above the pre-eclipse level. Nearly

mirroring this behavior (viz., with the omission of the

pre-ingress maximum) is a post-mid-eclipse rise to a local

maximum just prior to fourth contact and a subsequent

decline to the pre-ingress emission level.

As in the case of primary eclipse the question of

perfect symmetry arises, and the reply is the same: more

data points near fourth contact are needed to confirm or

deny symmetry.

Within secondary eclipse the ratio of maximum emission

to minimum emission is 1.3, maximum occurring at first

contact and minimum at mid-eclipse. The ratio of maximum








emission to the extra-eclipse level is 1.6. The ratio of

the minimum emission to the extra-eclipse level is 1.25.

Comparison of primary and secondary eclipses

The eclipse of the emission is much shallower, both

absolutely and relatively, at secondary minimum than at

primary minimum, the mid-eclipse emission level of the

former being 2.8 times higher than that of the latter.

Because secondary eclipse is central, but not total, the

emission at secondary mid-eclipse is composed of

contributions from both stars. On the other hand, during

primary eclipse the G star is completely occulted; therefore

the emission at mid-primary eclipse is contributed by the K

star alone.

Extra-Eclipse Behavior

With the exception of plates #45, #57, and #61 the

ranges of error for the extra-eclipse plates indicate a

virtually constant extra-eclipse emission level. There are,

however, very few extra-eclipse plates; therefore no general

conclusive statements can be made regarding extra-eclipse

behavior.

Coverage in the vicinity of phase 0.384 (plates #60,

#45, and #24) is, however, sufficient to state that there is

an emission peak at that phase. Comparison of error bars

(even the exaggerated ones determined by the noise-lobe

error method) demonstrates that the peak rises significantly

above the noise level.








Interpretation of the Graphical Relation

Variability of the Emission

Performed as an internal check of the consistency of

the spectrograms with the emission profiles, microscopic

visual examination of the plates revealed that the Ca II

emission is visible at all phases. It is not entirely

eclipsed at either minimum, thereby corroborating Sanford's

(1951) and Weiler's (1978) observations that the emission is

present outside of as well as within eclipse. The

difference between equivalent widths of adjacent data points

of the equivalent width-phase curve exceeds the computed

range of error, even when the more extreme of the two error

calculations is considered. The emission is therefore very

definitely variable, in confirmation of the observations of

Sanford (1951), Babaev (1974c), Weiler (1975, 1978), and

Naftilan and Drake (1977), and the conclusion of Kron (1952)

upon examination of Wyse's (1934) plates. Further, the

variations appear to be phase-dependent and/or time-

dependent, not random, as reported by Weiler (1978) and as

indicated by Babaev's (1974c) data.

Relative Strengths of the Emission

Because the grating dispersion used in this

investigation was not great enough to resolve the components

of the K line from each star, the emission in the graphical

relation represents a composite of the emission from both

stars. Consequently, no statements can be made in

confirmation or denial of Sanford's (1951) observations that








the ratio of the secondary's emission to the primary's

emission increased during the first half of the system

period and decreased during the second half of the period.

Again because of insufficient dispersion, no positive or

negative statements can be made regarding confirmation of

the observations of Sanford (1951) and Naftilan and Drake

(1977) that the emission from the secondary star is stronger

than that from the primary star.

Attempts to reconcile the intra-eclipse behavior of the

graphical relation of this investigation with the

intra-eclipse observations of Sanford (1951) and Naftilan

and Drake (1977) appeared to fail at first glance.

Examination of their K-line profiles at primary and

secondary mid-eclipse revealed a higher level of emission at

primary eclipse than at secondary eclipse, whereas the

present investigation indicated just the opposite.

This problem was resolved upon closer inspection of the

manner in which both of the previous investigators analyzed

their data. These observers performed their calculations of

the equivalent width of the emission at a given phase by

comparing the intensity of the emission to the intensity of

the continuum level at that phase rather than by comparing

the emission to an absolute, unchanging continuum standard

level (as was done in the present investigation).

As seen in Sanford's (1951) line tracings, it is indeed

true that at primary minimum the emission rises above the

continuum level; whereas at secondary minimum the emission








does not quite reach the level of the continuum, both

emission peaks being the same width at the base. The

continuum level at primary mid-eclipse is, however, only 54%

of the continuum level at secondary mid-eclipse (Chambliss,

1976). When the equivalent width of the emission for each

star was calculated using their data, but comparing both

emission levels to the same standard continuum level (the

extra-eclipse level), the same conclusion resulted as was

obtained in the present investigation: the equivalent width

of the emission is greater at secondary mid-eclipse than at

primary mid-eclipse.

Sanford's and Naftilan and Drake's conclusion that the

emission of the primary star is weaker than that of the

secondary star remains unchanged by the above-instituted

change in the level of the continuum to which the emission

was compared because the dispersion they used was great

enough to completely resolve the emission components from

the primary and secondary stars, thereby allowing direct

comparison of the relative amounts of emission from both

stars at each phase (except at eclipses).

Observed Surface Distribution of the Emission

There is considerable evidence, both direct and

indirect, that the emission is not uniformly distributed

over the surfaces of the stars in AR Lac. Extra-eclipse

variability seen by previous observers and in the present

investigation constitutes evidence of non-uniformity of

emission.








For a number of Ca II emission stars, Struve (1945),

Hiltner (1946), Struve (1946), and Gratton (1950) found

evidence favoring the permanent localization of the emission

at the tips of the tidal bulges of the stars) producing the

emission. Struve (1948), although acknowledging that the

localization of the emission of AR Lac had not been

investigated, inferred that it was confined to the

tidal bulges by analogy with RZ Cnc and RW UMa.

Weiler (1978) suggested that his observation of a

substantial change in the equivalent width of the emission

over a short period of time during the partial phases of

secondary minimum ingress (a diminution of 4A in 35m) could

be indicative of "the eclipse of a localized emission area

on the KO IV star" (Weiler, 1978, p.88) because this

dramatic change could not be explained by the eclipse of a

uniform distribution of emission over the stellar surface.

Sanford (1951), Struve (1952), and Naftilan and Drake

(1977), on the other hand, found that the broadening of the

Ca II emission in AR Lac corresponds to synchronous

rotational broadening, thereby indicating that the emission

emanates from all parts of the stellar surfaces) or at

least from complete equatorial bands. Kron (1952) had

concluded that the distribution of the emission around the

entire equator of the star does not necessitate that the

distribution be homogeneous--the emission could be

concentrated in patches well distributed in longitude and

not fixed permanently in certain areas.








The asymmetry of the line profiles in the present

investigation provides a piece of evidence that the

distribution of light over the stellar surface is

non-uniform (Huang and Struve, 1960). The variations in the

emission in the vicinity of the eclipses and the emission

peak at phase 0.384 indicate the presence of strong,

localized emission sources. The presence of the emission

throughout the system's cycle indicates that there is also

probably some distribution of emission over the entire

equatorial region or the entire surfaces) of the starss.

The exact nature of the emission sources) (size,

position, distribution) is uncertain from the data in this

investigation because there is insufficient time/phase

resolution in the vicinity of each contact and insufficient

spectral resolution overall. Better resolution would

establish more precisely the changes in the emission as it

is eclipsed so that an accurate determination could be made

of the phases at which the emission decrease begins and ends

during each eclipse.

Model for the Surface Distribution of the Emission

A model was constructed to account for the observations

in this investigation. A model with uniform distribution of

emission could not explain the character of the variations

in the emission; therefore a model with non-uniform emission

was chosen--a composite incorporating three emission

sources:








(1) distributed emission from all parts of the stellar

surfaces or at least from complete equatorial

bands, the emission arising from well-distributed

spots or patches

(2) strong emission permanently localized at the

extremities of the tidal bulges of the stars

(3) strong emission from a localized source other than

the bulge-extremities.

The distributed emission accounts for the presence of

the underlying "background" of emission observed in this

investigation throughout the system's cycle and also for the

observations (Sanford, 1951; Struve, 1952; Naftilan and

Drake, 1977) that the broadening of the emission corresponds

to that which would be observed from a source which spans

the full diameter of the star rather than being concentrated

only in a small area.

The presence of emission sources at the extremities of

the tidal bulges explains most of the observational features

seen in this investigation in the vicinity of and within

eclipse (see Primary eclipse). Compatibility of the results

of this investigation with the observations of Sanford

(1951) and Naftilan and Drake (1977), who determined that

the emission from the K star (the secondary) is numerically

greater than that from the G star, requires the sum of the

emission from the sub- and anti-stellar bulges of the K star

(Ks and Ka) to be greater than the sum of the emission from

the sub- and anti-stellar bulges of the G star (Gs and Ga).









The non-bulge localized source accounts for the

emission peak at phase 0.384.

Model for the Generation of the Observed Behavior of the
Emission with Phase

Combination of the model pictured above with the system

motion revealed the details of the explanation of the

equivalent width-phase relation.

Primary eclipse

This model cannot explain the pre- and post-primary-

eclipse emission depressions because severe contradictions

are encountered. The explanation for these depressions is

therefore left to circumstellar matter and a consequent

increase in absorption rather than a decrease in emission.

(See Correlations of Photometry and Spectroscopy.)

An increase in the visible area of the emission

concentration of the substellar bulge (Gs) of the G star and

on the antistellar bulge (Ka) of the K star as the stars

revolve accounts for the pre-first contact increase in the

emission prior to primary eclipse.

The first-contact emission maximum occurs because more

of these two areas is visible than at any other phase

(except fourth contact). Comparison of the emission level

at this maximum to the emission at the quadratures (when

one-half of each emission area is visible) leads to the

conclusion that the sum of the substellar emission (Gs) from

the G star and the antistellar emission (Ka) from the K star

is greater than the sum of the anti-stellar emission (Ga)








from the G star and the substellar emission (Ks) from the K

star. This result is compatible with the results of Sanford

(1951) and Naftilan and Drake (1977) if the substellar

emission (Gs) of the G star is greater than or equal to the

substellar emission (Ks) of the K star. (There is no

evidence to preclude this possibility.)

The post-first contact decline in emission can be

attributed to the eclipse of the substellar emission (Gs) of

the G star while the contribution from the antistellar bulge

(Ka) of the K star remains constant (because the entire area

of this emission is visible from first to fourth contact).

Between second and third contacts the emission is entirely

due to the anti-stellar area (Ka) on the K star.

The emission increase to a maximum at fourth contact is

caused by the reappearance of the substellar emission (Gg)

of the G star while the emission from the K star remains

constant.

The post-fourth contact decrease in emission occurs as

the K-star anti-stellar emission (Ka) area and the G-star

substellar emission (Gs) area are disappearing around the

limb.

Secondary eclipse

The increase to a maximum at first contact of secondary

eclipse is caused by more of the K-star substellar emission

(Ks) area and more of the G-star antistellar emission (Ga)

area rotating into view. At first contact the maximum

amount of both of these areas is visible.




Full Text

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PAGE 219

81,9(56,7< 2) )/25,'$



VARIATIONS OF THE H AND K EMISSION LINES
OF SINGLY IONIZED CALCIUM
IN THE ECLIPSING BINARY STAR SYSTEM AR LACERTAE
BY
SARA WITHEROW HOFFMAN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA

Copyright 1983
by
Sara Witherow Hoffman

For
Stardust
Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation
http://www.archive.org/details/variationsofhkemOOhoff

ACKNOWLEDGMENTS
To all those who aided me during my work on this
dissertation I would like to express my appreciation.
I would like to thank the members of my committee:
Dr. Frank Bradshaw Wood, Dr. John P. Oliver, Dr. Howard L.
Cohen, Dr. Alex G. Smith, and Dr. Charles F. Hooper, Jr.
I would like to offer my thanks to Dr. Wood for serving
as chairman of my committee and escorting me at commence¬
ment. In addition, I greatly appreciated his assistance in
my attempts to find rare references and his lending to me
his personal copies of papers. I would also like to express
my deepest gratitude to him for making possible the
replacement of the University of Florida spectrograph with
the University of South Florida spectrograph when the former
instrument was sent to Mt. John Observatory. I am also
greatly appreciative of his relating to me those fascinating
details of astronomical history which could be recounted
only by one who had actually experienced them.
To Dr. Oliver I would like to express my greatest
appreciation for acting as my research adviser and acting as
co-chairman of my committee. His most generous expenditure
of his time, his lending of his support, and his
contribution of his expertise with photometric and
IV

electronic equipment were invaluable aids to me in pursuing
the objective of completing a project of great interest to
both of us.
I am very grateful Dr. Cohen for his support, advice,
and guidance.
To both Dr. Smith and Dr. Hooper I would like to offer
my sincerest thanks for the very helpful information they
conveyed to me, but primarily I would like to thank them for
their recognition and support at critical points in my
career.
For his precision construction of the slit-viewing
optics from my drawings I would like to express my great
appreciation to Mr. Eli Graves.
To Marty deGeorge I would like to state again how very
grateful I was that he provided the transportation for the
spectrograph back and forth between Gainesville and Tampa on
so many weekends.
I would like to thank Roger L. Scott for so willingly
providing on request sensitometry and astrophotography
information gained from his own experience.
To Paul
Gombola
I would like
to ex
press my
gra
titude
for
his act
rurate renderings of
the
figures
in
this
d i s:
sertation.
For his
exacting
performance
Ln the
painstak
ing
typing
and
printing
of this
dissertation,
I wou
ild like
to e
xpress
my
extreme g
ratitude
to Mr. Dan
R. Ric
:h. His
pat
ience,
v

endurance, and support during the very tedious production of
this document are most greatly appreciated.
I would like to offer my utmost thanks to Mr. Jean G.
Klein, Chairman of Natural Sciences, Santa Fe Community
College, for granting me a flexible teaching schedule and
spring terms with no teaching load so that my research could
be continued.
Thanks go also to Marinell Brown, who made the final
word processor corrections and printed the final copies of
this dissertation.
On a personal level my appreciation goes to my friends
who were supportive and understood that this project was
important enough for me to have to decline their social
invitations for a total time of years. For his steadfast
support during the early years of this project, I would so
very gratefully like to acknowledge Nelson L. Mathis--I'm
just sorry that this Christmas present is so belated.
To my fellow graduate students who honored me with that
sinfully original committee at the first BLACK HOLE I would
like to say: Thanks, guys, maybe I should've been in
microwave astronomy with Penzias and Wilson . . . (get it,
guys?)! And of course, I will be forever indebted to RLS
(?) and JTP (?) for the spectrophotometer I used to obtain
sensitometry spots. . .
I would also like to express my special thanks to my
family (human and fuzzy alike) for their much appreciated
support, both emotional and monetary, while I saw this
vi

project through. My great appreciation goes to my father,
Richard Thompson Hoffman, for answering my childhood
questions about stars, planets, calculus, and other math,
and to my brother, Richard Thompson Hoffman, Jr., for being
my childhood companion in adventures of scientific
discovery. My ultimate thanks go to my mother, Marguerite
Kinser Hoffman, for helping me with some of the tedium of
this work, for doing all the things she did to make this
zenith of educational achievement possible--among them
stimulating my mind from birth, showing me the excitement of
discovery, teaching me things far beyond my years,
enthusiastically allowing me the freedom to pursue my
dreams, and then sticking by me while I pursued them.
vi 1

TABLE OF CONTENTS
ACKNOWLEDGMENTS iv
LIST OF TABLES xii
LIST OF FIGURES xiii
ABSTRACT xiv
SECTION I A HISTORY OF OBSERVATIONS OF H AND K
EMISSION AND THE AR LACERTAE SYSTEM 1
Prologue 1
Introduction 1
Early Observations of H and K Emission 2
Early Observations of AR Lacertae 4
Early Photometry 4
Early Spectroscopy 6
Correlation of Photometry and Spectroscopy 9
Early Polarimetry 9
The "AR Lac Group" and Other Stars with Ca II
Emission 9
Further Observations of AR Lacertae 15
System Elements 15
Spectroscopy and Photometry 16
Radio Measurements 19
Polarimetry and Other Measurements 19
Summary 20
SECTION II INSTRUMENTATION AND OBSERVATIONS 30
Instrumentation 30
Telescope 30
Spectrograph 30
Plates 32
Sensitometer 33
Densitometers 33
Calculator 35
Observing Program 35
vi i i

SECTION III DATA REDUCTION
40
Procedure and Theory 40
Plate-Tracing 40
Conversion of Deflections to Relative Intensities .. 43
Density-deflection relations: D(d) 43
Characteristic curves (D-log E curves): D(log E)
and D( E ) 44
Relative-exposure-deflect ion relations
and relative-intensity-deflection
relations: E (d) and 1(d) 45
Relative plate speeds 46
Photographic normalization of relative
intensities 46
Calculation of Equivalent Widths 47
Actual (absorption-plus-emission) line profiles .. 47
Emissionless profiles 49
The emissionless profile for the K star 49
Photometric scaling 54
The emissionless profile for both stars
in combination 55
Further photometric scaling 56
The emissionless profile for the G star 56
Synthesized emissionless profiles 57
Profiles of the K-line emission 62
The equivalent widths of the K-line emission 62
Determination of error in the equivalent widths of
the K-line emission 66
SECTION IV DISPLAY AND ANALYSIS OF REDUCED DATA .... 70
Data Display: The Graphical Relation 70
General Description 70
Eclipses of the Emission 73
Primary eclipse 73
Secondary eclipse 75
Comparison of primary and secondary eclipses 76
Extra-Eclipse Behavior 76
Interpretation of the Graphical Relation
Variability of the Emission 77
Relative Strengths of the Emission 77
Observed Surface Distribution of the Emission 79
Model for the Surface Distribution of the Emission . 81
Model for the Generation of the Observed Behavior
of the Emission with Phase 83
Primary eclipse 83
Secondary eclipse 84
Extra-eclipse behavior 86
Anisotropic model 86
IX

Temporal model 87
Spatial model 90
Conclusion 96
Correlations of Spectroscopy and Photometry 96
Eclipse correlation 97
Pre- and post-eclipse depressions 97
Distortion-wave-minimum--emission-maximum--
period-change relation 99
Period changes 99
Distortion wave minimum and Ca II emission
maximum 102
Conclusion 108
Summary 108
SECTION V GENERAL MODEL Ill
Introduction Ill
Spectroscopic Characteristics Ill
Ca II Emission Ill
Site of the emission Ill
The chromosphere 112
An extended envelope 114
Gas streams 114
The tidal bulges 114
The entire stellar surface 115
Patches 116
Mechanism for and motion of the Ca II emission ... 117
Eruptive activity 118
Collisions and thermal gradients 118
Gas streams 123
Binary character 124
Conclusion 125
Depressions in emission 126
Magnetic fields 126
Other Spectroscopic Features 127
Hydrogen, cerium, iron and other metals 127
Radio emission 128
Photometric Characteristics 129
Introduction 129
Depressions in the light curve 129
Irregular Light-Curve Variations and the
Photometric Distortion Wave 129
Pulsation as the agent 131
Ring, shell, or envelope as the agent 131
Gas streams as the agent 132
Starspots as the agent 132
Existence and observability of starspots 145
Conclusion 148
Period Changes 148
Introduction 148
Mass Loss as the Mechanism 149
Component Interaction as the Mechanism 152
Other Effects as the Mechanism 152
x

Correlations of Phenomena 153
Introduction 153
Spectroscopic-Photometric Correlation 153
Photometric-Infrared Correlation 155
Photometric-Radio Correlation 155
Luminosity Correlations 156
Conclusion 156
Evolution of Stars with Ca II Emission 156
Introduction 156
Stage of Evolution 157
Pre-main sequence 157
Post-main sequence 158
Circumstellar matter, component masses, and
population count 160
Ca II emission and Li absorption 165
Ages of the RS CVn Systems 168
Other Evolutional Effects 169
Summary 170
SECTION VI FUTURE INVESTIGATIONS 176
Introduction 176
Spectral Analysis 176
Equipment 177
Observations 182
Epilogue 187
REFERENCES 188
BIOGRAPHICAL SKETCH 197
xi

LIST OF TABLES
Table 1
Table 2
Table 3
Table 4
GENERAL CHARACTERISTICS OF RS CVn BINARY STAR
SYSTEMS AND PARTICULAR CHARACTERISTICS
OF AR Lac 23
RS CVn BINARY STAR SYSTEMS 29
RELATIVE EQUIVALENT WIDTHS OF THE Ca II
K-LINE EMISSION IN AR Lac 71
PHASE OF AR Lac AT DISTORTION WAVE MINIMUM,
EMISSION MAXIMUM, AND PERIOD CHANGE 105
x i i

LIST OF FIGURES
Figure 1 PROFILES OF THE Ca II K LINE IN AR Lac ...
Figure 2 CONSTRUCTION OF EMISSIONLESS PROFILES FOR
THE Ca II K LINE IN AR Lac
Figure 3 VARIATION OF THE RELATIVE EQUIVALENT
WIDTH OF THE Ca II K-LINE EMISSION WITH
ORBITAL PHASE IN AR Lac
Figure 4 THE ENHANCED MIGRATION CURVE FOR AR Lac ..
xi i i
51
52
72
107

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
VARIATIONS OF THE H AND K EMISSION LINES
OF SINGLY IONIZED CALCIUM
IN THE ECLIPSING BINARY STAR SYSTEM AR LACERTAE
by
Sara Witherow Hoffman
August, 1983
Chairman: Frank Bradshaw Wood
Cochairman: John P. Oliver
Major Department: Astronomy
The variability of the Ca II emission and the associa¬
tion of any such variation with the photometric behavior and
with other characteristics of AR Lac were the primary
questions considered in this investigation. In pursuit of
these objectives a series of spectrographic plates spanning
the entire orbital cycle of AR Lac was obtained by the
author during 1976-1977.
Reduction of the K-line emission data by photographic,
photometric, and spectroscopic scaling revealed emission
throughout the cycle and emission eclipses well-correlated
in phase with the photometric eclipses. Also observed were
(1) pre- and post-primary eclipse emission depressions fol¬
lowed and preceded, respectively, by pre- and post-primary
eclipse emission increases, (2) pre- and post-secondary
xiv

eclipse emission increases, and (3) an extra-eclipse local
emission maximum at phase 0.384.
The model constructed to account for these phenomena
consisted of (1) permanent emission distributed over the
entire stellar surfaces, (2) permanent emission regions
located at the tidal bulges of the stellar components, (3)
Ca II-absorbing circum-secondary material and (4) an
isolated emission region temporary in surface or temporal
location (a moving spot group or a flare, respectively).
The extra-eclipse emission maximum at phase 0.384 was
discovered to be congruent with the migration curve for the
photometric distortion wave minimum of AR Lac, as was
another apparent extra-eclipse emission maximum recorded at
a different epoch by a different observer. Data from yet
another source revealed that at a still different epoch an
extra-eclipse Ca II emission maximum coincided in phase with
the photometric distortion wave minimum at that epoch. On
the basis of these limited data an interrelationship of the
Ca II emission, the distortion wave, and the period changes
in AR Lac was therefore tentatively demonstrated.
A re-evaluation of contradictory reports regarding the
visibility of individual starspots led to the conclusion
that large spots would indeed be observable with equipment
of high precision.
A comprehensive physical and evolutional model for the
cumulative spectroscopic and photometric behavior of AR Lac
was constructed by augmentation of other models and
incorporation of the results of the present investigation.
xv

SECTION I
A HISTORY OF OBSERVATIONS OF H AND K EMISSION
AND THE AR LACERTAE SYSTEM
Prologue
The history presented herein is an approximate
chronology of the observations which are pertinent to the
present investigation. Because it is intended merely as a
chronicle of observations, no extensive interpretation or
discussion by the observers is presented; and only brief,
bracketed comments are offered by the author. Detailed
discussions are included in Sections IV, V, and VI.
Introduction
H and K emission, which is observed in the spectra of
numerous late-type stars and stellar systems, has confounded
astronomers for over a century. Prominent H and K emission
is exhibited by the eclipsing binary system AR Lacertae,
which has manifested itself as a puzzle of considerable
complexity not only because of its strong emission but also
because of its many other unusual characteristics. The
history of astronomical observation of H and K emission
began over a third of a century before AR Lacertae was
detected as a variable and more than half a century before
AR Lacertae was discovered to exhibit H and K emission.
1

2
Early Observation of H and K Emission
The H and K spectral lines are two of the solar lines
which were alphabetically designated by Fraunhofer in
1814-1815 (Abell, 1964) when he rediscovered the myriad of
dark (absorption) lines crossing the solar spectrum. The H
and K lines are resonance lines of singly ionized calcium
(Ca II).The H line, at wavelength 3968.47 A, is produced by
the 4p 2V\/2° ~ 4s 2S1/2 transition; whereas the K line, at
3933.67 A, arises from the 4p ^3/2° - 4s ^S\/2 transition
(Shore and Menzel, 1968). The H line is usually blended
with the H-epsilon line (3970.07 A) of the Balmer series of
hydrogen.
The discovery of H and K emission in the spectrum of an
astronomical object was made by Young (1872), who visually
detected emission reversals at the centers of Ca II
absorption lines in the sun (St. John, 1910). According to
Young, the lines were observed to be "regularly reversed on
the body of the sun itself, in the penumbra and the
immediate neighborhood of every important spot" (St. John,
1910, pp. 36, 37). Four years later, Draper made the first
photograph of the solar spectrum (Smithsonian, 1978). The
first photographic plates of the spectra of sunspots,
obtained in 1883 by Lockyer, revealed H and K emission
reversals over the spots. Subsequent plates obtained in
1886 and 1887 by Rowland exhibited both single and double
reversals. Hale's plates taken in 1891 demonstrated that
the reversals are not confined to the vicinity of sunspots,

3
but are instead found "in regions irregularly distributed
over the entire disk of the sun" (St. John, 1910, p. 37).
Hale's plates showed the double reversal of the H and K
lines reported by Rowland: a broad absorption feature
(which Hale termed HI or Kl) upon which is superposed an
emission line (H2 or K2) with a narrow absorption line (H3
or K3) at its center.
Emission reversals at the centers of absorption lines
of stellar spectra were first observed in 1900 by Eberhard
and Ludendorff, who detected an emission core in the Ca II K
line on a "very strongly overexposed" (Eberhard and
SchwarzschiId, 1913, p. 292) spectrum of Arcturus. Engaging
in further investigation of the phenomenon, Schwarzschild
recorded H and K emission reversals on spectral plates of
Arcturus, Aldebaran, and sigma Geminorum in 1913. By
comparison of the strength of the stellar emission to that
of the average spectrum of the sun, Eberhard and
Schwarzschild concluded that "the emission is much stronger
in these stars than in the sun" (Eberhard and Schwarzschild,
1913, p. 294). They stated further that "reversals of lines
in stellar spectra are not rare" (Eberhard and Schwarz¬
schild, 1913, p. 294).
By 1929 a veritable multitude of other stars, such as
Capella and epsilon Pegasi, had been discovered to exhibit H
and K emission superposed on absorption. Others, such as
Arcturus, Antares, and Betelgeuse, were discovered to have a
complex double reversal of the H and K lines similar to that

4
found in the sun (Adams and Joy, 1929a,b). A correlation
between emission strength and absolute magnitude was
discovered by Deslandres and Burson (1921, 1922), "the more
luminous giants having stronger emission lines" (Adams and
Joy, 1929b, p. 373).
Early Observations of AR Lacertae
Early Photometry
AR Lacertae was discovered to be variable by Leavitt
(Leavitt, 1903; Pickering, 1907a; Sahade and Wood, 1978).
For the next twenty years, though, its variability seemed
questionable, being confirmed by some observers (Pickering,
1907b; Munch, 1909; Wendell, 1913) and denied by others
(Hoffmeister, 1919; Zinner, 1922).
By obtaining a visual light curve from analysis of his
observations made in 1927 and 1928 , Loreta (1929) first
recognized AR Lac as an Algol-type system with a period of
1^98. By his own observations and by analysis of Loreta's
(1929) and Wendell's (1913) observations, Jacchia (1929)
confirmed Loreta's analysis of AR Lac as an eclipsing
binary.
The first photographic light curve of AR Lac was
published in 1931 by Rugemer (1931). In the following year
Schneller and Plaut (1932) published a second light curve.
These three investigators calculated the apparent visual
magnitudes and the relative sizes and luminosities of the
components, the orbital inclination, and a more precise
value for the period of the system. Their data also

5
established that the cooler star eclipses the hotter one at
primary eclipse, which is total. In addition, the depths of
the minima at both eclipses were determined. Application of
their photometric results to the HD Catalogue spectral
classification (G5), which they suspected might be a
composite, allowed rough determinations of the spectral
classes of the components as either G5 and K5 or GO and KO
for the smaller and the larger stars, respectively
(Schneller and Plaut, 1932; Harper, 1933).
From his photometric observations Himpel (1936)
classified AR Lac's components as G5 and gK5, the luminosity
class of the cooler star having been determined from its
surface brightness. In the light curve he noted a bump
during totality (primary minimum).
The first photoelectric observations of AR Lac (Sahade
and Wood, 1978), made in 1938 and 1939 by Wood (1946),
enabled him to complete his solution of the orbit in 1941.
(Publication of his dissertation was delayed until 1946
because there was "a small war on then": Wood, 1983.)
He determined that between the time of earlier observations
by Dugan and Wright and the time of his own observations,
the period of the system had undergone an abrupt change,
thereby necessitating the calculation of new orbital
elements. From light-curve variations which occurred only
outside primary minimum, Wood (1946) inferred that the
brighter (G5) component is variable. Although it was later
discovered (Blanco and Catalano, 1970) that Wood's

6
comparison star, HD 209813 (HK Lac), is a variable, Wood's
observations were not invalidated, because he had compen¬
sated in his data reductions for what he termed "large night
errors" (Wood, 1946, p.13). His results are therefore quite
harmonious with more recent observations using nonvariable
comparison stars.
While attempting to measure the limb darkening coef¬
ficient of the K0 component of AR Lac, Kron serendipitously
discovered "small abrupt irregularities" (Kron, 1947, p.
264) in the light level during primary minimum ingress and
egress, thereby complementing Wood's (1946) observations of
anomalous photometric variations only outside primary
minimum. Kron interpreted his observations as Wood had
interpreted his: viz., that the primary star (G5 star) is
intrinsically variable. Kron also reported several
observations of strong asymmetry between minima. Comparison
of data from several epochs showed variability of the
asymmetry and variability of the skewness of secondary
minimum. Prominent ellipticity and reflection effects were
evident, as was a "very high degree" (Kron, 1947, p. 264) of
limb darkening for the K0 star.
Early Spectroscopy
Spectrograms obtained in 1932 by Harper revealed AR Lac
to be a double-line spectroscopic binary. He made an
attempt to classify the spectral types of the components
more precisely, but was not entirely successful because
clouds precluded his obtaining any plates at primary

7
minimum, when the spectrum of the cooler component alone
would have been visible. He did, however, publish the first
radial velocity curves for the system and was able to
establish the spectroscopic elements within "reasonable
agreement" (Harper, 1933, p. 148) with the previous
photometric elements determined by the three Germans. His
analysis determined that the masses of the components are
very nearly equal, the larger star (1.42M0) being only
O.O1M0 more massive than the smaller more luminous one. He
found the lines of the primary to be sharper than those of
the secondary. The three-to-one disparity in the relative
luminosities of these components of almost equal masses and
very similar spectral types (G5 and G2, respectively, by his
spectrograms) caused Harper to express some puzzlement.
The discovery of H and K emission reversals in AR Lac
was announced by Wyse (1934). He had detected sharp
emission cores in the broad H and K absorption lines in the
spectrum of the cooler component. He classified the spectra
of the components as G5 for the brighter and KO for the
fainter. The luminosity class of the primary (brighter) was
ascertained to probably be main sequence, whereas the
luminosity and the density of the secondary placed it
intermediately between the main sequence and the giants.
Joy and Wilson (1949) tabulated previously unpublished
data obtained by Sanford (1951), who had discovered in 1945
that Ca II emission is present not only in the AR Lac
secondary but also in its primary. They listed the

8
spectral-luminosity classifications of the components as
sgG5 and sgKO, the luminosity class of the primary
heretofore having not been explicitly specified except for
Wyse's (1934) tentative main-sequence classification.
New spectroscopic elements for AR Lac were published in
1951 by Sanford (1951), whose data indicated that the orbit
is circular. The spectra showed the absorption lines to be
very broad and shallow for such late-type stars, a
characteristic which he ascribed to the lines' being
appreciably broadened by synchronous rotation. Measurements
of the equivalent widths of the Ca II emission (H2 and K2)
and the underlying absorption (HI and Kl) for each component
showed the emission contributions from both stars to be
variable with phase. Additionally, the ratio of the
primary's to the secondary's emission increased from phase
0.0 to 0.5 and decreased from phase 0.5 to 1.0. Radial
velocities computed from the emission lines were 6.4 km/sec
less than those from the absorption lines. Assuming that the
breadth of the
Ca
II emission
indicates
that it
emanates
from all parts
of
the stellar
surfaces
or from
complete
equatorial zones, Sanford calculated the radii of the
components to be about 85% of the value determined by Wood,
who had included a large coefficient of limb darkening.
Sanford's measurements indicated the masses to be 1.3 M0 and
1.31 M0 for the primary and the secondary, respectively.

9
Using spectra obtained in 1954, Roman (1956) noted the
presence of H and K emission and classified the spectrum of
AR Lac as
K2 III
at
primary
eclipse and K2
III
+ F8 at
secondary
eclipse,
her
results
confirming yet
again
that no
two observers obtain exactly the same results for AR Lac.
Correlation of Photometry and Spectroscopy
From the photometric elements of AR Lac and Sanford's
(1951) spectroscopic data, Eggen (1955) derived the absolute
visual magnitudes, the masses, and the radii of the
components.
While analyzing several systems with light-curve
variations not explainable by tidal effects, the reflection
effect, or eclipse, Kron (1952) noted a rotational
periodicity of these photometric variations in AR Lac, RT
And, RS CVn, and YY Gem. He further observed that all four
systems exhibit emission lines. In YY Gem, changes in the
Ca II emission strength were observed to show a pattern of
amplitude and period behavior similar to that of the
light-curve variations.
Early Polarimetry
Seeking to measure the polarization of the H and K
emission in AR Lac, Struve (1948) obtained null results; but
he was able to establish an upper polarization limit of 10%
for the system.
The "AR Lac Group" and Other Stars with Ca II Emission
In his study of spectra of eclipsing binaries, some
displaying Ca II emission, Wyse noted an "unexpected

10
tendency" (Wyse, 1934, p. 41) for late-type secondaries to
exhibit hydrogen emission.
Swings and Struve (1941) and Struve (1945) investigated
stars which exhibit late-type absorption features combined
with bright lines of high excitation. Struve (1945)
observed that "in single stars emission lines are rare for
these types [A through K] " (Struve, 1945, p. 79); whereas
"binaries of types G and K very often exhibit bright lines
of Ca II, and the number of these cases is also considerably
in excess of what might have been expected from the
frequency of occurrence of these lines in single stars"
(Struve, 1945, p. 79).
Upon surveying emission-line stars again, Struve (1946)
recognized a fledgling group of binaries characterized
primarily by bright lines of Ca II. Additional identifying
features of this grouping were (1) spectral type usually
later than F5, (2) resemblance of the emission lines to
those of normal single K-type dwarfs, (3) usually single or
slightly broadened lines, which are (4) superposed on deep,
broad Ca II absorption, and are (5) usually visible
throughout the cycle, but in some systems are strengthened
at primary minimum or weakened at secondary minimum.
A list of 445 stars and star systems known to exhibit
Ca II emission, published by Joy and Wilson (1949), verified
Eberhard and SchwarzschiId 1s (1913) . suspicion that H and
K emission is not a rare phenomenon in stars. Joy and
Wilson's comparison of intensity levels at various parts of

11
each spectrum showed that although the emission is usually
much weaker than the local continuum, the broad H and K
absorption is so strong that it provides a low-intensity
background against which the faint emission is easily
observed. Visual comparison of emission in stars of the
same spectral-luminosity type produced no correlation
between emission strength and any other physical
characteristics. At the dispersions used they noted no H3
or K3 in subgiants or dwarfs. In the sun, giants, and
supergiants, they observed the red component of the emission
(the red component of H2 and K2) to be more intense than the
violet. Further, they stated that the emission intensity is
probably variable in many stars.
A new decade dawned with Gratton's review of
characteristics of stars which exhibit Ca II emission. He
opened his discussion by stating that for late-G or early-K
binaries "these emission lines are much stronger than those
observed in single late-type stars such as alpha Boo
[spectral class K2 (Abell, 1964)], being real emission lines
rather than a reversal of the absorption lines" (Gratton,
1950, p. 31). [However, the author can find no previous
statement of this assertion, or any reports of observations
substantiating this statement, not even in the very
references from which Gratton purportedly obtained this
information. Perhaps he misread or misunderstood Struve's
(1945) statement regarding the frequency of occurrence of
the emission, not the strength of the emission.] Gratton

12
discovered a period-luminosity relation for binaries with
Ca II emission.
Tables of quantities for 426 stars whose spectra
exhibit H and K emission lines were published in 1954 by
Bidelman, who repeated Gratton's (1950) assertion, though
not quite so positively: "The Ca II emission lines are
probably stronger in binaries than in single stars"
(Bidelman, 1954, p. 178). [Perhaps his compendium of
references would offer supporting evidence; however Gratton
(1950 ) is among them . . .] Bidelman also noted from his
survey the likelihood that all late-type giants exhibit
some, "usually self-reversed" (Bidelman, 1954, p. 178), Ca II
emission and that there exist some "surprising variations
in intensity" (Bidelman, 1954, p. 178) among stars of the
same spectral class.
Spectrograms of the Fraunhofer lines obtained by McMath
et al. revealed that in the solar H and K lines (1) the line
intensity was similar between the disc and the chromospheric
bulge, and (2) the line cores were observed to "merge
smoothly with the chromospheric emission bulge" (McMath et
al., 1956, p. 7) as the limb was approached. In addition,
asymmetry of the emission profile persisted to the limb; and
the K emission was enhanced over plages.
Measurements of the H and K emission lines in the sun
by Wilson and Bappu (1957) showed them to be of nearly equal
width and of intensity ratio 1:2. Stellar evidence, though
not conclusive, seemed to indicate a similar picture.

13
Enlarging upon the work of Adams and Joy ( 1929a,b), Wilson
and Bappu discovered a relationship between emission-line
width and absolute magnitude. In G, K, and M stars the
K-line emission width varies as the one-sixth power of the
absolute luminosity, the emission-line width being
independent of spectral class and emission-line intensity.
This relationship has become known as the Wilson-Bappu
effect.
While investigating single stars, visual binaries, and
galactic clusters with H and K emission, Wilson (1963)
observed that the spectroscopic binary component in each of
two visual binaries (ADS 2644 and ADS 8119) exhibits a
preponderance of Ca II emission compared to its single
visual companion. In addition, he noted that in the sun a
strong correlation exists between the local chromospheric
magnetic field and the intensity of the Ca II emission, a
condition which he inferred could obtain in other stars
also.
At Lick Observatory, spectroscopy by Preston and
simultaneous UBV photometry by Kilston showed that the
Cepheid-like variable BL Her exhibited "well-marked emission
lines of hydrogen and Ca II for about 2h during rising
light" (Lick, 1966, p. 779 ) and that "the emission and the
atmospheric velocity reversal occur during a still-stand on
the light curve" (Lick, 1966, p. 779).
Oliver (1971, 1974) tendered the suggestion that AR Lac
and similar systems belong to a group characterized by (1)

14
Ca II emission, (2) a KO subgiant secondary which does not
fill its Roche limiting surface, (3) a mass ratio near 1.0,
and (4) light-curve variations which are attributable to the
cooler component. He proposed that this group be designated
the RS Canum Venaticorum binary systems. In his
investigations he discovered that several members of the
group exhibit (1) asymmetries in their light-curve minima
and shoulders and (2) a photometric "quasi-sinusoidal
distortion wave" (Oliver, 1974, p. 252), comprising nearly
sinusoidal extra-eclipse variations which migrate epoch by
epoch toward earlier phase.
The discovery of "significant variations" (Weiler,
1975, p. 1) in the H and K emi ss ion-1 ine intensities of
several RS CVn systems was announced by Weiler (1975,
1978). For three of the systems (UX Ari, RS CVn, Z Her) he
further determined that the maximum of emission intensity
and the minimum of the photometric distortion wave coincide
in orbital phase. In AR Lac he found the emission
variations to be basically random.
In an extensive review of the observational properties
of the RS CVn binary systems (and other related systems),
Hall (1976) proposed a working definition [reminiscent
of Oliver, 1971, 1974] composed of those observational
characteristics exhibited by all twenty-four systems so far
identified as belonging to the group. [For a list of these
characteristics as they apply to AR Lac, see Table 1.]
Members of one of the related groups of stars exhibit flare

15
activity, which Hall proposed may occur in RS CVn stars
also, but go unobserved because of their greater intrinsic
luminosities.
Late in the following year, Young and Koniges (1977)
published the results of their study of the Ca II emission
and other spectral characteristics of late-type binaries [AR
Lac was not included]. They found that systems with periods
near 20 days typically have the strongest Ca II emission.
Popper's evidence (1977) had shown that the emission is
strongest when one of the components is evolved. Young and
Koniges determined that both the strength of chromospheric
emission and the strength of tidal coupling are directly
related to the ratio of the radius of the star to its Roche
lobe. As for other spectral characteristics, their
spectrograms showed no emission in the Na D lines and no
strong Li I (6708 A) line for any of the systems. [The
latter characteristic is of interest because it is
apparently an age discriminator. See Section V.]
Complementing the findings of Young and Koniges, Naftilan
and Drake (1977) observed no evidence of Li 6708 in AR Lac
either.
Further Observations of AR Lacertae
System Elements
In attempts to improve mass determinations in binary
systems Popper (1967) acknowledged AR Lac as being the only
subgiant system with well-determined masses, which he
calculated as 1.32 ± 0.06MQ and 1.31 ± 0.07 M@ for the

16
primary and the secondary, respectively. He quoted the
radii as 1.8 R@ and 3.0 R0, respectively, adding that they
are less well-determined than those of the components of
other systems.
V - R photometry of AR Lac (and other binaries) by Lacy
(1979) allowed a new determination of its mass, radius,
absolute magnitude, and distance. He determined that the
primary of the system is underluminous compared to his
theoretical zero-age main sequence.
Spectroscopy and Photometry
Three-color photometry of AR Lac in 1972, 1973, and
1974 by Chambliss (1976) produced a new set of photometric
elements, from which the effective temperatures of the
primary and the secondary were calculated to be compatible
with spectral-luminosity classes G2 IV and K0 IV,
respectively. In the light curve Chambliss observed an
0.04-mag intrinsic photometric variation (Chambliss,
1975a,b; 1976) which shifted in phase from season to season
(Chambliss, 1976), behavior which constituted a photometric
distortion wave (Chambliss, 1975b; Hall, Richardson, and
Chambliss, 1976). The wave was later discovered to be
varying in amplitude (0.04-0.1 mag) and migrating toward
decreasing orbital phase (Hall, Richardson, and Chambliss,
1976). Chambliss' (1976) data also indicated that the
coefficient of limb darkening is low for the primary and
high for the secondary. Attempts to correlate optical
variability with radio outbursts yielded null results.

17
Babaev (1974a,b,c,d; 1975a,b; 1976) published seven
papers dealing with spectroscopy and photometry of AR Lac.
From his radial velocity curves he derived revised
spectroscopic elements. His profiles for the H and K lines
exhibited changes in the emission reversals during ingress,
egress, and eclipse. Measurements of the equivalent widths
of the H and K lines showed variation throughout the orbital
cycle and a pronounced absorption maximum at phase 0.6489.
His three-color light curves exhibited irregularities within
as well as outside of eclipse.
Supplementing Babaev's work, Weiler (1975, 1978)
further investigated AR Lac's migrating photometric
distortion wave and its emission-line intensity variation
with phase. He could discern no correlation between the two
phenomena, and his observations showed "basically random"
(Weiler, 1978, p. 77) emission intensity variation.
Hall, Richardson, and Chambliss (1976) discovered by
reviewing data obtained by previous observers that the
photometric distortion wave of AR Lac migrates toward
decreasing orbital phase and that the migration rate is not
constant, but instead has varied smoothly from one cycle
every 50 or 60 years to one cycle every 10 or 15 years. The
grand climax of their work was the discovery of a
relationship which could be used to predict the epochs of
future period changes in AR Lac. Graphs of (1) orbital
phase of the migrating photometric distortion wave minimum
versus epoch and of (2) orbital phase of the photometric

18
distortion wave minimum at which period changes have
occurred versus epoch appeared to coincide. Period
decreases occurred
when the
wave minimum was at phase 0.
25;
increases, at
0.75.
Moderate
metal
underabundances
in both components of
AR
Lac were measured
by Miner
(1966) ,
who reported that
all
eclipsing binaries
so far
measured
had been found to
be
metal poor.
Naftilan
and
Drake
( 1977 )
determined that
the
displacements
of the emission cores
from the centers of
the
Balmer lines
of
the AR
Lac secondary component
are
symmetrical about the absorption-line centers. Rapid
changes in the emission profiles over very short time
intervals were also observed. Their spectra showed further
that the emission-1ine broadening for both stars is
consistent with that of synchronous rotation, and that for
all the stronger emission lines the emission of the
secondary is much stronger than that of the primary. The
secondary was found to be moderately metal-deficient;
whereas the primary was found to have normal solar
abundances, Miner (1966) notwithstanding. In addition, the
microturbulence velocity for the secondary was found to be
anomalously high for a subgiant, being more in keeping with
values usually observed in supergiants,
primary was relatively high also.
That for the

19
Radio Measurements
Hjellming and Blankenship (1973) announced their
discovery of variable radio emission from AR Lac at 2695 MHz
and 8085 MHz.
Further radio observations of AR Lac by Owen and
Spangler established an upper angular limit of about 1" on
the size of the radio emitting region and a lower volume
limit of "much larger than the stars in the system" (Owen
and Spangler, 1977, p. L43), the latter being determined by
the failure of a clearly defined eclipse to appear in the
radio emission. Their data exhibited no evidence of the
previously deduced circular polarization of the radio
emission.
In 1978 Feldman (1978) reported the observation of a
large radio flare in AR Lac.
Polarimetry and Other Measurements
Measurements of V- and R-band polarization in binary
systems by Pfeiffer and Koch (1977) indicated that AR Lac
displays polarization which is constant and no different
from that of the interstellar medium. No results were
available for tests to determine (1) the shape of AR Lac's
polarization spectrum compared to that of the interstellar
medium or (2) the variability of AR Lac's electric vector
with wavelength.
An infrared excess was measured for AR Lac by Atkins
and Hall (1972), and an ultraviolet excess which increases
with decreasing wavelength below 4600 A was discovered by
Rhombs and Fix (1977).

20
Continuing to demonstrate that it is no ordinary
system, AR Lac apparently underwent further period changes
in 1975 as evinced by observations of minima from 1973-1976
by Scarfe and Barlow (1978)
and in 1977
by
observations of
minima from 1960-1982
by
Nha et al.
(1982) .
[Neither
observation is included
in
Table 4 or
in
Figure
4.] Soft
x-rays were detected
emanating from
AR
Lac
by Walter
(1978). Observations by Nha and Kang (1982) indicated that
the K0 star may exhibit long-term light variations. The
amplitude of AR Lac's migrating photometric distortion wave
increased to 0.1 between 1978 and 1979 (Hall, 1980). During
this period of time the wave also migrated extremely
quickly, changing position by 0.4 phase units (Hall, 1980).
The minimum of the photometric distortion wave was at about
phase 0.9 in 1979, and the amplitude of the distortion wave
was very low—less than 0.01 mag (Catón, 1981).
Summary
The presence of H and K emission occurs with great
frequency in late-type (G, K, and M) stars. It is
apparently observed in all types of binaries more frequently
than in single stars. In some close binaries the emission
is much stronger than in single stars, but whether this
holds as a general rule has not been verified.
In the sun the ratio of the strength of H to K emission
is 1:2, a condition which evidence suggests may exist in
other stars also. H3 and K3 are observed only in the sun,
giants, and supergiants. In these stars the red component

21
of H2 and K2 is more intense than the violet. A correlation
was reported between emission strength and absolute
magnitude, the more luminous giants having stronger emission
lines. This discovery has been superseded by the more
recent discovery of a more accurate relationship—that
between Ca II emission-line width and absolute magnitude in
G, K, and M stars. This relation is expressed by the
Wilson-Bappu effect: viz., that the K-line emission width
varies as the one-sixth power of the absolute luminosity.
The emission-line width is independent of both spectral type
and emission-line strength. There appears to be no
correlation between emission strength and any other physical
characteristics of stars of the same spectral-luminosity
class.
In many stars the emission intensity is variable
outside eclipse, and the emission undergoes eclipse as the
stars revolve. In some cases there is an enhancement of
emission at primary minimum and a diminution of emission at
secondary minimum.
Evidence indicates that the solar correlation between
chromospheric magnetic field strength, Ca II emission
intensity, and plages and sunspots may obtain in other stars
also. In binary systems there seem to be direct
relationships between the strength of chromospheric
emission, strength of tidal coupling, and the ratio of the
radius of the star to its Roche lobe, and between the
strength of chromospheric emission and the evolutional stage

22
of the star. Stronger emission correlates with a more
advanced evolutional stage.
Many of the binary systems which exhibit H and K
emission also exhibit asymmetry and irregular fluctuations
in their light curves.
Virtually all the eclipsing binaries for which
abundances have been measured exhibit metal deficiencies.
AR Lacertae is a typical RS Canum Venaticorum binary
star system. In excess of 25 such systems have been
discovered; all but three are eclipsing binaries. Table 1
lists the characteristics of RS CVn systems in general and
of AR Lac in particular. Table 2 lists the currently known
RS CVn systems and some of their vital statistics.

23
Table 1
GENERAL CHARACTERISTICS OF RS CVn BINARY STAR SYSTEMS
AND PARTICULAR CHARACTERISTICS OF AR Lac
RS CVn systems form a class of spectroscopic
which are distinguished by three characteristics
1974; Hall, 1976):
The orbital period is between 1^ and 14^.
The hotter component is of spectral class F or G
and of luminosity class IV or V.
Spectra at phases outside eclipse exhibit strong
Ca II H and K emission. ("Strong" is defined to
mean stronger than the normal H and K emission
reversals in late-type single stars of the same
spectral class. )
Lac fulfills these three defining criteria for
membership in the RS CVn classification:
(1) It has an orbital period of 1^983 (Loreta, 1929).
(2) The spectral-luminosity class of its hotter
component is G2 IV (Chambliss, 1974).
(3) The system exhibits strong H and K emission at
phases outside eclipse (Wyse, 1934; Sanford,
1951).
There are a number of other characteristics which AR
Lac has in common with varying numbers of the other RS CVn
systems (Hall, 1976). Spectral characteristics shared with
many of the other systems are:
(1) The system is a double-line spectroscopic
eclipsing binary (Harper, 1933).
(2) The H and K emission is from the cooler' star or
from both stars. The latter is the case for AR
Lac (Sanford, 1951).
(3) The spectral-luminosity class of the cooler
component is close to KO IV. The secondary of AR
Lac is classified KO IV (Wyse, 1934).
(4) The system exhibits H-alpha emission outside
eclipse (Weiler, 1975, 1978).
(5) The system exhibits an infrared excess in one or
both components. It is observed in both
components of AR Lac (Atkins and Hall, 1972).
(6) The system exhibits an ultraviolet excess. In the
ultraviolet AR Lac is too bright by an amount
which increases with decreasing wavelength below
4600 A (Rhombs and Fix, 1977).
(7) The system exhibits radio emission (Hjellming and
Blankenship, 1973).
Photometric characteristics which AR Lac has in common
with one-third to one-half of the other RS CVn systems are:
(1) The light curve of the system exhibits an
extra-eclipse quasi-sinusoidal wave-like
distortion (Chambliss, 1975b) which migrates
toward decreasing phase (Chambliss, Hall, and
Richardson, 1975).
The
binaries
(Oliver,
(1 )
(2)
(3)
AR

24
Table 1 - continued
(2) The depth of primary minimum is variable. This is
a natural consequence of the distortion wave
(Hall, 1976).
(3) The displacement of secondary minimum (asymmetry)
is variable. This is a natural consequence of the
distortion wave (Hall, 1976).
(a) no asymmetry observed (Taylor, 1941)
(b) strong asymmetry (Wood, 1946)
(c) variable asymmetry (Kron, 1947; Hall, 1976 ;
Theokas, 1977).
(4) The light curve exhibits irregular variations
(Wood, 1946; Kron, 1947; Babaev, 1971; Chambliss,
1975b; Hall, Richardson, and Chambliss, 1976;
Hall, 1976).
Physical characteristics which AR Lac has in common
with one-third to one-half of the other RS CVn systems are
(Oliver, 1974; Hall, 1976):
(1) The mass ratio of the components of the system is
near unity. For AR Lac it has been computed
between 0.987 and 1.008 (Harper, 1933; Sanford,
1951; Wood, 1946; Kopal, 1958; Popper, 1967;
Oliver, 1974; Babaev, 1975; Popper, 1976;
Chambliss, 1976; Hall, 1976; Popper and Ulrich,
1977; Weiler, 1978).
(2) The system is detached; that is, neither component
fills its Roche lobe (Wood, 1950; Kopal, 1958;
Plavec and Grygar, 1965; Oliver, 1974; Chambliss,
1976; Morgan and Eggleton, 1979)
Orbital characteristics which AR Lac and a few of the
other RS CVn have in common are:
(1) The system has a varying orbital period. Between
1932 and 1982 AR Lac appears to have undergone
several abrupt period changes, one almost as much
as 3s (Wood, 1946; Chambliss, 1976), another of
about 20m (Nha et al., 1982).
(2) Period changes are correlated with the migration
of the photometric distortion wave. For AR Lac,
period increases have occurred at epochs when the
orbital phase of the minimum of the distortion
wave was 0.75; decreases, when it was 0.25
(Chambliss, Hall, and Richardson, 1975).
Other observed characteristics of AR Lac are:
1. Photometric Characteristics:
(a) magnitudes (Chambliss, 1976):
(1) apparent magnitudes:
my primary = 6.75
my secondary = 6.41
my system max = 6.09
(2) absolute magnitudes:
My primary = 4.01
My secondary = 3.64
My system = 3.06

25
Table 1 - continued
(b) coefficient of limb darkening:
(1) 0.8 from spectral classes (Wood, 1946)
(2) secondary has very high value (Kron, 1947)
(3) 0.7-0.8 for primary: from Wood's (1946)
data (Kopal and Shapley, 1952)
(4) secondary high: 1.0 in U; primary low: 0.6
in U (Chambliss, 1976)
(c) secondary more uniformly bright than primary
(Wood, 1946; Chambliss, 1976)
(d) nearly central total primary eclipse, annular
secondary eclipse (Schneller and Plaut, 1932)
(e) duration of totality = 2h10m ± 15m (Hall, Rich¬
ardson, and Chambliss, 1976)
(f) variable skewness of secondary minimum (Kron,
1947 )
(g) ellipticity and reflectivity effects prominent
(Kron, 1947)
(h) depressions preceding first contact and following
fourth contact of primary eclipse:
(1) observed (Kron, 1947)
(2) 0.05 mag (Catalano, 1973, 1975)
(3) flanking primary eclipse (Naftilan and Drake,
1977 )
(i) variable amplitude of the quasi-sinusoidal
wave-like distortion:
(1) variable throughout cycle, peak at phase
0.6293 in V,B (Babaev, 1974d)
(2) probably variable, ranging from 0.04 mag to
0.1 mag in blue (Hall, Richardson, and
Chambliss, 1976)
(3) large 0.1-mag amplitude in 1978-1979 after
decades of erratic fluctuations (Hall, 1980)
(4) very low amplitude in 1979 (less than 0.01
mag) (Catón, 1981)
(j) smoothly varying rate of migration of the quasi-
sinusoidal wave-like distortion:
(1) varied smoothly from 1 cycle/50-60 yrs to 1
cycle/10-15 yrs during a 40-yr time period
(Hall, Richardson, and Chambliss, 1976)
(2) rate increased to- 0.4 phase units during
1978-1979 (Hall, 1980)
(3) phase of distortion wave approximately 0.9 in
1979 (Catón, 1981)
(k) smoothly decreasing period of migration of the
photometric distortion wave from 1900-1980 = 45-15
yrs (Chambliss, Hall, and Richardson, 1975)
Spectroscopic Characteristics:
a. General
(1)the lines of the primary are sharper than
those of the secondary (Harper, 1933;
Sanford, 1951; Struve, 1952; Naftilan and
Drake, 1977)
2.

26
Table 1 - continued
(2) absorption lines of primary deeper than those
of secondary except from phase 0^289-0^637
(Sanford, 1951)
(3) absorption lines of primary strongest when
primary receding fastest, weakest when
primary approaching fastest (Sanford, 1951)
(4) flat shallow absorption profiles of the
secondary (observed in the lines of Ce)
characterize the intervals preceding and
following primary minimum (Sanford, 1951)
(5) variable changes in line profiles on the
ascending and descending branches of the
radial velocity curve of the secondary
(Struve, 1952)
(6) on the ascending branch of the secondary's
radial velocity curve its strong absorption
lines (such as Fe I 4045) are strikingly
narrow (Struve, 1952)
(7) when the secondary's lines are narrow, it is
conspicuous only in the stronger lines (like
Fe I 4045), even for lines in the same
multiplet (Struve, 1952)
(8) when the secondary's absorption lines are
narrow, the corresponding emission lines
remain broad (Struve, 1952)
(9) Na I D lines of the secondary show the same
structure as other strong lines in the blue;
their overall strength is normal for stars of
this spectral class, rotation accounted for
(Naftilan and Drake, 1977)
(10) equivalent width of Ca II lines variable
throughout cycle, pronounced Ca II absorption
maximum at phase 0.6489 (Babaev, 1974c)
(11) the absorption lines of the Ca II triplet in
the infrared are weak (Hiltner, 1947)
(12) no evidence of Li I 6708 (Naftilan and Drake,
1977; Young and Koniges, 1977)
(13) metal abundances:
(a) both components underabundant (Miner,
1966 )
(b) primary has solar abundances, secondary
moderately underabundant (Naftilan and
Drake, 1977; Young and Koniges, 1977)
(14) polarization:
(a) none detected (Struve, 1948)
(b) no evidence for circular polarization at
radio wavelengths (Owen and Spangler,
1977 )
(c) polarization in V band constant, same as
that of interstellar medium (Pfeiffer
and Koch, 1977)

27
Table 1 - continued
(15) no spectral evidence for a third body ever
found (Hall, Richardson, and Chambliss, 1976)
b. Emission
(1) all emission lines of the secondary are much
stronger than those of the primary:
(a)
ratio of 5:1
for the Ca II
emission
•Lines (Joy and
Wilson
, 1949)
(b)
holds for all
lines
examined
(Naftilan
and Drake, 1977
’)
the
Ca II emission
lines
are presei
nt within
as
well as outside e
id ipse
:
(a)
observed from
his own plates
(Sanford,
1951 )
(b)
from Wyse's 193
;4 plates: H and
K bright
at primary mil
nimum
totality
(Sanford,
1951 )
the
radial velocity
of the H and K
emission
is
6.4 km/sec less
than the radial
velocity
of
all absorption
1 ines
in each
component
(Sa
nford, 1951)
the
equivalent width
i of the Ca II em
ission is
var
iable with phase:
(a)
the ratio of
the
primary's
to the
secondary's emission increases from
phase 0.0-0.5 and decreases from 0.5-1.0
(Sanford, 1951)
(b) variability observed on Wyse's plates
(Kron, 1952)
(c) basically random, no correlation with
phase (Weiler, 1975, 1978)
(5) possible short-term variation of Ca II
emission intensity:
weak self-reversal of K line not seen on
all plates; sharp red-displaced
absorption seen on one plate; plates
from phases 0.983 - 0.003 (Naftilan and
Drake, 1977)
(6) no Na I D-line emission has been detected
(Young and Koniges, 1977)
(7) emission features in hydrogen lines:
(a) H-alpha: during primary eclipse and at
phase 0.30 there are a possible central
emission feature and two weak emission
features on both sides of line center
and symmetric about line center in and
out of eclipse (Naftilan and Drake,
1977); line intensity variable (Weiler,
1975, 1978)
(b) H-beta: emission during totality
(Naftilan, 1975)
(c) H-gamma and H-delta: during primary
eclipse two emission features on each

28
Table 1 - continued
side of line center (Naftilan and Drake,
1977 )
(8) Fe I emission is variable with phase: it is
weaker from phase 0.0-0.5 and stronger from
phase 0.5-1.0, has a minimum at phase 0.25
and a maximum at phase 0.76 (Sanford, 1951)
(9) soft x-rays detected (Walter, 1978)
(10)variable radio emission:
(a) observed (Hjellming and Blankenship,
1973 )
(b) variable on a scale of greater than a
few hours; during secondary eclipse
there was a small increase in flux
density; at phase 0.98 there was a
depression of about 25% superposed on a
longer-time-scale rise (Owen and
Spangler, 1977)
(c) radio flare (Feldman, 1978)
3. Correlation of Optical and Radio Behavior
(a) no correlation of optical variations and radio
outbursts (Chambliss, 1976)
(b) no strong eclipse-like radio feature occurred
during optical eclipses (Owen and Spangler, 1977)
4. Physical Characteristics
(a) radii (Chambliss, 1976):
(1) Rprimary = 1*54 R0
(2) Rsecondary = 2.81 R0
(b) masses (Popper, 1967):
(1) ^primary = 1*22 ± 0.06 M0
(2) ^secondary = 1*31 ± 0.07 M0
(c) system is detached (Kopal, 1958)
(d) temperatures:
(1) 5600K for G2 IV, 4700K for K0 IV (Chambliss,
1976 )
(2) very nearly the same for U, B, V
light curves (Chambliss, 1976)
(e) microturbulence velocity:
secondary has an anomalously high value for a
subgiant (10 km/s); primary is not far behind (8
km/s) (Naftilan and Drake, 1977).
5. Orbital Characteristics
(a) i = 86° (Rugemer, 1931; Schneller and Plaut, 1932)
(b) P = 1^983 (Rugemer, 1931; Schneller and Plaut,
1932 )
(c) a = 8.92 R0 = 0.0429 AU (Chambliss, 1976)
(d) d = 40 pc (Chambliss, 1976)
(e) e = 0 (Sanford, 1951; Chambliss, 1976)

29
Table 2
RS CVn BINARY STAR SYSTEMS
Orbital
Distortion
Name3
V a
vmax
Period3
Spectral Type3
H and K Wave
(mag)
(days)
(hot + cool)
Emission*3,*' Amplitude3
(mag)
UX
Ar i
6.5
6.438
G5
V + K0
IV
Sd
0.03-0.10
CO
Aur
9.0
10.621
GO
+ ?
P(S?e)
0.06-0.12
SS
Boo
10.3
7.606
G5
V + G8
V
S
0.05-0.19
SS
Cam
10.0
4.824
F5
V + G1
V
s
0.11
AD
Cap
9.8
6.118
G5
+ G5
P+S
??
RU
Cnc
10.1
10.173
F9
V + G9
V
S
0.02-0.09
UX
Com
10.0
3.642
G5-
-9
se
0.10
RS
CVn
8.4
4.498
F 4
V-IV +
K0 IV
s
0.05-0.20
RT
CrB
10.2
5.117
GO
sd
0.04
ww
Dr a
8.8
4.630
G2
IV + K0
IV
s
0.06
z
Her
7.3
3.993
F4
V-IV +
K0 IV
s
0.03
AW
Her
9.7
8.801
G2
IV + K2
IV
s
??
MM
Her
9.5
7.960
G8
IV
s
0.06-0.12
PW
Her
9.9
2.881
GO
s
0.12
GK
Hya
9.4
3.587
G4
Sd
?
AR
Lac
6.9
1.983
G2
IV + K0
IV
P+S
0.04
RT
Lac
9.0
5.074
G9
IV + K1
IV
P+S
0.01-0.17
RV
Lib
9.0
10.722
G5
+ K5
P+Se
0.06
W
Mon
9.4
6.051
GO
s
0.01-0.09
LX
Per
8.1
8.038
GO
V + K0
IV
s
0.01-0.05
SZ
Psc
7.3
3.966
F8
V + Kl
V-IV
s
0.02-0.15
TY
Pyx
6.9
3.199
G5
+ G5
P+S
0.04
V711 Tau
5.9
2.8
G5
p+s9
0.07-0.21
RW
UMa
10.2
7.328
F9
V + K1
IV
s
0.11
RS
UMi
10.1
6.2
F8
se
??
HR
5110
5.0
2.613
F 2
IV + K
IV
sc
0.00
HD
5303
7.8
1.840
G2
V + F0
ph
0.3
HD
175742
8.41
2.879
K0
V + K5
V-M 2 V
?f
0.079
HD
178450
8.13
2.185
G6
V
?f
0.033
HD
224085
7.6
6.724
K2-
-3 IV-V
?f
??
? Detected, but not yet measured
?? Unknown
a Hall (1981), except where otherwise indicated
b Oliver (1974), except where otherwise indicated
c Conti (1967)
d Hall (1976)
e Popper (1976)
f Joy and Wilson (1949)
g Weiler (1976)
h Hearnshaw and Oliver (1977)
i Henry (1981a)
j Henry (1981b)
k P = emission in hotter star (primary);
S = emission in cooler star (secondary);
P+S = emission in both components

SECTION II
INSTRUMENTATION AND OBSERVATIONS
Instrumentation
Telescope
The telescope which was used in this investigation is
the Tinsley Newtonian-Cassegrain 76-cm instrument at
Rosemary Hill Observatory. The telescope was operated in
the f/16 Cassegrain mode. (See Wheeler, 1973, for the
equations used to calculate the parameters cited below.)
Spectrograph
The spectrograph which was used is a Boiler and Chivens
Model 26767 f/13.5 Cassegrain spectrograph equipped with a
corrector lens for the conversion of the incoming telescope
beam from f/16 to f/13.5, thereby providing a reciprocal
scale of 20"/nun in the slit plane. The focal ratio of the
spectrograph camera is f/3. The aluminized glass slit plate
has fixed slit widths of 28, 40, 56, 80, 112, and 160
microns. The 56-micron slit corresponds to an angular image
size of 1" at the slit plane. The decker plate has fixed
slit lengths (deckers) of 1.5, 3, 6, 13, and 25 mm. Two
holes of 0.5 and 0.75 mm were drilled into the decker plate
to be used as shorter slit lengths to allow shorter exposure
times.
30

31
The spectrograph is equipped with a variable-focus
collimator and an adjustable grating tilt. (The
spectrograph is worked at negative grating angles.) There
are two interchangeable 64mm X 64mm gratings. Grating I,
ruled at 150 lines/mm, produces a linear reciprocal
dispersion of 128 A/mm at 3933 A in the third order.
Grating II, ruled at 300 lines/mm, produces a linear
reciprocal dispersion of 60 A/mm at 3933 A in the third
order. Both gratings are blazed at a wavelength of 1.25
microns, and the wavelength of maximum energy in the third
order is 3776 A. The resolution limit of grating I is 0.14
A, and that of grating II is 0.068 A, both at 3933 A in the
third order.
The comparison source
is
a helium-argon glow lamp.
Positions are provided
for
the
insertion of
filters into
the comparison source
beam
as
well as into
the incoming
stellar beam.
The manufacturer-supplied slit-viewing eyepiece was
inadequate for observation of stars fainter than sixth
magnitude. (The small aperture of the exit pupil allowed
only about two-thirds of the beam of starlight reflected
from the slit edges to emerge from the system.) This
eyepiece was replaced with an improved design (devised by
Hoffman and Oliver) featuring an enlarged exit pupil and
increased magnification (15X rather than the previous 10X)
so that the slits and the deckers could be viewed in greater
detail.

32
An image tube was used for some spectra in attempts to
(1) reduce exposure times and (2) obtain spectra of the
sodium D lines in the second-order yellow.
An exposure meter (designed by Oliver) which employed
an end-window S20 EMI 9558A photomultiplier tube was
constructed. Although excellent for bright stars or a dark
sky, the meter was unable to discriminate between a faint
star and a bright sky background, thereby grossly
undercounting the stellar photons and rendering erroneously
lengthy exposure times. It was abandoned in favor of
directly timed exposures until a more suitable tube could be
obtained. (See Section VI.)
Plates
The spectroscopic plates used were backed plates of
emulsion type Ila-O, which were cut to 2-in x 2-in squares
from larger plates and then hypersensitized (both done by
the author). The hypersensitization/storage procedure for
the plates (Smith, 1975) consisted of (1) evacuation of the
plate-filled thick-walled aluminum plate-storage box, (2)
back-filling with anhydrous hydrogen, (3) storage of the
plates in the hydrogen for 2^, (4) flushing with anhydrous
nitrogen and (5) subsequent refrigerated storage of the
plates in the nitrogen at greater than 1 atm of pressure.
In addition, the plate box was sealed within a deflated
zip-lock bag containing a canister of silica gel desiccant,
the addition of the desiccant being an innovation suggested
by the author.

33
The IIa-0 emulsion has a linear resolution limit of 16
microns. At the dispersion of grating I at 3933 A in the
third order, the wavelength resolution limit of this
emulsion is 2.3 A. The corresponding wavelength resolution
limit for this emulsion in combination with grating II is
1.2 A.
Sensitometer
The Florida-Smithsonian Plate Sensitometer was used to
record spots of standard emulsion density on a sample plate
from each hypersensitization batch. Designed in 1969 by
Smith (1977a), this instrument is a variable-illumination-
constant-exposure-time tube sensitometer, which produces an
intensity scale of graduated emulsion densities (Jones,
1931, 1934). In order to minimize errors due to reciprocity
failure, (1) the sensitometry spots were exposed for times
as close as possible to those of the stellar exposures, and
(2) the sensitometry plates were developed by the same
procedure as that for the stellar plates (Wright, 1962).
Densitometers
A Model 520-A Photovolt transmission densitometer was
used to measure the densities of the spots on the standard
sensitometry plates and the densities of the unexposed areas
on the stellar plates.
A Joyce, Loebl and Co. Ltd. Model MK III CS double-beam
recording (scanning) microdensitometer with a Honeywell
strip-chart recorder was used to obtain tracings of the
lines on the spectrograms and of the spots on the

34
sensitometry plates. The controlled adjustments on the
recording (scanning) microdensitometer are the gain settings
for the level of the sample light beam relative to the
standard reference light beam, the heights and widths of the
upper and lower
slits
, the
focusing
of the image of
the
lower slit
onto
the
plane
of the
upper slit, and
the
focusing of
the
image
of the plate
onto the plane of
the
upper slit. Inadequacies in the microdensitometer system
necessitated its modification by Oliver, Parise, and
Hoffman: (1) The non-functioning logarithmic amplifier was
eliminated from the circuitry, thereby converting the
strip-chart deflection readout from emulsion-density units
to units which are a function of emulsion-transmission.(2)
The scanning speed of the microdensitometer and the chart
speed of the chart recorder were reduced in order to achieve
greater spectral resolution on the chart and to minimize
distortion of the line profiles. No attempt was made to
determine the instrumental profile for the reason that broad
lines (like H, Cr, and Ca II H and K) are virtually free of
instrumental effects (Wright, 1962). (3) The vertical range
("transmission" scale) of the chart recorder was extended by
the incorporation of a zero-level-maximum-level
potentiometer, which enabled the entire width of the chart
paper to be used. This modification also effected
enhancement of the visibility of small changes in
transmission level.

35
Calculator
A Hewlett-Packard Model 9810A calculator was
programmed to perform a linear regression to determine the
functional relationship between "transmission" level and
intensity at each wavelength.
Observing Program
Between 1971 and 1978, 153 spectra of single stars,
stellar systems, and planets were obtained. This series of
spectrographic observations marked the inception of
astronomical spectroscopy at the University of Florida.
The spectra of single stars were used to establish
(1) a relationship between apparent visual
magnitude and exposure time as a function of
spectral type and varying sky conditions, and
(2) an atlas of spectra of MK standard stars
(Johnson and Morgan, 1953) for the purpose of
spectral classification.
The primary portion of the program consisted of the
observation of the RS Canum Venaticorum binary star systems.
In order to determine which of the RS CVn systems are
observable and analyzable with the available optical
systems, selection criteria were established according to
the capabilities of the telescope-spectrograph system, the
scanning microdensitometer system, and the stars themselves.
Two exposure requirements imposed by the telescope-
spectrograph system and the physical parameters of the

36
star systems provided the basis for selection of observable
stars:
(1) It was necessary to obtain the shortest possible
exposure time in order to achieve adequate time
resolution to allow observation of detailed
changes in the H and K emission as a function of
phase, particularly at the phases at or near the
relatively short (about 2^) eclipses.
(2) The spectra had to be overexposed in order to
reveal the emission reversal. This requirement
resulted in exposure times approximately
25% greater than those necessary to produce a
density of 0.6 in the local continuum. Additional
exposure time was needed to compensate for haze,
enlarged discs, and large air mass.
These constraints restricted the observations to
systems of average visual magnitude brighter than 7.5.
Imposing this condition narrowed to only six the field of RS
CVn systems which could feasibly be observed. The six
systems which fulfill the observational criteria are UX
Arietis, HR 1099 (V711 Tauri), TY Pyxidis, Z Herculis, RZ
Eridani, and AR Lacertae. (RS CVn itself, however, was
observed on a few occasions for purposes of comparison.)
Although TY Pyx is one of the brightest of the RS CVn
systems, its extremely large zenith angle (58°. minimum) at
this latitude (30° N) forced observation through a large air
mass, which rendered the necessary exposure time too long to

37
allow sufficient time resolution. Seasonal burning of
undergrowth by nearby landowners required an additional
increase in exposure time (if the star could be seen at
all). The weakness of the emission in TY Pyx further
compounded the problem to the extent that the system was
eliminated from the observing program.
RZ Eri was subsequently deleted from the membership of
the RS CVn group for failure to satisfy the period
requirement (1^-14^) established by Hall (1976).
The four remaining systems which satisfy the magnitude
requirements are the stars which were regularly observed in
the program.
An additional system, HR 5110, was observed because it
was suspected of being an RS CVn system. No strong H and K
emission was observed; therefore it was deleted from the
program. Hall et al. (1978), however, list it as an RS CVn
system.
The inability of the scanning microdensitometer to
analyze plates of poor quality dictated the remaining
criterion for selection among the plates of systems which
fulfill the observational criteria.
Of the 67 plates of RS CVn systems, 3 were made using
the image tube in conjunction with the spectrograph in
attempts to (1) enhance time resolution by reducing exposure
times and (2) record data on the sodium D lines in the
second order yellow. The image tube, however, was abandoned
because it yielded plates of very poor spectral resolution

38
and very high fog levels. These effects were encountered
primarily because of arcing between the plate and the face
of the image tube due to the extremely high humidity. The
problem persisted despite the installation of a heating ring
to dissipate moisture.
Of the remaining 64 plates of RS CVn stars, 51 were of
sufficient quality to be analyzed. The 13 which could not
be analyzed were rendered unusable for one or more of the
following reasons:
(1) high fog level produced by long exposure to high
humidity,
(2) lines too thin due to inadequate exposure time
because of haze, clouds, etc., and/or
(3) lines insufficiently widened by use of short
deckers in attempts to reduce exposure times
(short deckers rendered the spectra so narrow that
too little information was recorded for analysis
with the available equipment).
The usable plates of the stars fulfilling the
observation criteria tallied 11 for UX Ari, 10 for HR 1099,
4 for Z Her, and 19 for AR Lac. (See Section VI for plans
for analysis of the first three systems listed.) The other
7 usable plates were of RS CVn stars which did not fulfill
the observation criteria.
AR Lac was the system chosen for analysis because for
this system the amount of data obtained was greater than for
any of the others and because the need for additional data

39
analysis was greater than for all of the others. Also, the
spectrograms of the other three aforementioned systems did
not offer enough coverage of their entire cycles to allow
any definitive conclusion to be drawn regarding the behavior
of their Ca II emission. The 19 spectrograms of AR Lac span
the entire orbital cycle of the system, an achievement which
required more than one epoch of observation. AR Lac's
nearly integral period (1^983) produces a rate of phase
change of only 0.004 phase unit per day (placing the system
at approximately the same phase at the same time on
successive nights), a circumstance which necessitates an
extended program of observation to obtain spectra at all
phases.
All of the spectra of AR Lac were recorded on IIa-0
spectrographic plates at a linear reciprocal dispersion of
128 A/mm with grating I (150 lines/mm). A slit width of 80
microns was used because it (1) corresponds almost exactly
to the diameter of the usual seeing disc (about 1"5) at
Rosemary Hill Observatory and (2) provides the minimum
resolution required to observe the desired detail in the
spectra. The spectra were widened by trailing along a slit
length (decker) of 1.5 mm. Exposure times ranged from 40m
on clear nights of good seeing to 90m on hazy nights or
nights of poor seeing.

SECTION III
DATA REDUCTION
Procedure and Theory
The following procedure was used to obtain and reduce
the data. Any theory necessary to the data reduction has
been incorporated into the discussion.
There does exist a problem of disparate nomenclature
among the five disciplines—astrophysics, optics, spectro¬
scopy, photography, and photometry—which enter into this
investigation. Each field has its own definition for items
such as intensity and brightness, and a term widely used in
one field may be unacceptable in another. Clarifications
are parenthetically included where two conflicting
nomenclatural systems are simultaneously encountered. If,
however, the discussion is confined to a single discipline
or to non-conflicting disciplines, no alternative terms are
listed; but archaic terminology has been replaced, where
necessary, by the proper modern term in the parlance of that
field.
Plate-Tracing
Three tracings of each stellar spectrogram were
obtained using the recording (scanning) microdensitometer.
The plates were scanned from 3889 A to 4026 A. On each
spectrum scan, tracings of the sensitometry plates were
recorded across the full range of the chart paper at the
40

41
same gain setting, slit width, and slit height as was the
spectrogram tracing.
Minimum deflection on the chart paper, indicating
maximum emission intensity recorded by the emulsion at a
given wavelength (maximum flux density received at the earth
at a given wavelength), was scaled to correspond to an
emulsion transmission of zero by adjustment of the
chart-recorder zero-level potentiometer while the sample
beam was passed through the densest (blackest) part of the
continuum in the vicinity of the H and K lines. The densest
part of the local continuum at H and K was determined by
microscopic examination to be at 4026 A.
Maximum deflection on the chart paper, indicating
minimum emission intensity recorded by the emulsion at a
given wavelength (minimum flux density received at the earth
at that wavelength), was scaled to correspond to an emulsion
transmission of 100% by equalization of the sample- and
reference-beam levels and adjustment of the chart recorder
maximum-level potentiometer while the sample beam was passed
through the plate fog (the "clear" area on the plate).
It was determined experimentally that a slit width
setting of 30 is optimum for obtaining the maximum amount of
light possible while still preserving the resolution of
detail in the line tracing. The focus of the plate image
onto the upper slit is critical to resolution.
As was stated in Densitometers, Section II, the
instrumental profile was not measured, a step which would be

42
necessary in order to determine the true line profile. This
step was unnecessary not only for the (previously stated)
reason that there is virtually no distortion in broad lines
(Wright, 1962) but also for the reason that the calculation
of equivalent width circumvents the problem because
equivalent width is independent of instrumental profile
(Aller, 1951; Stromgren, 1951; Thackeray, 1961).
In order to reduce noise introduced by the recording
microdensitometer and the chart recorder, point-by-point
averages of the three tracings of each stellar spectrogram
and its accompanying sensitometry spots were graphically
computed. The chart paper which must be used on the chart
recorder has a grid size too large to render a faithful
reproduction of the precision attained by the tracing system
and the plates; therefore the averaged tracings were
transferred point-by-point to 0.1-inch chart paper for
greater precision of deflection-reading. The resulting
tracings displayed deflection (ordinate) as a function of
wavelength interval (abscissa).
In order to convert the wavelength intervals to
Angstroms the wavelength scale factor for the chart paper
was calculated (1.18 ± 0.06 A/div) and applied.
The recorded deflection at each point in a line tracing
is a measure of the emulsion transmission (T), where T is
defined as the ratio of the measured photographic intensity
at a given wavelength to a standard photographic intensity.
In this case the standard was chosen to be the continuum at

43
4026 A, so that T = I/IcONT’ The electronics of the
scanning microdensitometer, however, could not be calibrated
so that deflection would be a direct readout of either
emulsion transmission or emulsion density (D = log 1/T).
Further conversion was therefore required.
Conversion of Deflections to Relative Intensities
Because the relationship between deflection and
intensity was unknown, it was necessary to determine that
correspondence through the application of the characteristic
curve for the emulsion. The deflections were converted to
relative intensity units by the following procedure.
Density-deflection relations; D(d)
The transmission densitometer was used to measure the
densities of the sensitometry spots on each sensitometry
plate and the densities of the clear areas on the stellar
plates. The correspondence of each spot-density to its
measured deflection on the scanning microdensitometer
tracing for each stellar plate established a relationship
between density and deflection at the gain setting used for
each tracing. A graph of deflection (abscissa) versus
density (ordinate) was plotted for each stellar plate.
Because the transmission densitometer is designed to
measure diffuse density and the scanning microdensitometer
is designed to measure specular density, a question might
arise regarding the possibility of encountering errors due
to the procedure employed herein. A comparison of densities
measured by the two instruments might yield a difference as

44
great as 50%, which would be equivalently expressed as a
ratio of 2:1 by the Callier factor, the ratio of specular to
diffuse density (Neblette, 1970). In the present
calibration, however, there were no such comparisons made.
Instead, emulsion densities measured with the transmission
densitometer were correlated with the deflections measured
by the scanning microdensitometer in order to establish a
scale of relative densities for the spectra traced by the
latter instrument. This procedure was necessitated by the
lack of an available density calibration for the scanning
microdensitometer. Because this procedure did not involve a
comparison of densities measured by the two different
methods, there was no additional error other than the usual
amount incurred by reading data from a strip chart.
Through the use of sensitometry spots to calibrate a
stellar spectrum (Wright, 1962), an unknown, but probably
small, error was encountered.
Both of the errors cited above are included in the
discussion in the segment entitled Determination of Error in
the equivalent width of the K-line emission.
Characteristic curves (D-log E curves): D(log E) and D(E)
By use of the sensitometer correlation established by
Smith (1977b) between sensitometry spot number and logarithm
of relative exposure, a characteristic curve, D(log E), was
plotted for each stellar plate. Spot number, representing
the logarithm of relative exposure (abscissa), was plotted
versus density (ordinate) for each stellar plate. The

45
characteristic curves were transferred data-point-by-data-
point to semilog paper in order to facilitate the reading of
the density-relative exposure coordinates. Relative
exposure (abscissa) was plotted on the logarithmic scale;
and density (ordinate), on the linear scale, in order to
obtain the functional relation D(E).
Relative exposure-deflection relations and relative
intensity-deflection relations; E(d) and 1(d)
Correlation of relative exposures with deflections
through the use of the data points on the density-deflection
graphs and on the density-relative exposure curves allowed
the construction of a relative exposure-deflection curve,
E(d), for each stellar plate. Plotted on semilog paper,
relative exposure (ordinate, on the logarithmic scale) was
expressed as a function of deflection (abscissa, on the
linear scale).
Because these graphs appeared to be very nearly linear,
a Hewlett-Packard 9810A linear regression program was used
to derive empirically an equation, E(d), for relative
exposure as a function of deflection for each stellar plate.
(The linearity correlation for each resulting equation was
greater than 0.99.) This step greatly facilitated the
process of determining the relative exposure resulting from
a given deflection recorded on the stellar plate tracings.
Without an available equation the relative exposure-
deflection graphs would have had to have been used to read
the relative exposure for each deflection-data-point on each

46
stellar plate. This procedure would have entailed hundreds
of individual correlations and would have taken considerably
longer to complete.
Upon establishment of the relative exposure-deflection
function, E(d), for each plate, the relative intensity-
deflection function, 1(d), for each plate was immediately
known because relative intensity is directly proportional to
relative exposure for a plate of given exposure time.
Relative plate speeds
The relative plate speed of two plates is the ratio of
the inverses of their relative exposures at a given
density. In order to compare on the same scale the relative
intensities of plates of different relative speeds, the
stellar plates would be standardized relative to the speed
of an arbitrarily selected sensitometry plate by simply
dividing the speed of each plate by the speed of the
sensitometry plate. In this investigation, however, only
ratios of relative photographic intensities of a given plate
were used; consequently the determination of relative speeds
was not necessary.
Photographic normalization of relative intensities
At each 0.1-inch grid-line of the wavelength axis of
each stellar plate tracing, deflection (in number of
0.1-inch intervals along the intensity axis) was read.
Substitution of each deflection into the Hewlett-Packard
9810A relative intensity-deflection equation for that
stellar plate and subsequent division of the calculated

47
relative intensity at each wavelength by the relative
intensity of the local continuum for each stellar plate
resulted in a printout of tabulated relative intensities
photographically normalized to the intensity of the local
continuum for each plate.
Calculation of Equivalent Widths
The equivalent width of the K emission was determined
by the following procedure.
Actual (absorption-plus-emission) line profiles
In keeping with standard spectroscopic methods (Keenan
and Morgan, 1951) the line profile for the K line was
constructed for each stellar plate by plotting the tabulated
relative intensities normalized to the intensity of the
local continuum (ordinate) as a function of wavelength
(abscissa) on 0.1-inch graph paper. These line profiles,
constructed from the original data, are superpositions of
the K absorption and the K emission for both stellar
components of the system at the orbital phase of the
spectrogram. The linear reciprocal dispersion of 128 A/mm
is too low by a factor of two to resolve the K-line
components of the individual stars at any phase. (See
Figure 1. )
At every phase the scaled line profile exhibits a
small, narrow emission core of variable strength and
position superposed on deep (except at primary minimum),
broad absorption about 30 A wide at the continuum level.
(See primary minimum, below.)
Unidentified
narrow

48
absorption
lines
flank and are
blended with
the
major
absorption
core
of the K line.
(See Figure
1. )
The
profiles in
this
investigation are virtually identical to
those observed at corresponding phases by Babaev (1974a).
The emission core broadening has variously been
attributed to turbulence in an optically thin layer (Wilson
and Bappu, 1957) and abundance in an optically thick layer
(Goldberg, 1964; Linsky and Avrett, 1970).
The absorption core is broadened by thermal motions,
microturbulence (Naftilan and Drake, 1977) and turbulence
(Abell, 1982), and rotation (Sanford, 1951). The
microturbulent and turbulent broadening is evident in the
anomalously broad bell-shaped Gaussian (Doppler) core, whose
width far
exceeds
tha t
of
normal thermal broadening.
The
rotational
effects
add
to
the core profile, rendering
the
core broader and shallower. The characteristic broad,
shallow shape of a rotationally broadened line is most
apparent at phases during primary eclipse, when only the
large, rapidly rotating K star is visible. (See Sanford,
1951. )
The true extent of any absorption wings is difficult to
discern in the profiles in thi
because of the lack of a
wavelength region so dense
1962). Linsky and Avrett
wavelengths shorter than 4000
continuum level except for
s investigation and in general
;rue continuum level in this
in spectral lines (Wright,
(1970) determined that for
A in the sun there is no true
an interval 0.08 A wide at

49
3999.89 A. Comparisons can be made to the profiles of other
observers, however. Line profiles published by Struve
(1948) exhibited broad absorption wings in the H and K lines
of AR Lac. Joy and Wilson spoke of the "great absorption
wings" (Joy and Wilson, 1949, p. 231) of the H and K lines
in late-type stars, and Weiler (1978) mentioned the overlap
of the wings of the H and K lines of RS CVn stars. Other
observers mentioned only that the H and K lines are
characterized by broad absorption and sharp emission. The
wings could be generated by rotational broadening alone or
by rotation plus abundance effects (collision, radiation,
and/or pressure broadening). These observers did not
attribute the wings to any particular process, but those in
Struve's (1948) paper match fairly well with a superposed
Lorentzian curve, the shape of which would be produced by
abundance broadening.
Emissionless profiles
By the following procedure an emissionless profile for
the K line of the system was constructed empirically for the
phase of each stellar plate.
The emissionless profile for the K star. Because the
primary eclipse of AR Lac is total (Scheller and Plaut,
1932), the actual (absorption-plus-emission) profile for the
K star alone could be determined by taking the graphical
mean of all the profiles during totality. (Only one
spectrogram was obtained at this phase.) The emissionless
profile for the K star alone was determined by visually

50
estimating by the following procedure what the appearance of
this line profile would be without the emission peaks. (See
Figure 2.)
The fact that the profile at totality was quite
evidently degraded considerably by emission and broadened
and shallowed by rotation were great hindrances; however, by
modeling the emissionless profile after the general
characteristics of the K line and after the general
appearance of the K line in the sun and in other late-type
stars, a reasonable picture, internally consistent with all
the data, was developed.
The great depth selected for the constructed
emissionless profile is justified by the fact that the K
line is a resonance line. The line centers of such lines
are characterized by an extremely low residual intensity,
which can be attributed to the apparent characteristic
tendency for resonance lines to be formed by the mechanism
of scattering rather than absorption. There are two
scattering processes: coherent and non-coherent.
In the coherent scattering process the probability of a
quantum's reaching the stellar surface from great depths is
very low because it is absorbed and re-emitted in no
preferred direction; consequently the line center is
virtually black (less than 1% of the continuum: Linsky and
Avrett, 1970). In actuality no line center is truly black,
though; for there is some probability of a quantum's
emergence.

;e>
100
80
60
40
20
0
£•
100
80
60
40
20
0
Figure 1
PROFILES OF THE Ca II K LINE IN AR Lac

52
a Primary Eclipse
Profiles
( K star )
( plate 34 )
b. Secondary Eclipse
Profiles
( G star plus
annulus of K star )
( plate 38 )
c. E*tra-eclipse
Profiles
( G star plus
K star )
( plate 18 )
1 scaled profile ( absorption plus emission )
2 empirically constructed theoretical emissionless profile ( obsorption )
3 emission profile ( I minus 2 )
d. Construction of the Absorption Profile for the G Star
4 some as c2
5 same as a2
6 empirically constructed theoretical emissionless profile for the
G star ( 4 minus 5 )
Figure 2
CONSTRUCTION OF EMISSIONLESS PROFILES
FOR THE Ca II K LINE IN AR Lac

53
For the cores of the H and K lines in the sun, however,
and probably in all other stars also, non-coherent
scattering is the process which renders the central
intensity non-zero (Linsky and Avrett, 1970). Non-coherent
scattering arises because lines are not perfectly sharp;
therefore a quantum absorbed in one part of the line is not
guaranteed to be re-emitted from the same part of the line.
This process results in a redistribution of the energy
across the line profile, transferring energy from the wings
to the core, thereby producing a greater central intensity
than does coherent scattering. In the observed solar K-line
absorption profile, smooth extrapolation of the sigmoid
curve of the Doppler core to the line center yields a
central residual intensity of only a few percent (4% at
most; i.e., I/^CONT = 0-04: Aller, 1963). Theoretical
absorption profiles for the solar K line present a similar
picture (Aller, 1963).
Modeling the emissionless line profiles after those of
the sun constituted an empirical method which produced
inexact results; consequently any calculated differences or
ratios between the emissionless profiles and the actual
profiles could be only relative values. Determination of
the absolute values of (rather than the relative changes in)
the line profiles would require the precise calculation of a
theoretical line profile. This procedure would involve the
calculation of a model atmosphere, which would include

54
(1) the determination of the line absorption coefficient
dictated by the chosen model atmosphere and (2) the
assumption of a line-forming mechanism (Aller, 1963). There
are apparently no completed model atmosphere calculations
for the AR Lac system or a similar one.
Other observers (e.g., Weiler, 1978) have constructed
emissionless profiles by utilizing the Ca II line shapes
observed in spectra of single stars of the same spectral or
spectral-luminosity class as the stars in the AR Lac
system. Because there is some emission in these single
stars, employment of this method did not avoid the problem
of deciding the depth of the line empirically, but merely
Doppler-narrowed it slightly because single stars of these
spectral classes display much less rotational broadening
than do stars of the same classes in binaries.
Photometric scaling. Each of the ten spectra obtained
at phases outside eclipse exhibits a superposition of the
spectra from the entire discs of both stars. As a
preliminary step to determining the emissionless profiles
for these combination spectra, their actual (absorption-
plus-emission) profiles were photometrically scaled on the
assumption that the U light level (the ultraviolet light
level as measured in the standard UBV photometric system)
outside eclipse is constant. This practice is equivalent to
assuming that the U light output of each star is (1)
isotropic over its surface and (2) invariant with respect to
t ime.

55
This assumption is not strictly true for AR Lac because
there are small irregular variations in the light curve out
of eclipse and additional periodic variations due to the
photometric wave-like distortion. The small irregular
variations amount to only 0.025 mag (Chambliss, 1976), and
the amplitude of the distortion wave during the epochs of
this investigation (1976-1978 ) was only 0.04 mag. The
combination of these two effects resulted in a total U
intensity variation of only 0.3%, which is negligible. The
extra-eclipse U light level therefore provides a virtually
constant level to be used as a reference standard by which
to (1) scale light levels at all phases and (2) make
absolute comparisons among data of various observers. All
extra-eclipse profiles were therefore photometrically scaled
to the same U light level, selected to be equal to the
maximum U light level (the extra-eclipse U light level) of
the system.
The emissionless profile for both stars in combina¬
tion. By alignment of the short-wavelength continuum edges
of all the extra-eclipse photometrically scaled actual
profiles, a composite was constructed to synthesize the
appearance of the actual combination spectrum of both
stars. Use of a composite rather than a spectrum at a
single phase tended to smooth any variations due to possible
differences in amounts of emission at different phases and
any Doppler shifting in position of emission peaks across
the absorption profiles at different phases.

56
To obtain the emissionless profile for the sum of the
K-lines of both stars, a smooth deep envelope was
constructed on the composite, which already exhibited a
center-line residual intensity of only about 8%. This
envelope was employed in the data analysis as the
representation of the combination emissionless profile at
all phases. (See Figure 2.)
Further photometric scaling. As a preliminary step to
determining the emissionless profile for the G star alone,
the K star's emissionless profile was photometrically scaled
so that it could be graphically subtracted from the
combination emissionless profile. On the assumptions that
(1) each star's photographically normalized U continuum is
equal to that star's fractional contribution to the total
extra-eclipse U light of the system and that (2) the
intensity at each wavelength in the line profile of each
star is proportional to that star's fractional contribution
to the total extra-eclipse U light level of the system (see
Binnendijk, 1960, pp. 180ff, 264ff), Chambliss' (1976)
photometric data were used to scale the K star's
extra-eclipse U continuum level to 44% of the total
extra-eclipse U continuum level of the system. (The value
used for the G star was, then, of course, 56%.)
The emissionless profile for the G star. With the K
star's extra-eclipse U continuum level scaled at 0.44 and
the extra-eclipse combination continuum level scaled at
1.00, the K star's emissionless profile was centered on the

57
combination emissionless profile and subtracted from it
point by point. The resulting emissionless profile for the
G star exhibited an extra-eclipse U continuum level of 0.56
with respect to the total extra-eclipse U continuum level of
the system. (See Figure 2.)
Synthesized emissionless profiles. After obtaining an
emissionless profile for each star, combination
emissionless profiles were synthesized for the phase of each
spectrogram by graphically adding the K- and G-star
emissionless profiles after they had been (1)
photometrically scaled to the proper proportion for that
phase and (2) Doppler-shifted relative to each other
according to their relative radial velocity at that phase.
Basing the emissionless profiles (i.e., the absorption
profiles) for all phases on the emissionless profiles for
one phase is tantamount to assuming that (1) any changes in
the actual (absorption-plus-emission) profiles are caused by
variations in emission rather than in absorption or in
both--(Weiler (1978) assumed this—and that (2) the
absorption profile of each star is the same shape for all
phases and for all time (i.e., that the absorption profile
is uniform over the surface of the star at all times). The
following procedure was employed to generate the syntheses.
The combination emissionless profile for each phase
outside eclipse was formed simply by graphically adding the
Doppler-shifted emissionless profile of the G star at a
given phase (its continuum photometrically scaled to 0.56)

58
and of the K star at that phase ( its continuum photo¬
metrically scaled to 0.44). All of the extra-eclipse
combination emissionless profiles were therefore scaled to a
U continuum level of 1.00.
Synthesis of emissionless profiles for eclipse phases
required additional photometric scaling. During phases
of partial eclipse of stars with uniform luminances, the
fractional U contribution from each star relative to the
total II light of the system at that phase is equal to the
unocculted fraction of the star's disc area. As previously
stated, the U continuum contribution of each star is also
this fraction; and the intensity at each wavelength in the
absorption line profile is assumed to be proportional to
this fraction.
The components of AR Lac, however, are not of uniform
luminance. The limb darkening in the K star is high; that
for the G star is relatively low (Chambliss, 1976).
Chambliss calculated the limb darkening coefficient for each
star by determining the values which yielded photometric
solutions consistent with his data. By this process he was
forced to one extreme with the K star--obtaining 1.0 as its
limb darkening coefficient in the U. The U limb darkening
coefficient for the G star was calculated to be 0.6. In the
present investigation, the value for the K star was assumed
to be 0.8 (thereby softening somewhat Chambliss' extreme
value), but the value for the G star was placed at the other
extreme--it was assumed to be 0.0.

59
Because the G star was assumed to be of uniform
luminance, the disc-fraction rule was applicable during the
partial and total phases of primary minimum, when the K star
is occulting part or all of the G star, respectively. For
example, at one of the partial phases of primary minimum the
total U light from the system was 0.89 of the total
extra-eclipse U light level of the system. Relative to the
total extra-eclipse level of the system, the K star's
contribution at this phase was 0.44, because the entire disc
of the K star was visible and it was contributing its
maximum amount possible: 0.44 of the total extra-eclipse U
level. Relative to the total extra-eclipse U light level
0.45 remained for the G star to contribute. For the
emissionless profile at this phase, the G star's U continuum
level was therefore scaled at 0.45; and the K star's, at
0.44. The sum of their continuum levels then equalled 0.89,
the total U continuum level visible at that phase relative
to the total extra-eclipse U continuum of the system. The
intensity at each wavelength in each emissionless profile
for each star was proportionately scaled to the U continuum
contribution from that star.
The disc-fraction rule does not obtain during secondary
minimum, when the G star is occulting part of the
non-uniform K-star's disc and the K-star's limb darkening
therefore comes into play. During ingress and egress of
secondary minimum, the U continuum of the system is at a
higher level than it would be if the luminance of the K star

60
were uniform (because the light lost by occultation of the K
star's limb is only 20% of what would have been lost if the
star were uniform). Conversely, during mid-secondary
eclipse, the U continuum of the system is at a lower level
than it would be if the K star were uniform in luminance
(because the bright center of the K star is being occulted,
leaving visible only the limb, which is 80 less luminous
than the disc-center).
Even though the disc-fraction rule does not obtain in
these instances, once the proper proportions of light are
determined for each star, the intensity at each wavelength
in the absorption profile of each star is, as usual,
proportional to that star's fractional U continuum
contribution normalized to the total extra-eclipse U
continuum of the system. In this case it would be each
star's fractional "limb-darkened U continuum contribution."
If the limb darkening of the K star had been ignored, errors
from negligible to approximately 3% for ingress and egress
of secondary minimum and of approximately 3% for phases
within secondary minimum would have been incurred in the
equivalent widths of the K emission, the magnitude of the
error depending on the amount of surface area occulted
(i.e., on phase) and on the value selected for the limb
darkening coefficient.
The value determined by Chambliss for the K star's limb
darkening and that used in the present investigation for the
G star's limb darkening are admittedly somewhat unrealistic.

61
Inclusion of a (probably reasonable) G star limb darkening
factor of 0.5 in the present calculations would only lower
somewhat the values of the K-line emission calculated for
the partial phases of primary eclipse, a consequence which
would have no effect on the general behavior of the emission
during primary eclipse, on the general conclusion reached,
or on the model formulated. Omission of the G star's limb
darkening generates errors ranging from negligible to almost
30% in the equivalent width of the emission for the partial
phases of primary eclipse, the error depending, as
previously stated, upon the phase and upon the value
selected for the limb darkening coefficient.
Chambliss (1976) also acknowledged a general problem
encountered with limb darkening and gravity brightening in
the G star of AR Lac. The assumption of the standard cosine
law of limb darkening and of a uniform variation of flux
with gravity does not represent the actual fall-off in
luminance at the limb of that star or the gravity-variation
of luminance over the surface of that star because the star
has large dark spots—discontinuous concentrated areas of
light-diminution rather than a continuous decrease in light
level as the limb is approached. The proper functional
dependence for limb darkening is unknown. Gravity
brightening was ignored in the present calculations.
In summary, the appropriate photometric scaling
criteria for each phase were used to scale the emissionless
profiles for each star at each phase.
The two scaled

62
emissionless profiles were then centered on each other,
Doppler-shifted by the proper amount to account for the
relative radial velocity at that phase, and finally
graphically added to obtain the combination emissionless
profile due to the contributions of both stars at that
phase. Radial velocity curves obtained by Harper (1933)
were used to determine the Doppler shift of the K star
relative to the G star at each phase. Harper's curves were
selected because they appeared to be the more reliable of
the two sets of curves available, the others being those of
Sanford (1951).
Profiles of the K-line emission
The profile of the K-line emission at each phase was
determined by graphically subtracting the properly scaled
combination emissionless profile from the properly scaled
actual (absorption-plus-emission) profile at that phase.
(See Figure 2.) Somewhat similar Ca II emission profiles
are found in Greenstein (1960).
The equivalent widths of the K-line emission
As previously stated and applied, the profile of a
spectral line is the graph of the ratio of the line
intensity at each wavelength in the line to the intensity of
the nearby continuum; i.e., the spectral intensities are
normalized to the continuum intensity.
A measure of the strength of a spectral absorption line
is its total absorption relative to the level of the nearby
continuum. Graphically speaking, it is the area which the

63
line profile subtracts from the nearby continuum. In order
to express line strengths independent of instrumental
effects such as diffraction and finite resolving power, the
artifice of the equivalent width was devised (Aller, 1951;
Stromgren, 1951; Thackeray, 1961).
The equivalent width (W) of a spectral line is the
width (in wavelength units) of a rectangular line of zero
residual intensity relative to the local continuum and of
the same area as the actual line. In other words, the line
of equivalent width W absorbs the same amount of intensity
from the continuum as does the actual line profile. The
graphical representation of the equivalent width of a line
is a perfectly black rectangular profile extending from zero
intensity to the level of the local continuum and of the
same area as the line profile (Stromgren, 1951; Aller,
1951). In equational form,
IdX ,
ICONT_/
where
W = equivalent width of the spectral line (A),
IgoNT = intensity of the local continuum (ergs/cm^/sec)
(Jones, 1931 , 1934 ),
ÍX = intensity at wavelength X ( ergs/cm^/sec),
Xi,X 2 = short- and long-wavelength extremities of the line
profile at the level of the local continuum (A).

64
Investigation of the strengths of the emission
reversals in absorption lines necessitated the determination
of the equivalent widths of the emission alone. The
equivalent width of the emission profile (We) at each phase
was calculated by subtracting the equivalent width of the
scaled combined emissionless profile (W~) for that phase
from the equivalent width of the scaled actual
(absorption-plus-emission) profile (W+) for that phase:
where
therefore
We = W+ - W",
1X+ 'j d X ,
ICONT-'
TX~1dX ;
ÍCONT-1
We
£xT
CONT
dX
CONT
dX .
From this expression for We it can be seen that it was not
necessary to actually calculate W+ and W“, but only to
subtract the relative intensities of the absorption-plus-
emission profile and the emission profile, a method which
greatly simplified the calculations.

65
Because no equation
intensity as a function of
performed numerically by the
was known
wavelength,
rectangular
for relative line
the integration was
method:
We
where
e >
=1 —— = intensity at wavelength A; relative to
^CONT . L
local U continuum (dimensionless),
AA = wavelength increment between wavelengths at
which relative intensities are measured;
1.2 A = chart resolution limit.
Because the chosen integration step-size (1.2 A) was
smaller than the resolution limit of the IIa-0 plates at
128 A/mm (2.3 A), a more exact numerical method (e.g.,
Simpson's one-third rule) was unwarranted because it would
have produced more precision in the result than was inherent
in the data.
The equivalent width of the K-line emission at each
phase is tabulated in Table 3, Section IV.

66
Determination of error in the equivalent widths of the
K-line emission
Sources of error in the calculations of the equivalent
widths of the K-line emission were
(1) photographic errors, including emulsion grain clumps,
non-uniform emulsion density, and sensitometry methods
(2) electronic noise in
(a) the recording microdensitometer
(b) the chart recorder
(c) the transmission densitometer
(3) the plotting of points for graphs and the reading of
points from graphs
(4) variations in light curves and scatter of photometric
data points
(5) the photometric distortion wave
(6) the wavelength scale for the recorder chart
(7) the radial velocity curves.
Errors incurred due to photographic grain clumps or
non-uniform density were minimized by tracing the
spectrograms with a slit of the greatest height and width
possible without incurring degradation of resolution within
the line profile. Errors from these sources were therefore
rendered negligible. Sensitometry errors were of unknown,
but probably small, magnitude.
Electronic noise was smoothed by averaging multiple
tracings of each spectrogram. All of the tracings of any
one spectrogram were virtually identical. Use of their
average therefore generated negligible error.

67
Plotting of points and construction of smooth curves
through those points was performed with very fine-pointed
writing instruments on graph paper of a scale large enough
to represent the precision of the raw data. Readings of
points from graphs were made to the same precision as that
to which the points were plotted.
The error ultimately calculated for the equivalent
widths is an internal error only, generated by the method
employed to obtain and analyze the data; i.e., it is not an
error relative to any absolute standard.
Error analysis was carried out by two methods:
(a) "Data analysis method": The mathematical rules for
error analysis were applied to the values computed in
successive intermediate calculations leading to equivalent
width, a procedure which incurred compound errors propagated
by the mathematical operations on the inexact values which
were employed in the calculations. The error for each
spectrogram depended upon the particular values used in the
calculation of its equivalent width. In order to
demonstrate which changes in equivalent width with phase
exceeded the normal computational error (i.e., were "real"
changes in equivalent width), it was sufficient in this
investigation to calculate only a maximum error for all
spectrograms. If this calculation had proved insufficient
for the determination of the validity of a particular
equivalent width, the necessary individual error would have
been computed. The itemized list of the errors computed by

68
this method is as follows:
(1) The calculation of the photographically normalized
values of the relative intensities resulted in a maximum
error of ± 2.0%. This value includes the errors incurred by
plotting and reading data points on graphs.
(2) The combined photometric errors (due to individual
variations in light curves, scatter, and the distortion
wave) in the U light curves used to photometrically
normalize the U continua of the spectrograms contributed a
maximum error of ± 0.3% in the relative photometric
intensities of the spectrograms.
(3) The error in the calculated value of the wavelength
scale for the recorder chart was ± 4.7%.
(4) The error in the radial velocities contributed
negligible error to the calculated Doppler shifts.
(5) Because all of the quantities containing these
errors were multiplied or divided to obtain the equivalent
width, the combined error was their sum: ± 7.0%.
(b) "Noise-lobe" method: By assuming that all lobes on the
actual profiles were noise, maximum and minimum values for
the K-line emission equivalent width were calculated. The
maximum profile was constructed by inscribing on the
photometrically scaled actual profile a smooth inner
envelope which eliminated all intruding lobes. The minimum
profile was constructed by circumscribing a smooth outer
envelope which eliminated all extruding lobes. Subtraction
of the areas subtended by these two profiles and division of

69
this difference by two yielded for each plate a sort of
average equivalent-width error (in A). In general, this
method produced errors far greater than the maximum 7.0%
computed by the data analysis method. Because the lobes of
the actual profiles appear in virtually every spectrogram,
regardless of phase, it seems rather unlikely that they are
noise. (They are, in fact, merely some of the many
unidentified lines which are at wavelengths in the vicinity
of the H and K lines and which are blended with them. No
correction for them was applied, and no attempt was made to
subtract them from the line profile; therefore they, too,
contribute to the We measurements' being relative rather
than absolute.) This method is deemed, therefore, to
provide, for the most part, a gross exaggeration of the
errors incurred in this investigation. For purposes of
comparison of changes in equivalent width from phase to
phase, however, and in order to demonstrate beyond any
reasonable doubt the mathematical significance of the
differences in the calculated values for the equivalent
widths at different phases, this method is useful. Where
any question might arise regarding the mathematical validity
of stating that a difference exists between two equivalent
widths, this extreme method can be used to demonstrate
unequivocally that the difference is well above any
reasonably assumed value for a noise level.
The results of the equivalent-width calculations for AR
Lac are summarized in Table 3, Section IV.

SECTION IV
DISPLAY AND ANALYSIS OF REDUCED DATA
Data Display; The Graphical Relation
General Description
A graph (Figure 3) was constructed to display the
relation between the relative K emission-line equivalent
width and the orbital phase of the AR Lac system (data in
Table 3). Data points were connected in order of phase by
dotted lines merely to illustrate the general contour of the
relation and to facilitate the visual scanning of the
emission changes, rather than to imply the graphical
representation of a function W(phase). There are too few
data points over large spans of the domain to be able to
graphically or equationally represent a true functional
dependence. Line-terminated error bars indicate for all
data points the ± 7.0% variation in K emission-line
equivalent width as computed by the data-analysis method.
Circle-terminated error bars indicate the non-constant
variation as computed by the noise-lobe error method, which
was employed only when necessary to establish beyond any
reasonable doubt whether a particular data point lay within
data noise or was instead indicative of a real departure
from the general trend of equivalent widths in that phase
region.
70

71
Table 3
RELATIVE
EQUIVALENT
WIDTHS OF THE
IN AR Lac
Ca II K-LINE
EMISSION
Phase
Plate
Epoch
We (A)
±7.0%
(year)
Error (A)
.002
34
1976.6130
5.49
0.38
. 060
56
1977.6989
15.20
1.06
.115
57
1977.7318
8.26
0.58
.130
58
1977.7536
11. 10
0.78
. 377
60
1977.9071
12.20
0.85
.384
45
1976.9402
17.35
1.21
.385
24
1976.5663
11.78
0.82
.406
18
1976.5555
14.59
1.02
.415
46
1976.9403
19.69
1.38
. 456
41
1976.6209
16.79
1.17
.458
37
1976.6155
17.27
1.21
.498
38
1976.6157
14.71
1.03
.504
42
1976.6211
15.28
1.07
.560
50
1977.0605
20.19
1.41
.724
59
1977.7895
12.15
0.85
.857
61
1977.9097
13.19
0.92
.902
21
1976.5637
12.36
0.87
.923
28
1976.6017
17.34
1.21
.939
33
1976.6127
12.01
0.84
Phase:
fraction of the period of revolution of the
system
Plate:
the ordinal number of the plate, indicating
the temporal order in which it was obtained
Epoch: the epoch of the observation, listed as the
year and the day + month + hour of the
observation as a decimal fraction of a year
We: the relative equivalent width of the K-line
emission at the corresponding phase, in A
+ 7.0% Error: 7% of We, the error determined by the "data
analysis method," in A
See Figure 3

I
I-
Q
Z
UJ
<
>
3
O
UJ
UJ
>
H
<
Ul
tr
PHASE
I 17% ERROR (“DATA ANALYSIS" METHOD)
I VARIABLE ERROR ("NOISE-LOBE" METHOD)
4 CONTACTS
-~J
M
Figure 3
VARIATION OF THE RELATIVE EQUIVALENT WIDTH OF THE Ca II K-LINE EMISSION
WITH ORBITAL PHASE IN AR Lac

73
A cursory comparison of the error bars for all the data
points indicates that the emission exhibits prominent
eclipse features (local relative minima in the emission) and
some extra-eclipse variations.
Eclipses of the Emission
Well-defined eclipse minima in the emission and
pronounced near-symmetry about the mid-eclipse phase
characterize both primary and secondary eclipses. Phases
were computed using the ephemeris in Hall, Richardson, and
Chambliss (1976).
Primary eclipse
From the graph it is seen that as primary eclipse is
approached, the emission level dips slightly just prior to
first contact, then rises to a local maximum at first
contact. This maximum is followed by a sharp decline to a
mid-eclipse local minimum, which lies well below the
pre-eclipse emission level. Following mid-eclipse is a rise
to a local maximum just prior to fourth contact, a
subsequent decline to a local minimum lying above the
mid-eclipse level, and a sharp rise to a post-eclipse level
slightly below the pre-eclipse level. The existence of the
pre-ingress depression in the emission is somewhat doubtful
because the error bars of the two adjacent data points (#61
and #21) share some common ground. The post-egress
depression may be a real phenomenon rather than noise,
because there is a lack of commonality in the error bars of
the three data points (#56, #57, and #58) which define it.

74
The data exhibit a lack of perfect symmetry about
mid-eclipse. The existence of near-symmetry strongly
suggests that symmetry does exist, but is in some manner
veiled. The veiling agent is probably a selection effect:
namely, that data were obtained only at certain phases,
which were not chosen for their symmetry about mid-eclipse.
The presence of additional data points at phases symmetrical
relative to mid-eclipse would probably reveal the suspected
symmetry. In further support of this suggestion it is noted
that there is a large span (0.04 phase unit) between the two
points defining pre-ingress depression (#61 and #21),
whereas there is only 0.015 phase unit between the two
post-egress plates (#57 and #58). If it can indeed be
contended that the depressions are symmetrical (and there is
nothing in these data or in those of others to preclude
symmetry), then between #61 and #21 there could be a much
lower value of equivalent width (at about phase 0.885)
similar to that of #57.
The lack of symmetry between the levels of pre- and
post-depression emission levels can also probably be
attributed to the paucity of data points at symmetrical
phases relative to primary mid-eclipse. A data point at
phase 0.14 (just beyond #58) might well have returned to the
pre-ingress level. No concrete conclusion can be drawn
regarding perfect symmetry without additional data at the
required phases.

75
Within primary eclipse the ratio of maximum emission to
minimum emission is 3.7, maximum occurring at first contact
and minimum at mid-eclipse. The ratio of maximum emission
to the average extra-eclipse level (at the shoulders of the
pre- and post-eclipse depressions) is 1.4. The ratio of the
average extra-eclipse level to the minimum emission level is
2.4. The minimum emission level at mid-eclipse is the
absolute minimum for the entire orbital cycle.
Secondary eclipse
As secondary eclipse is approached on the graph, the
emission rises to a local maximum prior to first contact (at
phase 0.384). (See Extra-eclipse Behavior.) The emission
then declines to the previous level before rising to a
slightly higher local maximum at first contact. Following
first contact is a decline to a mid-eclipse local minimum,
which lies slightly above the pre-eclipse level. Nearly
mirroring this behavior (viz., with the omission of the
pre-ingress maximum) is a post-mid-eclipse rise to a local
maximum just prior to fourth contact and a subsequent
decline to the pre-ingress emission level.
As in
the case of
primary
eclipse
the
question
of
perfect symmetry arises,
and the
reply is
the
same: more
data points
near fourth
contact
are needed to
confirm
or
deny symmetry.
Within secondary eclipse the ratio of maximum emission
to minimum emission is 1.3, maximum occurring at first
contact and minimum at mid-eclipse. The ratio of maximum

76
emission to the extra-eclipse level is 1.6. The ratio of
the minimum emission to the extra-eclipse level is 1.25.
Comparison of primary and secondary eclipses
The eclipse of the emission is much shallower, both
absolutely and relatively, at secondary minimum than at
primary minimum, the mid-eclipse emission level of the
former being 2.8 times higher than that of the latter.
Because secondary eclipse is central, but not total, the
emission at secondary mid-eclipse is composed of
contributions from both stars. On the other hand, during
primary eclipse the G star is completely occulted; therefore
the emission at mid-primary eclipse is contributed by the K
star alone.
Extra-Eclipse Behavior
With the exception of plates #45, #57, and #61 the
ranges of error for the extra-eclipse plates indicate a
virtually constant extra-eclipse emission level. There are,
however, very few extra-eclipse plates; therefore no general
conclusive statements can be made regarding extra-eclipse
behavior.
Coverage in the vicinity of phase 0.384 (plates #60,
#45, and #24) is, however, sufficient to state that there is
an emission peak at that phase. Comparison of error bars
(even the exaggerated ones determined by the noise-lobe
error method) demonstrates that the peak rises significantly
above the noise level.

77
Interpretation of the Graphical Relation
Variability of the Emission
Performed as an internal check of the consistency of
the spectrograms with the emission profiles, microscopic
visual examination of the plates revealed that the Ca II
emission is visible at all phases. It is not entirely
eclipsed at either minimum, thereby corroborating Sanford's
(1951) and Weiler's (1978) observations that the emission is
present outside of as well as within eclipse. The
difference between equivalent widths of adjacent data points
of the equivalent width-phase curve exceeds the computed
range of error, even when the more extreme of the two error
calculations is considered. The emission is therefore very
definitely variable, in confirmation of the observations of
Sanford (1951), Babaev (1974c), Weiler (1975, 1978), and
Naftilan and Drake (1977), and the conclusion of Kron (1952)
upon examination of Wyse's (1934) plates. Further, the
variations appear to be phase-dependent and/or time-
dependent, not random, as reported by Weiler (1978) and as
indicated by Babaev's (1974c) data.
Relative Strengths of the Emission
Because the grating dispersion used in this
investigation was not great enough to resolve the components
of the K line from each star, the emission in the graphical
relation represents a composite of the emission from both
stars. Consequently, no statements can be made in
confirmation or denial of Sanford's (1951) observations that

78
the ratio of the secondary's emission to the primary's
emission increased during the first half of the system
period and decreased during the second half of the period.
Again because of insufficient dispersion, no positive or
negative statements can be made regarding confirmation of
the observations of Sanford (1951) and Naftilan and Drake
(1977) that the emission from the secondary star is stronger
than that from the primary star.
Attempts to reconcile the intra-eclipse behavior of the
graphical relation of this investigation with the
intra-eclipse observations of Sanford (1951) and Naftilan
and Drake (1977) appeared to fail at first glance.
Examination of their K-line profiles at primary and
secondary mid-eclipse revealed a higher level of emission at
primary eclipse than at secondary eclipse, whereas the
present investigation indicated just the opposite.
This problem was resolved upon closer inspection of the
manner in which both of the previous investigators analyzed
their data. These observers performed their calculations of
the equivalent width of the emission at a given phase by
comparing the intensity of the emission to the intensity of
the continuum level at that phase rather than by comparing
the emission to an absolute, unchanging continuum standard
level (as was done in the present investigation).
As seen in Sanford's (1951) line tracings, it is indeed
true that at primary minimum the emission rises above the
continuum level; whereas at secondary minimum the emission

79
does not
quite
reach
the
level of
the
continuum,
both
emission
peaks
being
the
same width
at
the base.
The
continuum
level
at primary mid-eclipse
is,
however, only
54%
of the continuum level at secondary mid-eclipse (Chambliss,
1976). When the equivalent width of the emission for each
star was calculated using their data, but comparing both
emission levels to the same standard continuum level (the
extra-eclipse level), the same conclusion resulted as was
obtained in the present investigation: the equivalent width
of the emission is greater at secondary mid-eclipse than at
primary mid-eclipse.
Sanford's and Naftilan and Drake's conclusion that the
emission of the primary star is weaker than that of the
secondary star remains unchanged by the above-instituted
change in the level of the continuum to which the emission
was compared because the dispersion they used was great
enough to completely resolve the emission components from
the primary and secondary stars, thereby allowing direct
comparison of the relative amounts of emission from both
stars at each phase (except at eclipses).
Observed Surface Distribution of the Emission
There is considerable evidence, both direct and
indirect, that the emission is not uniformly distributed
over the surfaces of the stars in AR Lac. Extra-eclipse
variability seen by previous observers and in the present
investigation constitutes evidence of non-uniformity of
emission.

80
F'or a number of Ca II emission stars, Struve ( 1945),
Hiltner (1946), Struve (1946), and Gratton (1950) found
evidence favoring the permanent localization of the emission
at the tips of the tidal bulges of the star(s) producing the
emission.
Struve (1948), although
acknowledging
that
the
localization
of the emission of
AR
Lac had
not
been
investigated
, inferred that it
was
confined
to
the
tidal bulges by analogy with RZ Cnc and RW UMa.
Weiler (1978) suggested that his observation of a
substantial change in the equivalent width of the emission
over a short period of time during the partial phases of
secondary minimum ingress (a diminution of 4A in 35m) could
be indicative of "the eclipse of a localized emission area
on the K0 IV star" (Weiler, 1978, p.88) because this
dramatic change could not be explained by the eclipse of a
uniform distribution of emission over the stellar surface.
Sanford (1951), Struve (1952), and Naftilan and Drake
(1977), on the other hand, found that the broadening of the
Ca II emission in AR Lac corresponds to synchronous
rotational broadening, thereby indicating that the emission
emanates from all parts of the stellar surface(s) or at
least from complete equatorial bands. Kron (1952) had
concluded that the distribution of the emission around the
entire equator of the star does not necessitate that the
distribution be homogeneous—the emission could be
concentrated in patches well distributed in longitude and
not fixed permanently in certain areas.

81
The asymmetry of the line profiles in the present
investigation provides a piece of evidence that the
distribution of light over the stellar surface is
non-uniform (Huang and Struve, 1960). The variations in the
emission in the vicinity of the eclipses and the emission
peak at phase 0.384 indicate the presence of strong,
localized emission sources. The presence of the emission
throughout the system's cycle indicates that there is also
probably some distribution of emission over the entire
equatorial region or the entire surface(s) of the star(s).
The exact nature of the emission source(s) (size,
position, distribution) is uncertain from the data in this
investigation because there is insufficient time/phase
resolution in the vicinity of each contact and insufficient
spectral resolution overall. Better resolution would
establish more precisely the changes in the emission as it
is eclipsed so that an accurate determination could be made
of the phases at which the emission decrease begins and ends
during each eclipse.
Model for the Surface Distribution of the Emission
A model was constructed to account for the observations
in this investigation. A model with uniform distribution of
emission could not explain the character of the variations
in the emission; therefore a model with non-uniform emission
was chosen—a composite incorporating three emission
sources:

82
(1) distributed emission from all parts of the stellar
surfaces or at least from complete equatorial
bands, the emission arising from well-distributed
spots or patches
(2) strong emission permanently localized at the
extremities of the tidal bulges of the stars
(3) strong emission from a localized source other than
the bulge-extremities.
The distributed emission accounts for the presence of
the underlying "background" of emission observed in this
investigation throughout the system's cycle and also for the
observations (Sanford, 1951; Struve, 1952; Naftilan and
Drake, 1977) that the broadening of the emission corresponds
to that which would be observed from a source which spans
the full diameter of the star rather than being concentrated
only in a small area.
The presence of emission sources at the extremities of
the tidal bulges explains most of the observational features
seen in this investigation in the vicinity of and within
eclipse (see Primary eclipse). Compatibility of the results
of this investigation with the observations of Sanford
(1951) and Naftilan and Drake (1977), who determined that
the emission from the K star (the secondary) is numerically
greater than that from the G star, requires the sum of the
emission from the sub- and anti-stellar bulges of the K star
(Ks and Ka) to be greater than the sum of the emission from
the sub- and anti-stellar bulges of the G star (Gs and Ga).

83
The non-bulge localized source accounts for the
emission peak at phase 0.384.
Model for the Generation of the Observed Behavior of the
Emission with Phase
Combination of the model pictured above with the system
motion revealed the details of the explanation of the
equivalent width-phase relation.
Primary eclipse
This model cannot explain the pre- and post-primary-
eclipse emission depressions because severe contradictions
are encountered. The explanation for these depressions is
therefore left to circumstellar matter and a consequent
increase in absorption rather than a decrease in emission.
(See Correlations of Photometry and Spectroscopy.)
An increase in the visible area of the emission
concentration of the substellar bulge (Gs) of the G star and
on the antistellar bulge (Ka) of the K star as the stars
revolve accounts for the pre-first contact increase in the
emission prior to primary eclipse.
The first-contact emission maximum occurs because more
of these two areas is visible than at any other phase
(except fourth contact). Comparison of the emission level
at this maximum to the emission at the quadratures (when
one-half of each emission area is visible) leads to the
conclusion that the sum of the substellar emission (Gs) from
the G star and the antistellar emission (Ka) from the K star
is greater than the sum of the anti-stellar emission (Ga)

84
from the G star and the substellar emission (Ks) from the K
star. This result is compatible with the results of Sanford
(1951) and Naftilan and Drake (1977) if the substellar
emission (Gs) of the G star is greater than or equal to the
substellar emission (Ks) of the K star. (There is no
evidence to preclude this possibility.)
The post-first contact decline in emission can be
attributed to the eclipse of the substellar emission (Gs) of
the G star while the contribution from the antistellar bulge
(Ka) of the K star remains constant (because the entire area
of this emission is visible from first to fourth contact).
Between second and third contacts the emission is entirely
due to the anti-stellar area (Ka) on the K star.
The emission increase to a maximum at fourth contact is
caused by the reappearance of the substellar emission (Gs)
of the G star while the emission from the K star remains
constant.
The post-fourth contact decrease in emission occurs as
the K-star anti-stellar emission (Ka) area and the G-star
substellar emission (Gs) area are disappearing around the
1 imb.
Secondary eclipse
The increase to a maximum at first contact of secondary
eclipse is caused by more of the K-star substellar emission
(Ks) area and more of the G-star antistellar emission (Ga)
area rotating into view. At first contact the maximum
amount of both of these areas is visible.

85
Examination of the graphical relation shows that the
first-contact maximum of secondary eclipse is greater than
that of primary eclipse. This observation leads to the
conclusion that the sum of the anti-steller emission (Ga)
from the G star and the substellar emission (Ks) from the K
star is greater than the sum of the anti-stellar emission
(Ka) from the K star and the substellar emission (Gs) from
the G star. This contradiction of the conclusion drawn
during primary eclipse can be resolved if Ka and Gs are not
wholly visible at first contact of primary eclipse, but Ks
and Ga are wholly visible at first contact of secondary
eclipse.
The emission decrease to a minimum at mid-secondary
eclipse is explained by Ks beginning to be eclipsed while Ga
remains in full view. The emission does not decline to as
low a level as at mid-primary eclipse either because (1) Ks
is not completely eclipsed or because (2) Ga is greater than
Ka if Ks is completely eclipsed. (A definite choice cannot
be made until the size of the Ks emission area has been
measured.) The only positive statements which can be made
are that Ga plus the contribution from the K star (if any)
at mid-secondary is greater than Ka and greater than the
emission level at the quadratures.
The post-mid-eclipse emission rise to a maximum at
fourth contact occurs as Ks reappears from eclipse and Ga
remains constant. At fourth contact (as at first contact)
both Ks and Ga are entirely visible, therefore producing a

86
maximum. The emission declines after fourth contact as a
result of these emission areas on both stars rotating around
the limb.
Extra-eclipse behavior
There are at least four ways in which the extra-eclipse
emission maximum at phase 0.384 could be interpreted:
(1) anisotropic emission of a highly directional
nature (designated the anisotropic model)
(2) a phenomenon of short time duration and fixed
surface position (designated the temporal model)
(3) a phenomenon of short time duration due to
rotation of surface position (designated the
spatial model)
(4) combinations of these.
Anisotropic model. The anisotropic model is rather
unlikely because there are no examples of Ca II emission
which is quite so directional as to cause such a sharp spike
(except perhaps some sort of Cerenkov radiation possibly
associated with the radio emission from AR Lac: Smith,
1983. See Radio emission, esp. Owen and Sprangler, 1977.)
In the sun, for example, Ca II emission can be observed from
all sunspot areas, be they mid-disc or near the limb. St.
John (1910) found that the measurement of the widths of the
Ca II lines at mid-disc was not generally possible, but the
intensity of the Ca II emission near the limb was "very much
greater than over the general disk" (St. John, 1910, p.
64). The emission did not, therefore, become stronger when

87
the emitting areas were observed on the normal than when
they were observed at an angle to the normal.
Temporal model. Temporal events include formation and
dissolution of an emission region (a starspot or starspot
group), the occurrence of a flare (or flares), and general
trends in emission level over several cycles or epochs.
The extra-eclipse peak observed in this investigation
extends over a phase interval from phase 0.377 (plate #60,
epoch 1977) to phase 0.385 (plate #24, epoch 1976). The
width of the base of the peak is 0.008 phase unit, which is
equivalent to 23ra of time. The maximum of the peak lies at
phase 0.384 (plate #45, epoch 1976). The emission intensity
of the peak maximum rises well above the levels of the two
flanking plates, their intensities being almost identical.
The error bars confirm this event as a real phenomenon. The
plates were obtained in
the
numerical order indicated
by
their plate numbers.
The three spectra
which
define
the peak observed
in
this investigation were
not obtained
during the
same cycle
of AR Lac or during the
same
epoch of
observation, and
the
chronological order of
the
plates
is not in
order
of
increasing phase. For
these
reasons
this peak
cannot
be
interpreted in a simple phase-sequenced temporal sense:
that is, as the observation of the entire or partial
sequence of events in any short-term phenomenon, either as
(1) the formation and dissolution of an emission region or
as (2) the rise and fall of emission during a flare.

88
Observation of either a starspot (or group) or a flare at
one point (plate #45) in the midst of activity is, however,
an acceptable interpretation for the event observed in this
investigation.
Babaev (1974c) made a similar observation of a peak at
phase 0.6489 and of width 0.1429 phase unit (eguivalent to
6^8 of time). These dimensions were derived upon the
assumption that the emission portion of the K-line maximum
he observed had the same width in phase units as the
composite (emission-plus-absorption) curve shown in his
paper. The same conclusions as were drawn in the present
investigation must be drawn regarding Babaev's peak, but for
a different reason: viz., that he made no mention of the
date(s) on which his observations were made, so that no
temporal continuity can be assumed.
The fact that neither of these observations can be
explained by either the starspot formation and dissolution
picture or the flare picture does not, per se, preclude the
occurrence of such events in AR Lac. Further considerations
are necessary in order to accept or reject these pictures.
For this gedankenexperiment it was assumed that all of the
data in each investigation cited above were obtained in
temporal order during the same cycle of the system. The
starspot model would not provide a valid interpretation of
these observations because the time intervals involved are
far too brief (by a factor of 40 at the minimum, when
compared to sunspot durations) for spots to form and

89
dissipate. (No theory is presently available, however, by
which to determine whether this short a duration time for a
starspot could occur in the RS CVn stars.) On the other
hand, these hypothetical data would lend themselves well to
the flare interpretation because events of similarly short
time duration, suspected of being flares, have been observed
in AR Lac, SZ Psc, SV Cam, and other binaries. Weiler
(1978) observed the pronounced diminution of the H and K
emission of AR Lac over a period of only 35m during the
partial phases of secondary eclipse. Because the decrease
was nearly seven times what would be expected from the
geometrical effects of eclipse, he interpreted the event as
the eclipse of a localized emission area (a relatively
long-term phenomenon—a spot). He might just as easily have
been observing the occultation of a flare-in-progress (in
contrast, a short-term event). Catón (1981) concluded that
if the scatter in Jakate's (1980) photometric observations
of SZ Psc is indeed above the noise level, it may provide
the first observational evidence of optical flaring in RS
CVn stars. Suspected flares of approximate duration 45m
were observed in SV Cam by Patkos (1981). Hall (1976)
considered that flares in RS CVn stars might well occur, but
not be observed because these systems are brighter than the
RS CVn-related dMe and dKe systems in which flares are
observed to occur. Naftilan and Drake (1977) observed in
the H and K emission of AR Lac short-term variations which
they considered as indicative of an active chromosphere.

90
These rapid variations could perhaps also be interpreted as
evidence for the occurrence of flares.
Because plates #24 and #60 fall at almost exactly the
same emission level over the course of two epochs (1976 and
1977, respectively), their level can probably be considered
to be the usual level of emission for AR Lac in that phase
region. The change in emission level represented by the
elevated value of plate #45 (epoch 1976) cannot, therefore,
be interpreted as the onset of a general trend toward lower
emission level in that phase region in successive system
cycles or epochs. (Because the stars in the AR Lac system
are intrinsically variable, however, it is probably not wise
to assume generally that any level is constant with either
time or phase . )
Spatial model. The spatial model consists of the
interpretation of the width of the emission peak as a phase
interval of emission visibility which is produced as the
active region which generates the emission is being carried
into and out of view by the rotation of the star upon which
it resides. The width of the peak in phase units determines
the time interval during which the region is visible.
Included in this model is the assumption that such an event
does not repeat itself identically in successive cycles, so
that it would not be possible to catch later on what was
missed at some phase in an earlier cycle or epoch. In other
words, the assumption is that the activity does change in
position and phase. (The width of the photometric

91
distortion wave maximum or minimum could perhaps also be
interpreted in this manner.)
The same opposition is raised regarding the spatial
model for the peak observed in this investigation as was
raised regarding the simple phase-sequenced temporal model:
viz., the observations were not made in chronological order,
nor were they closely spaced temporally. The observation of
the maximum of the peak could, however, be interpreted as
being just one moment of a spatial event.
As in the temporal case the inability of this model to
explain this particular set of observations does not in
itself rule out the occurrence of such events in AR Lac. In
order to determine the validity of such a suggestion, it
must first be determined whether such an event is within the
limits of observability (as was done in the temporal case).
A photometric analogy is utilized to serve this purpose.
Catón (1981) determined by a computer-generated model that a
group of cool starspots observed together on the stellar
surface would indeed produce a visible phenomenon: the
light-level diminution known as the photometric distortion
wave. When the spot group passes around the limb or is
eclipsed, the light level rises again to its usual level.
The observation of this phenomenon in AR Lac was first
announced by Chambliss (1975b). It has since been studied
by several observers. If Catón1s result can be extended to
Ca II emission regions, then it could be concluded that a
group of emission areas observed together on the surface

92
would produce an emission peak. No analysis similar to
Caton's photometric analysis has been performed to determine
the theoretical visibility of Ca II emission regions.
Babaev ( 1974c) may well have observed such a spatial event
if his observations were indeed made in chronological order
and were closely spaced in time. Weiler's (1978)
observation of the rapid and considerable emission decrease
during secondary eclipse phases may also provide an example
of an observation of the eclipse of a Ca II emission region
or group, just as he interpreted it. No follow-up
observations were made, however, to verify whether the
feature is a permanent one (fixed in the same position on
the star) or a semi-permanent one (changing in latitude,
longitude, or phase) of some duration.
Visibility of the phenomenon having been tentatively
established, a physical model to explain how the star
would produce such an event must be formulated, as was done
in the temporal case. For the sake of simplicity the
emission peak was assumed to be produced by only one of the
stars in the AR Lac system. It is known that the primary
(G) star is more variable photometrically than the secondary
(K) star
(Wood,
19 4 6;
Kron ,
1947 ) ;
however the
Ca
II
emission
of the
secondary is
stronger than that
of
the
primary
(Sanford,
19 51;
Naftilan and
Drake, 1977)
•
The
secondary is therefore chosen as the component supposedly
responsible for the emission peak. For the construction of
the model it was assumed hypothetically that, as in the

93
temporal case, the data in this investigation and in
Babaev's (1974c) observations were obtained in temporal
order and during the same cycle of the system. The emitting
region would therefore have been visible for an interval of
0.008 phase unit in this investigation (observations made
from 1976-1977) and for 0.1429 phase unit in Babaev's
investigation (observations made presumably from 1968-
1972). The interpretation of the combination of these two
pieces of data depends upon (1) the internal structure of
the star and (2) the tidal effects of binariness, which
determine the nature of the rotation of the star. In other
words, whether the star has a convective or a radiative
envelope and whether the star has a companion which raises
small or large tidal bulges determine whether the star
rotates differentially or like a solid body, respectively
(Hall, 1972).
Both components of AR Lac have gravity-brightening
indices consistent with deep convective envelopes
(Chambliss, 1976), and the KO IV secondary is cool enough to
have a deep convective envelope (Popper 1961). Hall (1972)
pointed out that Huang (1966) offered the "reasonable
supposition" that stars in a binary system should experience
differential rotation as long as "the tidal bulge raised by
the binary companion does not entirely suppress the natural
tendency to rotate differentially" (Hall, 1972, p. 325).
Hall therefore concluded that although the rotation of the
stars in RS CVn is observed to be the same as the system

94
period, it does not follow that they are strictly
synchronous. Synchronous rotation is merely the average of
the rotation over the entire stellar surface. Neither
component of AR Lac has an excessive tidal bulge—the
oblateness of the primary is 0.006, and that of the
secondary is 0.035 (Chambliss, 1976). AR Lac therefore
conforms to Huang's description and should consequently
rotate differentially.
Because there has been no theoretical model formulated
for differential rotation in stars with convective
envelopes, Hall (1972) suggested the sun as an example of a
star with a convective envelope, after which the
differential rotation of other stars with convective
envelopes might be modeled. The differential rotation of
the sun is such that the equator rotates the fastest, the
rotation rates of other latitudes being given by
y = 14°44/day - 3°0 sin2x/day,
where x is the latitude and y is the rotation rate in
longitude (°/day) (Allen, 1973). This solar differential
rotation is observed in the motion of sunspots at different
latitudes. As an average 11-year optical sunspot cycle
progresses, sunspots are formed successively equatorward in
latitude. This phenomenon is usually referred to as
"latitudinal sunspot drift" or simply "drift." The average
annual latitudinal drift rate is l?72/year, the drift rate
decreasing as the latitude of the spots decreases (Allen,
1973) .

95
Tentative establishment that the stars in AR Lac do
rotate differentially and that the differential rotation is
very likely in the same sense as that of the sun (faster at
the equator) allows the interpretation of the combination of
the two phase intervals of visibility of the emission
region. The smaller the phase interval of visibility, the
faster a feature is transiting the stellar surface due to
the rotation of the star. The faster a feature transits,
the closer the latitude of that feature is to the equator of
the star. By this model the observed decrease in the phase
interval of visibility between 1968-1972 and 1976-1977 would
indicate that during this period of time the emission region
had drifted toward the equator, just as sunspots do.
Because there has apparently been no general equation
derived for the rate of differential rotation as a function
of latitude (the rate being expressed in terms of the phase
interval of visibility of the emission), it is not possible
presently to calculate the latitude at which the emission
area lies. It could only be stated that (1) the emission
area is closer to or farther from the equator and that (2)
various differential rotation rates could be measured
observationally. There must, however, be some upper limit
on the rate of differential rotation, so that gravitational
stability within the star is maintained. An interval of
0.008 phase unit, indicating a time interval of 23m for the
region to rotate completely across the face of a star of the
size of the AR Lac secondary, might be a bit on the short

side for
preservation of such internal stability. This
short an interval probably also indicates too great a
departure from the synchronous rate for this system, this
statement being based on sunspot motion on the sun as a
model. The equator of the sun rotates 1.6 times as fast as
the poles (Allen, 1973), whereas in AR Lac the ratio of the
synchronous rotation rate to the 23ra interval is a whopping
124. Events of longer duration, such as the one which may
have been observed by Babaev (duration 0.1429 phase unit, or
6^8, thereby yielding a ratio of 7), might be possible.
Conclusion. Because of the lack of (1) temporally
ordered observations and (2) observations repeated at the
same phase in successive cycles of AR Lac, the question of
whether the cited observed behavior represents (1) a feature
relatively fixed spatially on the stellar surface and
observable either at one phase or migrating in phase or (2)
a transient temporal feature remains unanswered. Both
interpretations are not only reasonable, per se, but are
also supported by observations of emission phenomena which
are apparently of temporal and spatial nature (flares and
eclipses of emission regions, respectively) in AR Lac, other
RS CVn systems, and related systems.
Correlations of Spectroscopy and Photometry
There are a number of correlations which may be made
between the spectroscopic phenomena observed in this (and
other) investigations and photometric phenomena observed in
other investigations.

97
Eclipse correlation
The eclipse of the "background" K-line emission of AR
Lac observed in this investigation corresponds almost
exactly to the photometric eclipses of the system. (See
Figure 2). Other investigators (Babaev, 1974c, and Weiler,
1978) did not find such a correlation. Instead, they
observed rather random emission throughout the system's
cycle. If the relative strengths of the Ca II emission from
the components of AR Lac are variable with time (which seems
likely), the eclipse effect could be masked, thereby
allowing eclipses to be observed during some cycles and not
during others. These seemingly contradictory observations
would therefore be reconciled.
Pre- and post-eclipse depressions
A strong similarity between the spectroscopic and
photometric behavior of AR Lac has been observed by several
observers prior to and following primary eclipse.
These observations suggest that the spectroscopic and
photometric phenomena may have some relation, perhaps some
common mechanism producing them both.
In the present investigation depressions were observed
in the K-line emission of AR Lac at pre-first contact and
post-first contact phases of primary eclipse (phases 0.92
and 0.115, respectively).
Kron (1947) and Catalano (1973) reported depressions in
the light curve of AR Lac just before first contact and just
after fourth contact of primary minimum. Kron's light curve

98
showed the depth of the depressions to be 0.08 mag at phase
0.817, 0.06 mag at phase 0.883, and 0.06 mag at phases
0.141-0.197. Catalano measured the depths of the
depressions in his light curve to be approximately 0.05 mag
(as reported by Hall, 1976).
The photometric distortion wave could not be invoked as
the cause of these depressions because the distortion wave
minimum was found to be at other phases of these light
curves. Catalano (1973) and Naftilan and Drake (1977)
therefore made the proposal that the pre- and post-ingress
light curve dips might be indicative of a circum-secondary
envelope. As additional photometric evidence of such an
envelope, the scatter observed in the 1948 near-infrared
light curve obtained by Kron indicated the presence of an
extended atmosphere about the secondary star (Theokas,
1977). The system's infrared excess (Naftilan and Drake,
1977) and ultraviolet excess (Rhombs and Fix, 1977) also
indicate the possibility of a circum-secondary envelope.
In this investigation as well as in that of Weiler
(1978) it
was
assumed that
any
changes observed
in the
equivalent
widths of the Ca
II
line profiles are
due to
changes in
the
intensity of
the
emission. The
apparent
decreases in emission in the vicinity of primary eclipse
could, however, be alternatively interpreted as increases in
Ca II absorption. Such absorption increases could perhaps
be explained by occultation of the primary star by an
absorbing envelope, as was implicated as the cause of the

99
photometric depressions. A further basis for this
contention is the observation (Naftilan and Drake, 1977)
that the H-alpha emission components of AR Lac are
symmetrical about the line center of the secondary star's
line profile, both within and outside of eclipse. Naftilan
and Drake indicated that this symmetry lends itself well to
the interpretation that it is produced within a rotating
non-equilibrium envelope with two different velocity
regions.
Distort ion-wave-minimum—emission-maximum—period-change
relation
Hall, Richardson, and Chambliss (1976) noted that for
each of several RS CVn systems (RS CVn, SS Cam, RT Lac, CG
Cyg, V471 Tau, and AR Lac) there is a smooth graphical
relationship (a "migration curve" for each system) between
the phase of the minimum of the photometric distortion wave
and epoch. For each system, points representing the phases
at which period changes have occurred also lie along the
migration curve for that system, observed period decreases
having occurred when the phase of the system was 0.25, and
period increases, at phase 0.75. (See Table 4 and Figure 4
for the curve for AR Lac. For this curve the error in the
phase of the wave minimum is ±0.1 phase unit.)
Period changes. An interpretation of the observations
of period changes at particular phases in the migration
curves had previously been offered by Hall (1972), Arnold
and Hall (1973), Hall and Henry (1973), and Arnold, Hall,

100
and Montle (1973). The abrupt period decreases in these
systems occur when the minimum of the distortion wave is at
phase 0.25, which coincides with the time at which the
spotted area producing the distortion wave minimum is on the
leading edge of the star producing the wave. Ejection of
material from this region results in the stars' moving
closer together, thereby decreasing the period of the
system. The sudden period increases occur when the
distortion wave minimum is at phase 0.75, when the spotted
area is on the following edge of the star producing the
wave. Material leaving the region would cause the stars to
move farther apart, increasing the period of the system.
The correlation of the phase of the distortion wave
minimum and the phase of period changes allows the migration
curve to be used to predict the epoch and the sense of
future period changes in these systems. Hall, Richardson,
and Chambliss (1976) predicted that for AR Lac a period
increase had occurred in 1974 ± 3, when the minimum of the
distortion wave was at phase 0.75. (No 1971-1977 data had
been reduced at that time to enable them to verify their
prediction.)
Later on, however, Scarfe and Barlow (1978) .calculated
a new period for AR Lac from their observations made
sometime between 1973 and 1976. (The precise years for the
AR Lac data were not indicated.) Comparison of this new
period (1^9831955 ± 0^0000010) to the previous period
(1*^9831987 ± 0^0000005) calculated by usi ng data collected

101
during observations from 1966-1973 and published by
Chambliss (1976) yields a period decrease of 0S276. (Nha et
al. (1982) also reported a period decrease, of about 20m,
occurring in 1977.) Chambliss' data further indicated that
the phase of the minimum of the photometric distortion wave
during 1973-1975 was 0.72, which should have corresponded
approximately to a time of period increase according to
Hall, Richardson, and Chambliss' prediction.
At first glance the results of Scarfe and Barlow and
Nha et al. seem to cast doubt on the validity of the
predictive ability of Hall, Richardson, and Chambliss'
curve. During the time interval of the former
investigators' observations however, the migration rate of
the wave was changing very rapidly. (See Figure 4.) A
period increase, therefore, could have occurred at the
beginning of the interval (1971-1973), followed by a period
decrease at the end of the interval (1975-1977). These two
consecutive oppositely directed period changes might not
have been observed as two separate events for two reasons:
(1) the rapidity of the migration, which would result in the
O - C excursions' being of very low amplitude (Hall,
Richardson, and Chambliss, 1976) and therefore easy to
overlook; and (2) scarcity of data at close enough time
intervals to provide enough time resolution to distinguish
small changes. Also, if the period decrease was slightly
greater than the subsequent period increase, the net period
change would be observed as a slight decrease in period,

102
exactly as was observed by Scarfe and Barlow. They might
have observed the beginning of the period decrease, with Nha
et al. observing the full effect shortly thereafter. In
support of this idea, it is noted that the period changes of
AR Lac are not constant: they have been observed to vary
from a minimum of 0^0013 to a maximum of 0^036 (Hall,
Richardson, and Chambliss, 1976). These variations are very
probably related to the variations in the number and sizes
of starspots on the stars when the wave minimum is at phases
0.25 and 0.75. A greater number of spots of greater size
would eject more material, thereby producing a greater
period change. Neither the results of Scarfe and Barlow nor
those of Nha et al. are included in Figure 4.
Distortion wave minimum and Ca II emission maximum.
Coincidence of the phase of the photometric distortion wave
minimum and the Ca II emission maximum has been observed in
RS CVn and UX Ari by Catalano and Rodono (1974), Evans and
Hall (1974), and Hall, Montle, and Atkins (1975), all
reported by Weiler (1975). If it could be shown that the
phase and epoch of the emission maximum follow the same
curve as the phase and epoch of the photometric distortion
wave-minimum of AR Lac, then there would be a strong
indication of a definite relationship between these
phenomena in AR Lac also.
Weiler (1978) reported a sudden decrease in emission
occurring at phase 0.47 in 1974. If this decrease could be
interpreted to be a decrease from a maximum, then this

103
maximum could be plotted on Hall, Richardson, and Chambliss'
(1976) migration curve for AR Lac to determine whether this
point lies on the curve. This point fits the curve at least
as well as (and in some cases better than) the photometric
points which were used to define the curve. (This portion
of the migration curve is not well-defined because there has
been only one data point for the photometric distortion wave
published for epochs later than 1974: Catón, 1981, reported
that in 1979 the phase of the distortion wave minimum lay
between 0.87 and 0.93. See Figure 4.)
During 1968-1972 Babaev (1974a,b,d) made photometric
observations of AR Lac. His graph (1974d) of change in
m magnitude of AR Lac versus phase exhibited a maximum
D
at phase 0.6395 (obtained by averaging the phases of the
three points defining the maximum). The peak spanned phases
0.6190-0.7097. This maximum was assumed by Hall,
Richardson, and Chambliss (1976 ) to be the maximum of the
photometric distortion wave, thereby allowing them to
determine the phase of the minimum of the distortion wave to
be 0.1395 by subtracting 0.5 phase unit from the phase of
the maximum. (Hall, Richardson, and Chambliss used phases
0.65 and 0.15, respectively; however the actual peak shown
in Babaev's table of data is at phase 0.6293, and the region
of maximum is defined by two other points, at phases 0.6393
and 0.6499.) Presumably also during 1968-1972 Babaev
(1974c) made his spectroscopic observations of AR Lac,
although no years were specified for these observations.

104
His graph of K-line equivalent width versus phase exhibited
a pronounced maximum at phase 0.6489. The peak occupied the
phase interval 0.5785-0.7214, and corresponded to a maximum
in absorption, a minimum in emission. Comparison of
Babaev's photometric and spectroscopic data revealed that
the photometric wave maximum and the emission minimum
coincided in phase because their phase intervals
overlapped. If it can be construed that this occurrence
implies that the photometric wave minimum coincides with the
emission maximum, then the desired correlation is
demonstrated between the photometric and spectroscopic
phenomena. Upon the assumption that the latter relationship
is valid, points were plotted for Babaev's distortion wave
minimum and emission maximum on Hall, Richardson, and
Chambliss' graph. The fit of these points to the curve is
excellent. (See Figure 4.)
To lend additional support to the correlation between
the photometric distortion wave minimum and the
emission-line maximum, the data of the present investigation
indicate a pronounced maximum in the equivalent width of the
K-line emission at phase 0.384. This point agrees extremely
closely with the phase at which the distortion-wave minimum
should occur in 1976-1977 (as extrapolated from Hall,
Richardson, and Chambliss' curve). The point falls well
within the ±0.1 phase unit uncertainty quoted by Hall,
Richardson, and Chambliss (1976).

105
Table 4
PHASE OF AR Lac AT DISTORTION WAVE MINIMUM, EMISSION MAXIMUM,
AND PERIOD CHANGE
Epoch3
(year)
Phase of
Distortion
Wave Minimum3
Phase of
Emission
Maximum
Phase of
Period
Changes3
1926.5-1932.1
0.35
1928.7-1929.6
0.25
1928.8-1931.8
0.35
1931.3-1931.8
0.30
1932
.25 (decrease)
1938b
0.58b
1939b
0.96b
1938.5-1939.9
0.15
1939.0-1941.0
0.20
1938.9-1941.0
0.25
1937.6-1955.4
0.10
1940b
0.94b
1946.5-1947.0
0.95
1957
.75 (increase)
1960.5-1960.8
0.65
1966
.25 (decrease)
1969.7-1970.8
0.15
1968-1972°
0.15°
1968.5-1969.0
0.98
1972.8-1973.0
0.88
1974 ±3-4 (predicted)
.75 (predicted
increase)
1974.7d
0.47d
1974.8-1975.0
0.72
1975e
observed period
decrease6
1976.9Q
0.3849
1979f
0.87-0.93f
a
b
c
d
e
f
g
Hall, Richardson, and Chambliss (1976) except where otherwise
indicated
Kron (1947)
Babaev (1974c)
Weiler (1978)
Scarfe and Barlow (1978), not included in Figure 4 - no phase
published
Catón (1981)
Hoffman, present investigation
See Figure 4

Figure 4
THE ENHANCED MIGRATION CURVE FOR AR Lac
enhanced migration curve is a composite of three relations between
at which certain phenomena have occurred and the epoch
the system
(year) of
filled circles form the original
Chambliss, 1976). This curve was
minimum of the migrating photometric
The
(orbital) phase
occurrence.
The asterisk, the boxes, and the empty and
migration curve for AR Lac (Hall, Richardson, and
constructed by plotting the system phase at which the
distortion wave has been observed versus epoch of observation. From the graph it can be
seen that between 1900 and 1980, the distortion wave minimum has migrated in longitude
through three complete migration cycles, or three times around the star, each sucessive
cycle being completed in less time than the previous one. The migration cycle period has
decreased from 45 to 15 years during the length of time that AR Lac has been observed.
Also included on the original curve are the calculated (but not actually observed) system
phases of the occurrence of the distortion wave minimum at which period changes have been
observed as a function of epoch of observation. A relationship is therefore almost
definitely demonstrated between distortion wave minimum and period changes; but, as
indicated by the data, no simultaneous observations of both events have been made to
verify the phase of the distortion wave minimum at the very epoch of a period change.
The additional points for the indicated observers were inserted by the author to
construct the enhanced migration curve. The data of Kron and Catón represent the system
phases at which the distortion wave minimum was observed at various epochs. The data of
Babaev, Weiler, and Hoffman represent system phases at which apparent extra-eclipse Ca II
emission maxima have been observed at various epochs. Coincidence of these three data
points with the curve for the other two relations indicates a tenative relationship among
all three phenomena, tenative because in only one instance--that of Babaev's data--is
there an apparent phase concurrence of an observed (presumably)
emission mamimum with an observed distortion wave minimum during
epoch.
extra-eclipse Ca II
(presumably) the same

PHASE
0.75
0.50
0.25
0.00 -
0.75 -
0.50
0.25
0.00
0.75
0.50
0.25
0.00
0.75
+
I
tp
' 0
Can
ERROR i 10.1 PHASE UNIT
OBSERVED PERIOD DECREASE
OBSERVEO PERIOD INCREASE
EPOCH OF EARLIER. UNOBSERVED PERIOD INCREASE
HALL. RICHARDSON. AND CHAMBLISS (1976 ) PREDICTED EPOCH
RANGE FOR PERIOD INCREASE
KRON ( 1947 ) PHOTOMETRIC DISTORTION WAVE MINIMUM
CATON ( 1981 ) PHOTOMETRIC DISTORTION WAVE MINIMUM
X CaD
ACan
a—d
BABAEV (1974 )
EXTRA-ECLIPSE
Can
EMISSION MAXIMUM
0.50
X
WEILER (1970)
EXTRA-ECLIPSE
Can
EMISSION MAXIMUM
-
A
HOFFMAN
EXTRA-ECLIPSE
Can
EMISSION MAXIMUM
0.25
-
1
1
1
1
1 1
|
i
•
1900
1910
1920 1930
1940 1950
I960
1970
I960
EPOCH
107

108
It can be concluded tentatively, then, that in AR Lac
there does exist a phase correlation between the minimum of
the photometric distortion wave and the maximum of the
extra-eclipse K-line emission.
Conclusion. Combination of the data obtained in the
present investigation and in other investigations has
indicated a possible relationship among the minimum of the
photometric distortion wave, the period changes, and the
maximum of the K-line emission in AR Lac: namely, that all
three of these phenomena appear to lie along the same curve
of phase of occurrence versus epoch. It appears that when
the (dark) starspot region is facing earth (phases 0.25 and
0.75), energetic matter ejected from this region would
produce not only period changes in the system but also a
minimum in the photometric distortion wave and a maximum in
the observed K-line emission.
Summary
Examination of the spectral plates of AR Lac and the
graph of K-line emission intensity versus phase in this
investigation indicates that the K-line emission of AR Lac
is present throughout the cycle and is phase- and/or
time-dependent, not random. The variations consist of two
parts: the geometrical effects of eclipse and the physical
effects of non-uniform emission over the surfaces of the
components.On an absolute scale the emission is stronger at
secondary mid-eclipse than at primary mid-eclipse.

109
The nature of the graphical relation between the K-line
emission and phase indicates that there is emission
generally produced over the entire surfaces (or at least in
complete equatorial bands). There are also concentrations
of emission in fixed regions at the tips of the tidal bulges
of both stars. Further, there is (1) possibly some non-
phase-dependent flare-like Ca II emission activity or (2)
possibly a Ca II-emission region migrating in longitude and
drifting in latitude.
The photometric and spectroscopic observations of
others and the line-profile asymmetry of the present
investigations confirm the presence of the surface emission
and discrete concentrations of emission, but they do not
establish any of the characteristics of the latter. The
general distributed emission accounts for the observation of
emission throughout the cycle; the tidal bulge emission
areas account for the behavior in the vicinity of and within
eclipse. Either the possible migrating source or the
possible flare activity accounts for the observation of the
extra-eclipse emission peak. The width of this peak is
interpreted as the partial duration of visibility of the
concentrated emission region, which is either an active area
carried in and out of view by the rotation of the star or a
flare which happened to occur at that phase.
Both components of AR Lac have deep convective
envelopes and do not have dominant tidal bulges; therefore
they appear to be good candidates for differential rotation
and the solar model of spot drift toward the equator.

110
The pre- and post-primary eclipse decreases in emission
are attributed to an increase in absorption due to a
circum-secondary envelope, the presence of which is further
supported by UBV photometric light-curve pre- and
post-primary eclipse depressions, scatter in infrared light
curves, ultraviolet and infrared excesses, and the symmetry
of the H-alpha emission profile within and outside of
secondary eclipse.
The phase of the minimum of the photometric distortion
wave, the phase of the maximum of the K-line emission, and
the phases of period changes apparently all follow the same
curve when plotted as a function of phase versus epoch. The
seeming contradiction of a period decrease at phase 0.72 in
1973-1976 is resolved by considering that the rapid
migration of the wave during that period and the poor
epoch-resolution of the observations probably blended an
initial period increase and a slightly larger subsequent
period decrease to produce the very small net period
decrease reported during that time period.
The period increases and decreases coincide with the
times at which the spotted area would be on the leading and
following edges of the star, respectively. At these .times
the photometric distortion wave would be observed at minimum
and the Ca II emission at maximum.

SECTION V
GENERAL MODEL
Introduction
In culmination of this investigation, models for AR Lac
and interpretations of previous observations of AR Lac are
presented, discussed, and augmented by the author. The
results of the present investigation have been incorporated
to form an integral part of these augmented models in order
to synthesize a general comprehensive physical and
evolutional model for the AR Lac system.
Explanations for H and K emission, other spectroscopic
anomalies, and photometric variations began with models for
the sun. These solar models were soon followed by a
plethora of models for the many different types of stars and
stellar systems which exhibit these characteristics.
Spectroscopic Characteristics
Ca II Emission
Many suggestions have been made for the site, size,
mechanisms, and motion of the Ca II emission in the sun and
other stars. Conclusions regarding the structure of these
stars have been drawn by observing the behavior of Ca II in
emission and absorption.
Site of the emission
Several widely differing stellar layers and surface
positions have been proposed as the site of the Ca II
111

112
emission in the sun and other stars. It seems likely that
the emission might not arise from the same site in all
stars.
The chromosphere. Examination of the solar Ca II lines
indicated to Deslandres (1894) that the emission arises in
an ascending layer in the chromosphere.
Confirmation of the solar chromosphere as the site of
the emission came from observations that the H and K
emission cores of the solar disc "merge smoothly with the
chromospheric emission bulge" (McMath et al., 1956, p.7) and
that the line intensities of the disc and the bulge are
similar. These data and observations showing that the
K-line emission is enhanced over plages provided these
observers with "convincing evidence" (McMath et al., 1956,
p.7) that in the sun the Ca II emission arises in hot
columns in the very low chromosphere.
Struve (1946) proposed that the emitting star in RW
Ursae Majoris has an extended tenuous calcium chromosphere,
tidally extended far beyond its photosphere. The emission
would therefore be most apparent at phases 0.25 and 0.75.
Further evidence that the emission arises in the
chromospheres of stars has been obtained by several
investigators. Wilson and Bappu's (1957) data for the
widths and the intensities of stellar H and K lines seemed
to indicate that the emission is produced in an optically
thin chromospheric layer. Wilson (1963) asserted that the
intensity of the H and K emission "must almost certainly be

113
a measure of general chromospheric activity" (Wilson, 1963,
p.833). He added that, in contrast, theories of earlier
observers seemed "to imply that all stars of given mass and
chemical composition should have equally strong reversals"
(Wilson, 1963, p.832). In their model for achieving the
best fit of observed Ca II line shapes with theoretical line
shapes, Linsky and Avrett (1970) identified the emission
site as being the lower chromosphere and further specified
that the chromosphere must be optically thick at the line
centers. Naftilan and Drake's (1977) calculations of the
thickness of the Ca II emitting layer in the secondary of AR
Lac yielded values compatible with what would be expected
for a chromosphere. From the small differences generally
observed between the radial velocities of the Ca II emission
and the Ca II absorption in late-type binaries, Young and
Koniges (1977) concluded that the emission originates "in a
chromosphere which is rigidly attached to the star, and not
in some gaseous stream extending between the component
stars" (Young and Koniges, 1977, p.839). The observed rapid
changes in the emission profiles over very short time
intervals in AR Lac were interpreted by Naftilan and Drake
(1977) as indicating that the components have very active
chromospheres.
By application of this interpretation of intense Ca II
emission as indicative of a chromospheric origin, the
presence of the strong Ca II emission observed in AR Lac in
the present investigation confirms the chromosphere as the
layer of origination of the emission.

114
An extended envelope. When Joy (1941a,b) observed that
the H and K emission lines in WW Draconis are displaced in
the same direction as the absorption lines of the secondary,
but exhibit a smaller range of displacement, he suggested
that this characteristic could be explained by a model in
which the secondary is surrounded by an envelope of emitting
Ca II gas which has a pronounced tidal distortion in the
direction of the primary. He offered support for his theory
by further noting that the emission lines are weaker at
secondary minimum, when a large part of this inter-component
gas would be occulted by the primary.
Gas streams. Struve (1945) proffered the idea that Ca
II emission lines in binary systems are produced primarily
in inter-component gas streams detached from the components.
The tidal bulges. Observations of RZ Cancri by Hiltner
(1946) revealed that the Ca II emission was absent during a
portion of the partial phases before and after primary
eclipse and during the entire totality of primary eclipse.
Hiltner interpreted this behavior to mean that "the emission
has its origin at both extremities of the elongated primary
star" (Hiltner, 1946, p.166). From the localization of the
emission observed in RZ Cnc and RW UMa Struve (1948)
inferred that in AR Lac the emission is also "in a localized
cloud at the extremities of the tidal bulges" (Struve, 1948,
p.155) of the AR Lac secondary. After determining that
differential gravitational acceleration over the surface of
a rotating star would produce currents which might have

115
velocities great enough to generate emission lines Gratton
(1950) concluded that "the currents are much stronger near
the bulges, which may explain the localization of the
observed emission" (Gratton, 1950, p.38).
The behavior of the emission in the present investi¬
gation indicates that the tips of the tidal bulges of both
components of AR Lac are responsible for a part of the Ca II
emission. (See Section IV.)
The entire stellar surface. Struve's (1952) observa¬
tions of AR Lac caused him to reverse himself on his
previous inference of the tidal bulges as the emission
sites. His spectra verified that when the AR Lac
secondary's Ca II absorption lines are narrow, its emission
lines remain broad. From this circumstance Struve concluded
that the emission lines originate either from the entire
stellar surface or from complete equatorial zones rather
than from localized areas on the tidal bulges. Further, for
RS CVn, Weiler (1978) deemed the tidal bulge model
"inadequate" because Catalano and Rodono (1969) were unable
to confirm Hiltner's (1947) observation of the disappearance
of the Ca II emission at secondary minimum. Oliver (1982)
has also confirmed that the emission in RS CVn does not
disappear during secondary eclipse.
The results of the present investigation indicate a
source distributed across the entire diameter of .each star
to be one contributing component of the emission. (See
Section IV.)

116
Patches. Struve (1945) indicated that the Ca II
emission in binaries is occasionally produced in the
atmospheres of the components, rather than always in gas
streams. As evidence for this stand he offered the fact
that the emission lines are often seen at great intensity at
the midpoint of primary eclipse, when any inter-component
gas streams would be occulted by the secondary. This
observation suggested that the lines are produced not only
in the sub-primary hemisphere of the secondary but also in
its anti-primary hemisphere. The lack of observed
broadening or doubling of the lines indicated that the
emission-source size is not as large as the entire
hemisphere of the secondary.
Struve's (1946) radial velocity measurements and
observations of emission-intensity changes with phase in RW
UMa induced him to conclude that the emitting region is
dynamically attached to one of the components rather than
being a detached feature. His calculations of the
diminution of the emission-1ine intensity which would result
from a uniformly distributed region of RW UMa undergoing
eclipse yielded a value far less than what estimates based
on his observations indicated would actually be observed.
(He could not make the actual measurements because he had no
plates during primary minimum.) From these calculations he
deduced that in RW UMa the emitting source is a non-uniform
distribution over the stellar surface.

117
Kron1s (1950) studies of late-type dwarf stars with Ca
II emission and non-uniformly luminous surfaces (surfaces
with small brighter and fainter areas) led him to propose
that the emission originates in these small areas. The
broadening of the Ca II and other emission lines in
Sanford's plates of AR Lac suggested to Kron (1952) that AR
Lac's patchiness must extend over a large range of longitude
in the equatorial region rather than being concentrated in
isolated areas. Weiler (1978) observed an extremely large
change in the Ca II emission level of AR Lac over a very
short period of time between second contact and
mid-secondary eclipse. He interpreted this rapid change as
possibly indicating the eclipse of a "localized emission
area" (Weiler, 1978, p. 88) on the secondary because the
observation could not be explained in terms of the eclipse
of an emitting area uniform over the surface of the
secondary.
In the present investigation also, evidence points
toward a concentrated region of emission on one AR Lac
component as one of the sources of the observed emission.
(See Section IV.)
Mechanism for and motion of the Ca II emission
One of the long-standing problems of Ca II emission has
been the determination of the mechanism by which the
emission is produced. Various mechanisms and motions,
presenting both large- and small-scale views, some based
purely on observations and others based entirely on

118
theoretical considerations, have been suggested as the Ca II
emission agent.
No detailed measurements of the motions of the emission
or of the overall structure of the Ca II line profiles
were performed in this investigation; consequently no
suggestions for emission agents are offered from this
source. For completeness, however, a brief review of the
conclusions of other researchers is presented. (See Linsky
and Avrett, 1970, for a wealth of information on the solar
Ca II lines and some information on stellar Ca II lines.)
Eruptive activity. Eberhard and SchwarzschiId (1913)
surmised that stellar H and K emission lines are probably
produced by the same types of eruptive activity that produce
the solar emission lines: namely, sunspots, flocculi, and
prominences. Struve (1945) also concluded that the origin
of the Ca II emission reversal may be similar to that in the
sun. Similar conclusions were drawn by Struve (1945) and
observers at the Yerkes and McDonald observatories (Yerkes,
1948 ) .
Kron's (1950) investigations of late-type dwarf stars
with Ca II emission and non-uniformly luminous surfaces led
him to propose that the Ca II emission arises in these small
areas by activity similar to that associated with sunspots.
Collisions and thermal gradients. The structure of the
solar Ca II lines was interpreted as being indicative of
vertical and horizontal (latitudinal) circulation of singly
ionized calcium vapor in the chromosphere (Deslandres, 1894,

119
as reported by St. John, 1910). The measurements of both
investigators indicated that the emission (K2) arises in an
ascending layer, whereas the absorption (K3) arises in a
descending layer. St. John (1910) further determined that
the absorption wings (Kl) are produced in a layer below the
K2 layer. St. John proposed that the high energy of the
rising emitting layer might be produced by a temperature
increase resulting from the transformation of mechanical
energy into heat, a process which would be precipitated by
the loss of velocity in the opposing rising and falling
layers.
Following along the same lines as St. John, McMath et
al. (1956) explained the presence of low-excitation and
high-excitation lines by re-proposing Giovanelli's (1949)
model, which suggested that the chromosphere is structured
with alternating hot and cool gas columns (these have been
observed as chromospheric supergranulation: Linsky and
Avrett, 1970; Abell, 1982). McMath et al. modified this
model slightly by adding cool overlying patches.
Observations that K-line emission is enhanced over plages
led to the conclusion that the emission (K2) arises in the
hot columns. They surmised that the absorption core (K3) is
produced by the emission passing through the cool overlying
regions. Persistence to the limb of asymmetry in the
emission profile ruled out St. John's (1910) interpreta¬
tion that the asymmetry is caused by the rising and falling
of the hotter and cooler columns, respectively. Instead,

120
the speculation was raised that the origin of the asymmetry
might be the expansion of optically thick, rising hot gases.
From calculations of differences in gravitational
acceleration over the surface of zeta Andromedae, Gratton
(1950) determined that the resulting velocity of the
currents expected in a rotating star "might be large enough
to cause the local inversion of the thermal gradient which
is required for explaining the [Ca II] emission lines"
(Gratton, 1950, p.38).
Wilson and Bappu's ( 1957 ) data for the widths and the
intensities of stellar H and K lines produced a theory
somewhat reminiscent of the solar theories of St. John
(1910) and McMath et al. (1956). Wilson and Bappu's data
seemed to indicate a picture similar to what is seen in the
sun namely, that the H and K lines are of nearly equal width
and of intensity ratio 1:2. This result is in accord with
Doppler broadening by turbulence in an optically thin
chromospheric layer, rather than with abundance broadening
(a pure damping profile) at large optical thickness. (They
noted that Goldberg, however, had indicated that it might be
possible to explain the broadening by abundance in an
optically thick layer.) These results led Wilson and Bappu
to offer the following extremely tentative model to explain
both the emission-producing mechanism and the functional
dependence of Ca II emission-line width upon luminosity in
late-type stars. They proposed that in all late-type stars
an outward flow of material would travel to the height of

121
the lower chromosphere, where laminar flow would become
turbulent. The mean spread of the turbulent velocity would
be a function of the flow velocity, which would in turn be a
function of luminosity alone. In the layer of turbulence,
kinetic energy of flow would be transformed into heat, which
would be absorbed to increase thermal excitation; and this
excitation would in part be responsible for the line
emission. The turbulence would reduce the original outward
flow velocity to a slow outward drift. Above the emitting
region would lie a cooler absorbing region of material
slowly falling inward. (On a similar theme Sanford, 1951,
had suggested that the difference between the radial
velocities of the Ca II absorption and emission in AR Lac
could possibly result from outward flow of the emission
source relative to the absorption source. He had reasoned
further that the absorption-line shallowness and width,
which is uncharacteristic of stars of such late spectral
types, is produced by rotational broadening in components
rotating synchronously with the revolution period of the
system.)
In further concurrence with the idea of collisions of
opposing intrastellar streams of matter are the observations
of the Cepheid-like variable BL Her (Lick, 1966). Hydrogen
and Ca II emission lines were observed during the rising
portion of the light curve, the emission and the atmospheric
velocity reversal occurring during a stillstand on the light
curve, when collisions of layers of material would be
maximal.

122
Linsky and Avrett (1970), on the other hand, concluded
that the H and K line profiles and the existence of the
emission are "direct consequences" of (1) a rise in
temperature in the lower chromosphere, (2) line formation by
the mechanism of non-coherent scattering, (3) a chromosphere
which is optically thick at the line centers, and (4)
non-thermal broadening which increases with height.
Goldberg (1964) surmised that the observed large
variations in emission width over the surface of the sun and
among stars would probably be caused by chromospheric
density gradients and temperature gradients in strata above
the emitting level.
Acoustic energy flux, the commonly assumed heating
source for chromospheres, was investigated by Young and
Koniges (1977). They determined that both the strength of
chromospheric emission and the strength of tidal coupling
are directly related to the ratio of the radius of a binary
component to its Roche lobe. Stronger tidal coupling would
therefore imply stronger chromospheric emission. Expansion
of one of the stars as it evolves would further enhance the
effect of tidal coupling. Combination of this result with
Linsky and Avrett's (1970) argument that strong Ca II
emission is indicative of a large chromospheric temperature
gradient and with Stein and Leibacher's (1974) theory of
chromospheric heating by acoustic energy transport (with the
photosphere acting as a low-pass filter) evoked the
suggestion that tidal coupling may enhance the chromospheric

123
heating tremendously by increasing the density scale-
heights. This activity would shift the acoustic spectrum
toward lower frequencies (the low-frequency cutoff limit
varies inversely as the scale height) and result in much
greater dissipation of acoustic energy in the chromosphere.
The resulting enormous increase in the temperature of the
chromosphere would produce the observed Ca II emission.
(See Blanco et al., 1974, for results for main-sequence
stars.)
Thermal effects were echoed by Hall (1976), who
inferred that "the extreme degree of the chromospheric
activity and spottedness might mean that the affected stars
are thermally unstable" (Hall, 1976, p.46).
On an atomic level Struve (1946) argued that in
binaries the Ca II emission arises in part by the mechanism
of ordinary resonance scattering (normal radiative
excitation). He emphasized that the emission mechanism is
not fluorescence
or
any
of
the
unusual means
of line
formation known
to
occur
in
some
regions of the
sun or
thought to occur
in
some
stars.
Struve ( 1948) ,
however,
recanted his earlier pronouncement by contending that in AR
Lac the emission mechanism is fluorescence.
Gas streams. Swings and Struve (1952) summarized
Struve's previous conclusion that "all close binaries are
associated with gaseous streams of a nature resembling
whirlpools. These streams produce emission and absorption
lines which are superposed over the normal stellar spectra

124
of the two components" (Swings and Struve, 1952, p. 412).
Babaev (1974c) suggested that the variation of the H and K
emission throughout the orbital cycle of AR Lac may be due
to gas streaming.
Binary character. A quite different mechanism was
offered by Swings and Struve (1941), whose observations of
late-type systems with Ca -II emission suggested that the
very fact that these stars are binary rather than single may
be the underlying cause of the emission. They stated that
"binary character stimulates the formation of emitting
shells or layers" (Swings and Struve, 1941, p.245).
Observations in support of this hypothesis were made by
Wilson (1963), who observed two main-sequence visual binary
systems (ADS 2644 and ADS 1889), each with a spectroscopic
binary companion. The spectroscopic binary in each visual
system exhibited much stronger Ca II emission than its
single visual companion, a circumstance which induced Wilson
to speculate rather tentatively regarding close binaries,
"excessive H and K emission is stimulated either because of
their relatively rapid rotation or in some other manner by
the nearness of the companion star" (Wilson, 1963, p.835).
He indicated, however, that rotation could not be the only
factor because one single star in another visual binary (ADS
14270 A) exhibited an amount of rotational broadening
similar to that in the two spectroscopic binaries; but the
strength of the emission in this rapidly rotating single
star was no greater than in its companion, ADS 14270 B.

125
From the observation that stars of the same spectral type in
visual binaries and in open clusters have similar emission
strengths Wilson concluded that the emission intensity
results from a kind of "genetic factor" (Wilson, 1963,
p.838) traceable to the past history of the star: viz., its
present age and the circumstances of its birth. A similar
viewpoint regarding the effect of duplicity was expressed by
Popper and Ulrich (1977) when they noted that the basis for
differences in the behavior of single KO IV stars and the KO
IV stars in the RS CVn systems undoubtedly lies in the
binary nature of the latter. Binariness would affect
rotation rate, magnetic field, and gravitational potential
(Popper and Ulrich, 1977) and would generate tidal coupling
(Young and Koniges, 1977).
Conclusion. It would seem likely that the binary
nature of AR Lac, the other RS CVn systems, and, in fact,
all close pairs would tend to excite or enhance behavior
such as the following, which would in turn produce the
observed Ca II emission: (1) eruptive activity, (2) surface
currents and vortices (which would induce collisions of
material and inversion of thermal gradients), and (3)
chromospheric heating by acoustic energy transport.
On the atomic level the line-forming mechanism which
seems best able to account for the core emission is
non-coherent scattering in an optically thick chromosphere.
The emission cores are Doppler-broadened predominantly by
turbulence rather than thermally.

126
Depressions in emission
Pre- and post-primary-eclipse depressions in the Ca II
emission observed in the present investigation were
attributed to an increase in absorption due to the presence
of a circum-secondary envelope. This conclusion was the
option left when it was determined that these net decreases
in emission could not be explained by an actual decrease in
the emission activity and be consistent with the three-part
emission model. (See Section IV.) There is both
spectroscopic and photometric evidence of such an envelope.
(See Section V: Stage of Evolution.)
Magnetic fields
Wilson (1963) inferred from studies of the sun that
there could also be in some other stars a strong correlation
between the local chromospheric magnetic field strength and
the intensity of the Ca II emission.
Observations of the sun revealed that the solar H and K
emission-line flux is higher in plages than in the quiet
chromosphere. In the main-sequence stars examined by Blanco
et al. (1974), the H and K emission-line fluxes were similar
in magnitude to plage fluxes, a correlation from which the
presence of magnetic fields in stars with H and K emission
was indirectly inferred.
Adhering to the theory that magnetic fields protruding
through the surface of a star produce starspots, Mullan
(1974) suggested that tidal effects in binary systems might
enhance the breakthrough effect, much as the alignment of

127
Venus, Earth, and Jupiter raises substantial (600-km) tides
which could trigger activity tides on the sun. (The idea
may have merit for close binaries; but Smith, 1983, states
that planet-raised solar tides of any magnitude are "a
fable" reminiscent of the "Jupiter Effect.") The magnetic
fields would be generated and maintained by dynamos produced
by fast differential rotation in a deep convective zone,
exactly the situation which exists in AR Lac. The presence
of spots is therefore indicative of magnetic fields in AR
Lac.
There have apparently been no measurements of the
Zeeman effect undertaken for RS CVn stars in order to
attempt to confirm by direct observation the presence of
such magnetic fields.
Other Spectroscopic Features
A number of salient spectroscopic features besides Ca
II emission are exhibited by stars with Ca II emission
lines. From these spectral characteristics a variety of
conclusions regarding the nature of these stars have been
drawn. A very brief mention of these spectroscopic features
is included, again for the sake of completeness.
Hydrogen, cerium, iron, and other metals
Struve (1945) and McMath et al. (1956) attacked the
problem of the origin of hydrogen emission. Sanford (1951)
and Struve (1952) sought to explain the phase-variability of
lines of iron and cerium in AR Lac. Included in their
respective theoretical pictures were (1) atmospheric heating

128
by bombardment by intercomponent or circum-component
particles and (2) on the sub-primary face of the secondary a
large spot of turbulent gases which would be the site of
prominence activity.
Radio emission
From observations of radio emission and a large radio
flare in AR Lac (Hjellming and Blankenship, 1973; Gibson and
Hjellming, 1974), Naftilan and Drake (1977) concluded that
the radio emission mechanism in AR Lac is unlikely to be
thermal bremsstrahlung from circumstellar material because
of (1) the flatness of the radio spectrum and (2) the rapid
increase of the radio flux during the flare, and because (3)
the size of the emitting region would be so large that it
would engulf the entire system, and not merely be
circumstellar about the secondary, as was suggested by
Atkins and Hall (1972) and Milone (1976a,b).
Because the radio spectra of AR Lac are evocative of
strong solar microwave bursts (which are generally
considered to be synchrotron radiation), Owen and Spangler
(1977) concurred with other observers that magneto-
bremsstrahlung from "mildly" relativistic electrons (as
often seen in solar flares) is the most probably radiation
mechanism. That there was no clearly defined eclipse of the
radio emission indicated that the source volume is much
larger than the. stellar components.

129
Photometric characteristics
Introduction
Many single stars and binary stars with Ca II emission
exhibit light curve behavior such as irregular light
variations and variation of light level with rotation. Many
eclipsing binaries exhibit such characteristics as asymmetry
of eclipses and migration of a quasi-sinusoidal wave-like
distortion (the photometric distortion wave in RS CVn
stars). Various mechanisms have been proposed to explain
these anomalies.
Depressions in the Light Curve
Hall (1976) interpreted Catalano's (1973) observation
of an approximate 0.05-mag depression in the light curve of
AR Lac just prior to first contact and just after fourth
contact of primary minimum to be caused by the eclipse of
the primary by an envelope or shell of material surrounding
and possibly filling the Roche lobe of the secondary. This
enveloping structure would result from mass ejection from
the brighter hemisphere of the secondary. These pre- and
post-primary eclipse depressions were explained similarly by
Rhombs and Fix (1977), who suggested that the optical
thickness of the material in a circumstellar
high-temperature gas flowing outward from the cool component
would be sufficient to produce the depressions.
Irregular Light-Curve Variations and the Photometric
Distortion Wave
Wood (1946) inferred from light-curve variations which
occurred only outside of primary minimum that the AR Lac

130
primary is intrinsically variable. Babaev (1971) and
Chambliss (1976) confirmed the presence of irregular
photometric variations in AR Lac. Chambliss concluded that
the surface luminance of the secondary is more uniform than
that of the primary. His observation that primary minimum
is much less distorted than secondary minimum substantiated
earlier conclusions that the intrinsic variability of the
system can be attributed primarily to the primary.
Wood (1946) eliminated pulsation as the agent causing
the intrinsic variation of the AR Lac primary, concluding
that the period of the observed variations would have to be
on the order of only a few hours, much shorter than that
actually observed.
These variations could be a part of the photometric
distortion wave; or, alternatively, they might be small
flares.
Catón (1981) concluded that any irregularities observed
in the light curves during eclipses of RS CVn stars must be
caused by some type of low-level flaring.
Several agents such as pulsation, a ring or shell of
material, gas streams, and starspots, have been proposed as
being responsible for producing the migrating quasi-
sinusoidal wave-like distortion in the light curves of the
RS CVn systems. Various arguments pro and con regarding
these suggested models have been presented.

131
Pulsation as the agent
Being unable to explain by either the ellipticity
effect or the reflection effect the periodic
phase-persistent distortion of the light curve of RS CVn,
Popper (1961) proposed the cause to be an
orbital-period-synchronous pulsation of the cooler star.
Distortions not persistent with phase would have a different
origin, such as Kron's "patches."
Chambliss (1976), however, concurring with Wood (1946),
ruled out pulsation as the cause of the intrinsic
variability of AR Lac because the theoretical pulsation
constant for Population I variables yields pulsation periods
much shorter than the time scale of the observed variations.
Ring, shell, or envelope as the agent
First proposed in 1967, a model to explain the
migrating photometric distortion wave in RS CVn was revived
by Catalano and Rodono (1974). They suggested that the
primary is surrounded by an extended, non-uniformly
distributed, absorbing equatorial ring which is tilted
relative to the orbital plane. Changes in the projected
area of this ring on the primary as a function of phase
would cause the photometric distortion wave in the light
curve outside eclipse. Precession of the rotation axis of
the primary would produce the retrograde migration of the
wave in successive cycles. Regarding this tilted ring
model, Oliver (1975) offered several arguments which cast
severe doubt on its validity. He enumerated kinematical and

132
photometric reasons that the existence of such a ring would
be highly improbable, among them the apparent lack of a
mechanism for the formation of the ring, the rapid loss of
non-uniformity which would occur in such a situation, and
the difficulty in explaining the blueing of the light at
photometric distortion minimum if the ring surrounds the
primary rather than the secondary. He also cited the fact
that there existed no spectroscopic evidence for an
absorbing ring.
Gas streams as the agent
A reanalysis of all the data from previous light curves
of AR Lac was performed by Theokas (1977). He made
application of Kopal's (1959) suggestion that a shock wave
created by hypersonic gas streams from the secondary
impinging on the atmosphere of the primary would produce a
bright spot on the primary. He therefore arrived at the
conclusion that the asymmetry in the light curve of AR Lac
is produced by "light spots," in contrast to Hall's (1972)
dark spots. (See Starspots as the agent.) Support for the
idea was evinced by Batten (1973), who demonstrated that for
short-period binaries, streams are more likely to be
prominent than discs or clouds.
Starspots as the agent
Observations of "small abrupt irregularities" (Kron,
1947, p. 264) in the light level of AR Lac during primary
ingress and egress prompted Kron (1947) to interpret these
changes by following in the footsteps (perhaps unbeknownst

133
to him) of many nineteenth-century astronomers. His
predecessors had ascribed light changes in some variable
stars to the existence of surface spots which are
alternately visible and hidden as the star rotates (Russell,
1906). Kron described the phenomenon as "huge light and
dark patches" (Kron, 1947, p.264) which he observed being
eclipsed and re-emerging during the partial phases of
primary minimum, thereby producing "steps" (Kron, 1947,
p.264) in the shoulders of his eclipse curves. His
photometric data indicated that at least 20% of one
hemisphere of the primary is covered by patches and that the
size of an individual patch is 3-5% of the hemispheric
area. Observations over several cycles of the system showed
that the light-curve irregularities caused by the patches
repeated themselves in consecutive cycles, thereby
indicating that the patches disappear and reappear around
the limb as the star rotates. Over longer periods of time,
though, the character of the light variations changed,
indicating that the patchy areas move across the surface of
the star and that they "form and dissolve" (Kron, 1947,
p.264). Regarding Kron's hypothesis that the AR Lac primary
is covered with large areas of differing luminances, Struve
(1952) deemed it reasonable to suppose that the secondary
might also be "patchy" (Struve, 1952, p. 22).
Through the use of starspot models, however, Catón
(1981) determined that short-time variations in light level
in or out of eclipse (e.g. Kron's "steps" during primary

134
eclipse) would not be caused by spots. Photometric
variations due to the presence of spots would be gradual
rather than abrupt. The occultation and reappearance of
spots during eclipse would therefore have no significant
effect on the light curve within eclipse. Spots visible on
the stellar disc outside eclipse would, however, cause a
gradual fall (the photometric distortion wave) in the
extraeclipse light level. "This strongly suggests that any
activity observed during an eclipse of an RS CVn system must
be some type of low-level flare activity, rather than any
kind of geometrical effect related to spots" (Catón, 1981,
p.68). (See Existence and observability of starspots.)
While analyzing four systems (AR Lac, RT And, RS CVn, YY
Gem) with light-curve distortions, Kron (1952) interpreted
the periodicity of the distortions with the rotation to be
clear evidence that the distortions are produced by the
rotation. In the light curve of YY Gem he noted that the
distortions outside eclipse could not be explained by tidal
effects or by the reflection effect because of the asymmetry
of the extra-eclipse light curve. During primary eclipse
the character of the distortions took on the form of
large-amplitude high harmonics of the rotation period. Such
harmonics would be generated only by the eclipse of a
spotted region during rotation (Russell, 1906), and not by
the mere presence of a spotted area on the surface of the
rotating star. Outside eclipse no such harmonics in the
distortions were observed. Because of the asymmetry of the

135
extra-eclipse light curve, the distortions outside eclipse
could not be explained by tidal effects or by the reflection
effect. Because the presence of the harmonics indicated
that the source of the distortions undergoes eclipse, Kron
concluded that this source must be either on the surface of
the star being eclipsed or between the two stars. He
favored the former alternative because material between the
two stars would be of a density insufficient to emit enough
energy to be observed by broad-band photometry. He
demonstrated that in YY Gem the distortions in and out of
eclipse could be explained by variations in light which
would result from foreshortening, rotation around the
limb,and eclipse of non-uniformly luminous areas on a patchy
model, as in AR Lac.
Enlarging upon Kron's basic idea, Hall (1972) devised a
more detailed model to explain the photometric anomalies of
the RS CVn group. He proposed that the migrating distortion
wave and the inconsistencies in the minima could be
explained by a stellar "sunspot cycle" incorporating an
equatorially centered band of large dark areas (Oliver's
suggestion to Hall) 60 degrees wide in latitude and 180
degrees long in longitude. The band would drift in latitude
and move with differential rotation (Marks' suggestion to
Hall) as the cycle progresses. (Although in close binaries
it is usually considered that the stars rotate synchronously
with the orbital period, Hall abandoned the idea of strict
synchronous rotation, reasoning that it would be expected

136
that a star in a binary system would exhibit differential
rotation as long as the tidal bulge raised by its companion
does not override the natural tendency of the star to rotate
differentially.) For stars with radiative envelopes the
rotation is faster at the poles than at the equator. For
stars with convective envelopes no theory has been
formulated (apparently still to date); however, the sun
serves as an example: the rotation is faster at the equator
than at the poles. The cooler star in RS CVn is cool
enough to have a deep convective envelope (Popper, 1961).
Estimates of the gravity-brightening index of the AR Lac
system indicate that both components have deep convective
envelopes (Chambliss, 1976). Even on a differentially
rotating star, however, there would be one latitude, the
"corotating latitude" (Hall, 1976, p.325), which would
rotate synchronously with the system. No theory or
observational procedure has been developed for the
determination of the corotating latitude.
If the starspots are rotating faster than the
corotating latitude (i.e., if they lie on the equatorward
rather than the poleward side of the corotating latitude),
the migration of the spots (and the distortion wave) would
be retrograde. The rate of migration would increase as the
latitude of the spots decreases, the maximum migration rate
occurring when the spots are the farthest from the
corotating latitude (and closest to the equator). When the
spots make the discontinuous transition from the maximum

137
retrograde migration rate (when farthest from the corotating
latitude) to the minimum retrograde migration rate (when
closest to the corotating latitude), the photometric
distortion wave would be at a minimum; and the Ca II
emission would be at a maximum (Weiler, 1975, 1978). (Weiler
reasoned that the coincidence of the phase of the maximum of
emission intensity with the phase of the minimum of the
photometric distortion wave in three RS CVn systems (UX Ari,
RS CVn, Z Her) is, by analogy with the sun, consistent with
Hall's (1972) spotted-hemisphere-active- chromosphere
model. Weiler based his argument on the fact that solar H
and K emission is associated with sunspot regions and an
active chromosphere.) The changing latitude of the spots on
the star would therefore be manifested by a change in both
the migration rate and the amplitude of the distortion
wave. This behavior is similar to what occurs during the
sunspot cycle as depicted in the solar "butterfly diagram"
(Hall and Henry, 1978 ), but this analogy with the sun is
valid regarding spot position and migration rate only, not
amplitude of wave. When a sunspot cycle ends, the spots are
at the lowest latitudes and are at maximum rate of
"migration" in longitude; but, simultaneously, when the
sunspots make the discontinuous transition from the lowest
latitudes to the highest latitudes (and from the maximum to
the minimum longitudinal "migration" rate), the "solar
distortion wave" is at a maximum, not at a minimum.

138
During a sunspot cycle the change in the amplitude of
the "solar distortion wave" is observed to be produced by
the continually changing number of spots on the solar
surface. From cycle to cycle in the sun, the amplitude of
the solar distortion wave minimum (which occurs at the
maximum number of sunspots) also changes. Presumably,
during a given starspot cycle and from cycle to cycle the
sizes and numbers of spots would vary also, as in the sun,
thereby producing (1) the observed continual changes in the
amplitude of the photometric distortion wave and its
ostensibly accompanying Ca II emission over one cycle and
(2) the variations in the minima and maxima of both
phenomena from cycle to cycle. These occurrences would
perhaps render both phenomena virtually unobservable during
some portions of a spot cycle, or even over several epochs
during a long interval of very few spots. (Along these lines
Oliver (1971, 1974) suggested that the common origin of the
distortion wave and the Ca II emission [and their
consequently coupled behavior in amplitude change] might
resolve the controversy regarding the reported disappearance
versus non-disappearance of the emission during secondary
eclipse of RS CVn.) Further, Weiler's (1978) observation of
basically random variations of the Ca II emission in AR Lac
and Caton's (1981) observation that the amplitude of the AR
Lac distortion wave was extremely low in 1979 support this
suggestion. Apparently no theory presently exists upon

139
which to base sizes or numbers of starspots during a
starspot cycle or from cycle to cycle. Further, no detailed
study of the changes in the amplitude of the distortion wave
in RS CVn stars has been completed in order to determine
whether the changes in the number of spots follow a
latitude-amplitude and cycle-to-cycle pattern mirroring that
of the sun. Changes in the migration rate in RS CVn (Hall,
1972, from the data of Catalano and Rodono, 1967, 1969) and
in AR Lac (Hall, Richardson, and Chambliss, 1976) have been
correlated with distortion wave minima.
In the model described above the spots always remain on
the equatórward side of the corotating latitude; therefore
the photometric distortion wave would be observed to always
migrate retrograde. Several RS CVn systems (UX Ari, SS Cam,
RS CVn, UX Com, WW Dra, Z Her, PW Her, GK Hya, RT Lac, AR
Lac, RV Lib, SZ Psc, TY Pyx, RW UMa: Hall, 1976) exhibit
retrograde migration of the wave.
In contrast, two RS CVn systems (SS Boo: Hall and
Henry, 1978; and V711 Tau: Chambliss and Detterline, 1979 )
exhibit direct migration of the wave. In SS Boo the
migration was observed to reverse itself from retrograde to
direct. Hall and Henry (1978) explained this reversal by an
extension of Hall's spot model and modeled the starspot
cycle (the cycle of migration and drift) after the solar
"butterfly diagram." While the starspots are rotating
faster than the corotating latitude (and their latitude is
lower than the corotating latitude), they would behave as

140
described in the retrograde model. When the spots make the
discontinuous transition from maximum retrograde migration
rate (when they are farthest from the corotating latitude
and closest to the equator) to direct migration (when they
are at a higher latitude than the corotating latitude and
rotating more slowly than the corotating latitude), the
photometric distortion wave would be at a minimum; and the
Ca II emission would be at a maximum (Weiler, 1975, 1978).
The direct migration rate would be at its maximum as soon as
the transition occurs because the spots would then be at
their highest latitude, their farthest poleward of the
corotating latitude. As the spots of the new cycle then
begin their drift toward the equator, they would exhibit a
slowing of the direct migration rate to a minimum (of zero)
when they cross the corotating latitude. The migration
would then revert to retrograde and increase from a rate of
zero (at the corotating latitude) to a maximum. In this
model the spots drift back and forth across the corotating
latitude.
The "starspot cycle" model could be further extended to
a third case, one in which the spots always remain on the
poleward side of the corotating latitude. The migration
would then always be direct because the spotted area would
always be rotating more slowly than the corotating
latitude. When the spots make the transition from the
minimum direct migration rate (when they are closest to the
corotating latitude and to the equator) to the maximum

141
direct migration rate (when they are farthest from the
corotating latitude and the equator), the photometric
distortion wave would be at a minimum, and the Ca II
emission would be at a maximum.
Because the starspot cycles for the RS CVn stars may be
quite long (23.5 years for RS CVn: Hall, 1972; and a
smoothly decreasing 45-15 years from 1900-1980 for AR Lac:
Hall, Richardson, and Chambliss, 1975), many years of
observation may be needed to establish the migration-and-
drift category to which each system belongs. AR Lac does,
however, obey the relation Hall (1976) established for the
period of migration: (O - C) — pmigr^' which allows a
calculation of Pmigr i-n advance of actual observation. The
length of the starspot cycle for stars in each category
could be determined by measuring (1) the time interval
between the maximum and minimum duration of visibility of
the Ca II emission, (2) the time interval between the
maximum and minimum migration rates of the photometric
distortion wave, and (3) the time interval between the
absolute minima of the photometric distortion wave.
Measurements of the phase-interval of visibility of the
emission would provide a measure of the rate of differential
rotation and the range of differential rotation, just as
measurements of sunspot motions perform this function in the
sun.
If the proposed spatial model for Ca II emission
activity in AR Lac from 1968-1977 is indeed the case (see
Section IV), the picture presented by this model would

142
integrate well with Hall's (Hall, 1972; Hall and Henry,
1978 ) model for the starspot cycle in RS CVn stars. The
spatial model would allow a diminution of the duration of
the visibility of the Ca II emission to be interpreted as
the drift of the Ca II emission region to lower latitudes,
with an accompanying increase in the migration rate of the
distortion wave. An ever more rapidly increasing migration
rate would signal the approaching end of of a starspot
cycle, as perhaps would a decrease in the distortion wave
amplitude, the latter phenomenon indicating a decrease in
spot number and/or size, as observed in the sun as a sunspot
cycle terminates. Both of these effects have been observed
recently in AR Lac. Hall, Richardson, and Chambliss (1976)
noted that the retrograde migration rate of the distortion
wave in AR Lac is increasing, the rate of increase being
quite rapid over recent years. Catón (1981) observed that
the amplitude of the distortion wave was very low (less than
0.01 mag) in 1979. As a result of these observations, the
author predicts that the distortion wave in AR Lac will soon
(1) reverse its migration from retrograde to direct and/or
(2) exhibit a discontinuous change in its rate of
migration--to a much slower rate, which will again either
(1) increase or (2) decrease and then increase, depending
upon on which side of the corotating latitude the spots of
the new cycle begin appearing.
The foregoing picture assumes that the drift is driven
by a pole-equator temperature differential and that the

143
equatorward drift (i.e., as in the solar sense) of the spots
is caused by the poles' being hotter than the equator
(Mullan, 1974). If the poles were cooler than the equator,
the drift would be poleward, as is indicated to be the case
for the spotted flare star CC Eri (Bopp and Evans, 1973, as
reported by Mullan, 1974).
Mullan (1974) hypothesized that starspots are
convection cells which extend throughout a star's convection
zone and that the deeper the convection zone, the larger the
spot sizes. (Measures of the depth of the convection zone
would therefore provide a means of ascertaining the sizes of
starspots.) The drift category of a system might therefore
be indicative of the internal structure (depth of convective
zone and consequently, spot size) of the spotted
component(s) of a system or of its/their evolutional stage.
Mullan (1974) suggested that in stars which have
convective shells or envelopes rather than being convective
throughout the entire stellar radius, spots would exist at
latitudes away from the polar regions. Stars of this
description could fall into any of the three migration-drift
classifications, depending upon the latitude of the
corotating region. Mullan determined that in these stars
the variations in brightness produced by the rotation of the
spots across the stellar disc would be periodic, the
variations of greatest amplitude being observed in stars
which are almost completely convective. It is assumed that
the Ca II emission would follow the same pattern of

144
variation. The components of AR Lac are stars with deep
convective envelopes (Chambliss, 1976); therefore they would
be placed in the convective shell category, a classification
which is confirmed by the periodicity of the photometric
variations and the Ca II emission variations. The starspots
of AR Lac would be rather large, because starspot size
varies directly as the depth of the convection zone (Mullan,
1974).
Mullan suggested that in completely convective stars,
on the other hand, the multipolarity of the stellar magnetic
field might be such that the starspots would be confined to
the polar regions. Mullan indicated that this situation
would produce no periodic variation in the brightness of the
star; instead there would be only non-periodic changes in
brightness as the spots formed and decayed. Presumably the
Ca II emission would reflect the same non-periodic
irregularity. It might be concluded that in this case spot
migration would fall into the category of direct migration
only, the spots always being poleward of the corotating
latitude. For a completely convective star the spots would
be extremely large because the convection zone would be very
deep.
Perhaps there
migration-type and
For example, the
is some evolution of the stars from one
spot-location classification to another,
evolution might begin with completely
convective stars (having very large, pole-confined spots,
irregular light variations, and direct migration), proceed

145
through a stage with a deep convective shell (characterized
by intermediate-latitude, slightly smaller spots, periodic
light variations of slow migration rate, and alternating
direct-retrograde migration), and finally end in a stage
with a thin convective zone (with small spots close to the
equator, periodic light variations of fast migration, and
retrograde migration). On the other hand, such categories
might not be evolutional, but instead be determined by some
non-variable (or nearly so) characteristic of the star or
the system (e.g., mass, size, differential rotation rate,
separation, or period).
Existence and observability of starspots. The
existence of starspots (small faint or bright photometric
areas and/or Ca II emission areas) has been strongly
indicated in many stars, the sun being the only star on
which the phenomenon is visually observed.
The migrating photometric distortion wave in AR Lac
certainly provides evidence of the existence of large groups
of differentially rotating spots (Hall, Richardson, and
Chambliss, 1976).
Migrating starspots were indicated to Kron (1947) by
his photometric observations of "steps" in his light curve
and their night-to-night shift in phase on the shoulders of
primary minimum ingress and egress of AR Lac. He contended
that the steps were generated by individual spots
("patches") being occulted and reappearing, and that the
overall degradation of the shoulders and its shift in phase

146
was indicative of a group of spots in migration. Catón
(1981), on the other hand, concluded that detection of
individual starspots and the measurement of their sizes by
observing for irregularities in the light curve of the
partial phases of eclipse would be unlikely. His conclusion
was based on the determination of the theoretical
observability of starspots in RS CVn by construction of a
theoretical light curve by constraining the inter¬
relationship of the spot temperature and size so that the
spot flux remained constant and produced the observed
photometric distortion wave and depth of secondary eclipse.
The only irregularities exhibited by his theoretical curves
were on the order of a few ten-thousandths of a magnitude,
values which he concluded were one order of magnitude too
small to be observable even by the best earth-based
telescopes. He then strongly suggested that any
irregularities observed during the partial phases of
eclipses must therefore be produced by low-level flaring
rather than individual spots. The entire group of spots
could, however, be observed when they are all together on
the earthward surface of the star--the group generates the
photometric distortion wave. The discrepancy between Kron
and Catón could have at least two bases: (1) Each person
was observing a different star with different character¬
istics (AR Lac and RS CVn, respectively), and (2) each star
could have been at a different level of activity, with
numbers and sizes of spots sufficiently different to produce

147
the contradictory results. Further, Kron's probable error
for a single normal point was approximately 0.001 mag,
precise enough to allow him to easily observe the individual
departures of the "steps" from his normalized light curves—
the "steps" were typically depressed 0.01-0.05 mag below
Kron's smooth normal curves, two orders of magnitude greater
than Catón's required minimum for detectability. Neither
the shape of Kron's "steps" nor their pattern of phase shift
from night to night or epoch to epoch has the appearance of
random scatter or random events (such as flares). The phase
of the leading depression in each group regressed smoothly
from about phase 0.06 in 1938 to about phase 0.94 in 1940.
Although Kron's 1938-1940 observations (Kron, 1947) were not
included in Hall, Richardson, and Chambliss' (1976) analysis
of the migration of the distortion wave of AR Lac, the phase
shifts cited above
do
lie
in the
same region
of
the
migration curve for
AR
Lac
as the
observations
used
to
define that curve during that same time interval (those of
Gainullin, 1943; Wood, 1946; and Ischenko, 1963--see Figure
4). Kron therefore undoubtedly observed the distortion wave
in AR Lac nearly 30 years before its presence was announced
and apparently also observed large individual spots.
Detectability of large individual spots would then
provide a means whereby the depth of the convective zone
could be measured: the larger the spots, the deeper the zone
(Mullan, 1974). Values obtained by this method could then
be compared to those indicated by surface temperature

148
(Popper, 1961) and by gravity-brightening index (Chambliss,
1976 ) .
The observations of peaks of Ca II emission in AR Lac
by Babaev (1974c), Weiler (1978), and in the present
investigation also speak strongly in favor of starspots, or
isolated Ca II emission areas. The asymmetry of the Ca II
line profiles in the present investigation further indicates
a non-uniformity of light over the stellar disc (Huang and
Struve, 1960).
A final piece of evidence for the existence and
observability of starspots is the observation of
fluctuations in the light curve of HD 206860 (Blanco,
Catalano, and Marilli, 1978). The light variations of this
single star, unencumbered by the presence of a companion,
could be interpreted only as starspots because these changes
occurred periodically with the rotation of the star.
Conclusion
The starspot model provides the most self-consistent
explanation for the migrating photometric distortion wave,
and there is much observational evidence in its favor.
Pulsation and a tilted ring are clearly ruled out.
Period Changes
Introduction
Many systems, AR Lac included, have been observed to
undergo abrupt period changes. Very large O - C values
indicate that the period used in calculating the orbit of a
system differs considerably from the period of that system

149
at the epoch of the observations. Several explanations have
been offered for these period changes.
Mass Loss as the Mechanism
Following up on his discovery that AR Lac exhibited a
sudden period change, Wood (1950) offered as possible
explanations for such behavior in binaries: (1) faster-
than-synchronous rotation of the fainter component, a
process which would increase its tendency toward rotational
instability, which would in turn increase its tendency
toward mass loss (however, such non-synchronous rotation had
not then and has not now been detected in AR Lac), or (2)
eruptive prominences (similar to those on the sun) by which
large amounts of material escape from the star by being
explosively ejected beyond the Jacobi limiting surface. The
direction of ejection of the mass would determine whether
the period change is an increase or a decrease. Also, (3)
if the Roche model is not assumed in this analysis, then
changes within the star? could cause period changes. AR Lac
was the only system to exhibit a sudden period change and
not be near dynamical instability.
Lsechnikov (1955) concurred with Wood's interpretation
in terms of an ejection mechanism, as did Theokas (1977).
Assuming that the secularly expanding subgiants are
thermally unstable, Theokas utilized Martynov's (1977)
proposal that macroscopic motions in the atmospheres of such
stars could cause material to travel beyond the equi-
potential surface,
thereby escaping
the system.
The

150
decrease in angular momentum corresponding to this mass loss
would produce a period change. Biermann and Lust (1960)
found considerable spectroscopic evidence among many
observers of very great turbulence velocities in binary
components, these large velocities being indicative of
prominence activity on a very large scale with the resultant
ejection of material generating the measured period changes
in these systems.
Following along the same lines as Wood (1950), Hall
(1972) advanced the theory that changes in the orbital
period of RS CVn would be explained by mass loss from the
dark (spotted) hemisphere of the cool star, in much the same
way that material is ejected in solar flares. Ejection of
material from this dark region would occur on a continuous
basis, rather than intermittently. When the dark area is on
the leading edge of the star and mass is ejected primarily
in the forward direction, the period of the system would be
decreased. When the dark area is on the following edge of
the star, the period of the system would be increased.
(Hall, 1972, had originally stated that the period would be
increased by mass ejection from the leading hemisphere.
Arnold and Hall, 1973, corrected this to read as shown.
They also changed the mass-ejecting area of the star from
the fainter to the brighter hemisphere.) Velocities of
ejection would be on the order of those of solar flares:
viz., a few thousand km/sec. For an ejection velocity of
3000 km/sec, the annual mass loss required to produce the

151
observed period change is 10~^ M@/yr, admittedly very large,
Hall agreed. Some argument ensued, Catalano and Rodono
(1974) objecting to high-velocity impulse-type mass ejection
from the brighter hemisphere on the basis that it would be
expected that flare-type mass ejection would originate from
the darker hemisphere, where the spot activity is supposedly
occurring. They also objected to the large annual mass loss
required by the model. Hall (1975a) countered their first
objection by stating that the mechanism for mass ejection is
not known; therefore it would be presumptuous to assume that
one hemisphere (either bright or dark) is a more probable
site for the ejection activity. In further support he cited
Vogt's (1974, 1975) observations of the flare star BY Dra,
which apparently exhibits a dark region at some epochs and a
bright region at others, thereby suggesting that "active
regions on 'spotted stars' can be either dark or bright"
(Hall, 1975a, p.223). Hall (1975a) also offered in evidence
nine observed phenomena accounted for by his mass ejection
process, as opposed to only four phenomena accounted for by
Catalano and Rodono's (1967, 1974) tilted-ring model. Hall
(1976) further countered Catalano and Rodono's arguments by
offering as another possible ejection process the corotation
of the ejected mass out to some Alfven radius (Oliver's
suggestion to Hall: Oliver, 1983a), a mechanism which would
(1) allow the observed period changes to occur with less
annual mass loss because of the longer effective moment arm
of this radius compared to the orbital axis of the
mass-ejecting star, and (2) explain the presence of ejected

152
mass above the brighter hemisphere by allowing the curved
path of the ejected mass to extend from the darker
hemisphere to that part of the Alfven radius above the
brighter hemisphere. Hall (1972) indicated that the two
orientations of the dark area relative to the system when
period changes occur are when the dark area faces earth, at
phase 0.25 for period decreases and at phase 0.75 for period
increases. Correlation of respective period decreases and
increases at these two phases have also been observed in two
other RS CVn stars: SS Cam (Arnold, Hall, and Montle, 1973)
and AR Lac (Hall, Richardson, and Chambliss, 1976)--see
Section IV. Hall (1976) stated that there would be a
general tendency for periods of binary systems to decrease.
Mass loss from the system would produce a net loss of
angular momentum, thereby bringing on the period decrease.
Component Interaction as the Mechanism
Chambliss (1976) noted that in semi-detached or contact
system period changes v/ould be expected. AR Lac, however,
is detached by a wide margin (Oliver, 1974; Chambliss,
1976 ), as are all RS CVn binaries (Hall, 1976 ). Chambliss
interpreted AR Lac's substantial period changes as
indicative that there is much greater interaction between
its components than in "more normal" detached systems.
Other Effects as the Mechanism
While investigating the period changes in AR Lac, Hall,
Richardson, and Chambliss (1976) rejected several theories
previously presented by other investigators to explain the
period changes:

153
(1) Apsidal motion was ruled out because of the similarity
of the patterns of the O - C residuals for primary and
secondary eclipses and because of the lack of
sinusoidality of the O - C curves.
(2) Orbital motion about a third body was eliminated
because of the lack of suitable periodicity of the
O - C curve and because of the absence of spectroscopic
evidence for a third body.
(3) Mass transfer by the Biermann-Hall mechanism (Biermann
and Hall, 1973) was discounted, being inapplicable
because AR Lac is not semi-detached.
(They did not offer any explanation(s) to supersede these.)
Correlations of Phenomena
Introduction
There has been much evidence gathered to indicate that
several phenomena observed in both single and binary Ca II-
emission stars are related.
Spectroscopic-Photometric Correlation
Kron (1950) suggested that both the Ca II emission and
the flares observed in late-type dwarf emission stars
originate by sunspot-like activity in the photometrically
detected small brighter and fainter areas on the surfaces of
these stars. Noting that in AR Lac and probably in YY Gem
the intensity of the Ca II emission lines varies with
orbital phase led Kron (1952) to state, "The similarity in
the behavior of the emission lines with the behavior of the
photometric distortions lends weight to the conclusion that

154
the two phenomena have a common origin" (Kron, 1952,
p.315). Oliver (1971, 1974) concurred with Kron,
postulating that the emission in some systems might be
related to the moving photometric distortion.
Weiler's (1975, 1978) discovery that the phase of the
Ca II-emission maximum coincides with the phase of the
distortion-wave minimum in UX Ari, RSC Vn, and Z Her led him
also to the conclusion that there exists a relationship
between these spectroscopic and photometric phenomena.
Observations by Babaev (1974c,d) considered alone and
also in combination with the findings of the present
investigation appear to extend the distortion-wave-Ca II-
emission relation to AR Lac. The interpretation of Babaev's
data indicates that the observed minimum of the photometric
distortion wave and the observed maximum of the Ca II
emission coincide in epoch. In the present investigation
the observed Ca II emission maximum coincides in epoch with
the photometric distortion wave minimum predicted by Hall,
Richardson, and Chambliss (1976). Also, Weiler's (1978)
observation of an apparent extra-eclipse emission maximum
lies on this migration curve for AR Lac as do the data
points representing the observations cited above. (See
Section IV. )
Further evidence of a general relationship between
photometric and spectroscopic observations is provided by
the non-periodic variability of the H and K emission of HD
206860, a single GO V star, which was observed by Blanco,

155
Catalano, and Marilli (1978). They interpreted this
behavior to indicate chromospheric activity. Intrinsic
photometric variations of the star were observed to have a
period consistent with what would be expected for the
rotation period of a star of this spectral-luminosity type.
It was therefore surmised that the photometric variations
are caused by spots (active regions) associated with the
observed chromospheric Ca II emission activity.
Photometric-Infrared Correlation
Discovered by Hall, Montle, and Atkins (1975), a
relationship between the migrating photometric distortion
wave and the infrared excess in UX Ari indicated the
possibility that the same mechanism causes them both. A
similar relationship might exist in AR Lac and other RS CVn
systems.
Photometric-Radio Correlation
Observations by Guinan et al. (1979) of rapid migration
of the distortion-wave minimum and changes in the light
curve of HR 1099 (V711 Tau) evoked the suggestion that there
is an association between these occurrences and the radio
outbursts which were observed during the same time
interval. They concluded, "Assuming that the light
variations are caused by starspots on the active component,
it would appear that the configuration of the spotted
regions has changed significantly" (Guinan et al., 1979,
p.3). Although several attempts have been made, no correla¬
tion of optical behavior (eclipses and other variations) and

156
radio behavior (general variability and outbursts) has been
observed in AR Lac (Chambliss, 1976; Owen and Spangler,
1977). These observations were, however, by no means
exhaustive; there may yet be some relationship found.
Luminosity Correlations
Gratton (1950) determined that there is a
period-luminosity relationship for late-type binaries with
Ca II emission. The positions plotted on an (M, log P)
graph for all the systems studied fell between the limits
0.3M + log P = 1.0 and 0.3M + log P = 2.5. Wilson and Bappu
(1957) discovered a relationship between the logarithm of
the H and K emission-line widths and the absolute magnitude
of stars with Ca II emission: the line width varies as the
one-sixth power of the luminosity.
Conclusion
Based upon the results obtained in these observing
programs it seems evident that relationships between the Ca
II emission and the photometric distortion wave and between
the distortion wave and infrared and radio emission exist in
many of the RS CVn systems and perhaps will be discovered in
all of them. The two luminosity relations have been
verified for a wide range of system magnitudes.
Evolution of Stars with Ca II Emission
Introduction
There are many arguments which have been posed
regarding the age and evolutional stage of stars with Ca II
emission. In particular, much controversy has arisen

157
regarding the age and stage of the RS CVn stars. Attempts
have been made to find relationships between the ages of
these systems and their various physical, photometric, and
spectroscopic parameters.
Stage of Evolution
Pre-main sequence
The evolutionary status of binary systems with
undersize (not filling their Roche lobes) subgiant
secondaries was investigated by Roxburgh (1966), who
advanced the hypothesis that such systems are in a pre-main
sequence stage and that their present binary state has
resulted from the fission of a rapidly rotating single
star. Following up on Roxburgh's study, Field (1969)
considered eighteen such systems, AR Lac included. For the
primaries of all the systems, good agreement was obtained
between ages calculated from the radius and from the
effective temperature. This result indicated that the
pre-main sequence tracks chosen for the primaries were
"adequately" represented by his derived equation relating
mass, radius, and effective temperature of the primary as a
function of time. For the AR Lac secondary and for the
majority of secondaries considered, however, the radii
calculated from the primaries' ages differed considerably
from the observed radii of the secondaries, thereby
indicating that the hypothesis of a pre-main sequence stage
is in error. As a result of the fact that the
pre-main-sequence-contraction hypothesis was not

158
self-consistent for all the systems studied, he proposed
that "Kopal's [1958] 'systems with undersize subgiant
secondaries' form an observational rather than an
evolutional class of objects" (Field, 1969, p. 419). Based
in part upon the extreme strength of the H and K emission in
the RS CVn systems, Hall (1972; 1974; 1975a,c), too, made
the suggestion that they are in a stage of pre-main sequence
evolution, thereby placing them at a phase between the T
Tauri stars and the late-type dwarf emission stars.
Post-main sequence
To the contrary, Oliver (1974) favored the view that
the systems in the RS CVn classification are in a
long-lived, somewhat evolved stage, this conclusion being
based on the observed characteristics of the components and
on the large number of systems in this group.
Biermann and Hall (1976) argued that the most probable
stage of evolution for the RS CVn systems is that they are
in a post-main sequence thermal phase following fission of a
rapidly rotating single main-sequence star. In particular,
Hall (1975b) concluded that WW Dra could not be in a
pre-main sequence stage because both components of the
system are more massive than their F8 V visual companion,
ADS 10152 B. Given the usual premise that stars in a system
are formed coevally, the more massive stars would have
evolved to a more advanced evolutional stage than the less
massive one in the same length of time. The facts that (1)
the RS CVn systems occupy the Hertzsprung gap, (2) they are

159
not associated with regions known to be presently engaged in
star formation, (3) the post-main sequence lifetimes are 100
times as long as the pre-main sequence lifetimes of stars of
the same mass and size, (4) the more massive star in a
system usually has the larger radius, and (5) two systems
have low-luminosity main-sequence visual companions which
could not have evolved to the main sequence ahead of the
higher-mass, higher-luminosity components of the
spectroscopic binaries constitute five pieces of
"circumstantial evidence" (Popper and Ulrich, 1977, p.L131)
from which Popper and Ulrich also inferred that these stars
are in a post-main sequence evolutional stage. They
suggested that these systems have evolved through the main
sequence by the normal processes of single-star evolution.
In the post-main sequence phase the RS CVn instabilities
would become manifest when the stars have exhausted their
core hydrogen and have developed convective envelopes. At
this stage normal single-star evolution would be accelerated
by mass exchange or loss through a mild stellar wind from
the larger component as the stars expand toward the giant
stage (Popper and Ulrich, 1977). Oliver (1974) proposed a
model with slow mass transfer (much like the solar wind)
"leaking" mass through the inner Lagrangian point. In
support of this picture Popper and Ulrich offered the fact
that mass flow is evidenced by the observed period changes
in these systems; and active surfaces and extra-stellar mass
are revealed by the observed strong Ca II emission, the

160
variable H-alpha emission, the infrared excess, and the
variable radio emission. From Popper and Ulrich's (1977)
theory, Naftilan and Drake (1977) inferred that AR Lac is in
a thick-shell-burning phase of evolution.
Further evidence of a post-main sequence stage for Ca
II emission systems was provided by Young and Koniges
(1977). The observations that longer-period systems without
Ca II emission are less evolved and have larger orbital
eccentricities versus the "strong tendency" (Young and
Koniges, 1977, p. 841) for systems of similarly long period
and with H and K emission to be evolved and to have zero
eccentricity led Young and Koniges to propose that the time
scale for circularization of orbits is long on the stellar
evolution time scale. For stars from 1-3M0 in longer-period
systems (15^-30^) circularization would take place during
the post-main sequence phase when tidal coupling would be
stronger because of the increased radii of the stars. For
the shorter period systems, however, circularization would
be completed during the main-sequence stage. Following this
line of reasoning, the fact that AR Lac is a short-period
binary (1^983: Rugemer, 1931) with an orbit of zero
eccentricity (Sanford, 1951; Chambliss, 1976) therefore
indicates that it has completed its main-sequence stage.
Circumstellar matter, component masses, and population
count. Additional evidence of evolutionary stage is
provided by the presence or absence of circumstellar matter,
measurements of the masses of the stellar components in

161
binaries, and the population count of the systems in
existence.
The observations in the present investigation and in
other investigations (Kron, 1947; Sanford, 1951; Catalano,
1973; Hall, 1976, Rhombs and Fix, 1977; Naftilan and Drake,
1977; Owen and Spangler, 1977) of pre- and post-primary
eclipse depressions in the Ca II emission and in the light
curve of AR Lac indicate the presence of a circum-secondary
cloud of material. Further, Rhombs and Fix (1977),
indicated that the most likely source of the apparent metal
deficiency in the AR Lac secondary (Miner, 1966; Naftilan
and Drake, 1977) is free-free emission from circumstellar
high-temperature gas flowing outward from the cool
component. The emission from this circumstellar material
would fill in absorption lines and diminish the equivalent
widths of weak metal lines. Miner's (1966) line of
reasoning, however, had produced a contradicting result. He
deemed it improbable that the metal deficiency which is
found in every eclipsing binary would stem from their all
having been formed in metal-poor regions. He contended that
there must be some mechanism in these systems which is
responsible for depleting metal content or masking
absorption by metals. Mass ejection would not fulfill the
necessary requirements because it would be more likely to
deplete the hydrogen-rich outer layers, thereby producing
just the opposite of the desired effect. Further evidence,
however--see below--overruled Miner.

162
Measurements of the infrared excess of AR Lac led
Atkins and Hall (1972) to the conclusion that it seems to be
an intrinsic property of the star rather than being an
extrinsic characteristic arising from a source such as a
circumstellar dust cloud. Countering this view, Rhombs and
Fix's (1977) observations of AR Lac indicated that free-free
emission from high-temperature circumstellar material
flowing outward from the secondary would account for the
observed infrared excess. In addition, they stated that
this emission from this material would be the most probable
source of AR Lac's ultraviolet excess, which increases below
4600A as wavelength decreases.
Observations of the hydrogen spectrum of AR Lac
prompted Naftilan and Drake (1977) to propose that a
circum-secondary envelope exists in the AR Lac system,
thereby also challenging previous statements to the
contrary. They determined that the symmetry of displacement
of emission cores from the centers of the Balmer lines of
the secondary of AR Lac indicates the presence of a
circum-secondary non-equilibrium corotating envelope or disc
which would intermittently lose mass to the primary.
The existence of this circumstellar material in the AR
Lac system indicates that some mass exchange has occurred
(and is perhaps still occurring, because the cloud may be
unstable). Mass exchange is an additional characteristic of
a post-main sequence phase. Oliver (1974) and Popper and
Ulrich ( 1977 ) each proposed for the RS CVn systems a model

163
which involved a solar-wind-like slow mass transfer. This
mass flow is revealed in the RS CVn stars by their enhanced
chromospheric activity (Morgan and Eggleton, 1979) and by
their period changes (Popper and Ulrich, 1977.).
In all early investigations the larger of the two
components of AR Lac was measured to be the slightly more
massive one, so that evolution of the larger, more massive
star was advancing slightly faster than that of the smaller,
less massive one, in the traditional sense. In his mass
measurements of improved precision, however, Popper (1967)
determined that the masses of the two stars are reversed.
The RMS errors overlap though, thereby indicating that the
stars are of essentially equal masses. The components
therefore sit on the fence with regard to evolutional
analysis on the basis of mass. Perhaps the mass exchange is
such that the two stars see-saw back and forth
evolutionally: as one's mass increases and the other's
decreases, one surges ahead for a short period; then the
other accumulates enough of the former's cast-off mass to
tip the scales in its favor, and it surges ahead. This type
of activity would take an extended period of time, thereby
causing the RS CVn stage in the lives of the system
components to be an enduring one rather than an ephemeral
pre-main sequence one.
This picture would confirm Oliver's (1974) assertion
that the RS CVn stage is a long-lived (post-main sequence)
one in view of the large number of these systems in

164
existence. To lend additional support to a high population,
Hall (1976) calculated the space density of the RS CVn
systems to be very large. Further, new RS CVn systems are
continually being discovered.
Popper and Ulrich (1977) contended that the RS CVn
characteristics arise when the core hydrogen is exhausted
and convective envelopes have developed. Morgan and
Eggleton (1979) concurred, asserting that the RS CVn
characteristics would be most probable in systems in which
the more massive component has evolved to the base of the
giant branch, but has not exceeded its Roche lobe, and the
less massive component has evolved to a point just before or
just after core hydrogen exhaustion. Further, mass loss by
a stellar wind from the more evolved component could be
consistent with the enhanced chromospheric activity observed
in these stars.
Additional evidence of the evolutional stage of the AR
Lac components, presented by Lacy (1979), is somewhat
contradictory. It appears definite that neither component
is on the ZAMS, but other data place the stars in mildly
questionable states. According to Lacy's (1979) data, the
low luminosity of the AR Lac primary places it below the
ZAMS, a characteristic which Lacy associates with primaries
of systems which have undergone mass exchange. The large
radius of the primary, however, places it above the ZAMS.
The low luminosity and the radius of the primary further
indicate that the star has not yet reached the point of

165
core-hydrogen exhaustion
The
results for
the
secondary are
slightly
less
ambiguous.
Its
radius
and luminosity
establish
its
pos ition
above
the
ZAMS.
Its
large radius
indicates
that
it has
reached
the
stage
of
core-hydrogen
exhaustion
, but
its low
luminosity
points
toward an earlier
stage.
Based on the facts that mass exchange has occurred,
that the radii of both stars place them above the ZAMS, and
that both stars are close to, if not at, the point of
core-hydrogen exhaustion, it can probably be concluded from
the data of Morgan and Eggleton and Lacy that both stars are
in stages following rather than preceding the main sequence.
Ca II Emission and Li Absorption. The strengths of
both Ca II emission and Li absorption have been found to be
indicators of aging and evolutional stage.
An inverse correlation between the chromospheric
activity and age in main-sequence stars was discovered by
Wilson (1963). He suggested that the chromospheric activity
would be a function of the average magnetic field strength
and indicated by the strength of the Ca II emission. He
pictured all main-sequence stars of the same spectral type
being born with approximately the same average magnetic
field strength, which could not be maintained due to
insufficient dynamo action. The average magnetic field
strength would therefore diminish with age. The diminution
of the field strength would be attributable to the
transformation of the magnetic energy into other forms which

166
could be radiated away by the star. Further evidence
(Wilson and Skumanich, 1964) indicated that H and K emission
intensity in main-sequence stars is an indicator of age
alone and is independent of the circumstances of birth.
Blanco et al. (1974) confirmed that the K-line emission flux
and the surface magnetic field for main-sequence stars
decrease with increasing stellar age. They determined
further that for stars of the same age the K-line emission
flux is a function of spectral type, exhibiting a maximum at
KO.
Inducing a line of reasoning parallel to those of
Wilson and Blanco et al., the extreme strength of the Ca II
emission in the RS CVn systems was partially responsible for
Hall's (1972) placement of the stages of these systems in an
intermediate position between those of the T Tauri stars and
the late-type dwarf emission stars.
Contradicting the foregoing results, Wilson's (1976)
comparison of a group of single stars having strong Ca II
emission to a group with weak Ca II emission demonstrated
that the space velocities of both groups extend over similar
ranges. From this evidence Wilson concluded that the degree
of chromospheric activity is not a function of age, but is
instead determined by some intrinsic property of the star.
Opposing Wilson's (1976) view, Young and Koniges (1977)
arrived at the conclusion that strong chromospheric
activity, indicated by strong Ca II emission, is not
exclusively attributable to youth. They indicated that

167
there is a growing consensus that in binaries with Ca II
emission the situation is, in fact, quite the contrary:
chromospheric activity, as indicated by the Ca II emission
strength, intensifies as the components evolve. They
confirmed this conclusion by their own spectra of late-type
binaries with strong Ca II emission, which showed no Li I
6708 absorption line. (Young and Koniges stated that Li is
thought to be present only in very young stars — see Li,
below.) Coupling this spectroscopic evidence with Popper's
(1977) evidence that Ca II emission in binaries is strongest
when one of the components is evolved completed the link
between strength of emission and aging. Based on this
relation, the AR Lac system's strong Ca II emission observed
in this investigation therefore also places AR Lac in a
classification of evolved stars as determined by Popper's
(1977) evidence that Ca II emission in late-type binaries is
the signature of evolved systems rather than of unevolved
ones.
The relationship between the Li 6708 absorption lines
and evolutional stage was discovered as the result of the
efforts of several observers. Conti (1970) stated that
every young star he had observed exhibits considerable
amounts of Li, a characteristic he considered to indicate
for "certain that that star was not evolved" (Conti, 1970,
p. 100). Although it is observed that "some old stars exist
with appreciable amounts of Li (Conti, 1964; Wallerstein,
1966; Feast, 1966)" (Wallerstein and Conti, 1969, p. 109),

168
the absence of the Li feature would allow one to be
"reasonably sure that the star was not a contracting case"
(Conti, 1970, p.100). No Li 6708 has been observed in AR
Lac (Naftilan and Drake, 1977; Young and Koniges, 1977),
thereby almost certainly assuring its position in a
non-pre-main sequence stage.
The general conclusion regarding Ca II emission and
aging is that the overwhelming evidence points toward the
emission intensity's being a direct function of age and not
an intrinsic property of the individual star as Wilson
(1976) suggested.
Overall, the observations regarding evolution strongly
favor a post-main sequence stage for the RS CVn systems.
Ages of the RS CVn Systems
Read from Field's (1969) graph, the age for the AR Lac
primary is 1.125 X 10^ years. The age for the AR Lac
secondary is not in accord, however, thereby rendering this
age calculation invalid for the AR Lac system.
Hall (1972) gave no numerical value(s) for the age(s)
of the RS CVn systems; he merely indicated that their ages
are between those of the T Tauri stars and the late-type
dwarf emission stars.
Montle ( 1973 ) computed the age range for the RS CVn
stars to be from 1-4 X 10^ years (average age 2 X 10^ years)
on the basis of their average distance from the plane of the
galaxy and their average velocity perpendicular to the
galactic plane, quantities which he calculated from their

169
distances, galactic latitudes and longitudes, systemic
radial velocities, and proper motions.
Using Wielen's (1974) calibration of velocity-
dispersion-versus-age with Montle's (1973) value of 10
km/sec for the velocity dispersion of the RS CVn stars, Hall
(1976) determined their ages to be about 2 X 109 yr.
The result of Morgan and Eggleton's (1979) calculation
concurred with Hall's (1976), but was arrived at by a
different method. The probability of occurrence of eclipses
of depth about 0.8 mag or deeper in binaries which have
circular orbits and have not evolved to the point of mass
tran
sf er
is maximized
f o
r an
age of 2 X
109 yr
at
the
aver
aged
RS CVn charac'
ter
istics
: fairly low
masses
(primary
mass
1-2M0),
mass rat
,io
close
to unity,
hotter
star
of
spec
tral
type
later than
about
F0, cooler
larger
star
of
spec
tral
type
about K0
IV,
and period 2-10^.
Popper and Ulrich
(1
977) determined the age o
f the
RS
CVn
grouj
p to
be 3 X li
39
years
by analysis
of the
ve loc
ity
dispersion relative to the local galactic standard of rest.
The measurements made in the present investigation do
not provide evidence which can be used to establish the age
of AR Lac. The valid results cited above, however, indicate
that the ages of the systems in the RS CVn group lie between
1 X 10^ and 3 X 109 years.
Other Evolutional Effects
Naftilan and Drake (1977) found the macroturbulence
velocity for the AR Lac secondary to be anomalously high for

170
a subgiant, a characteristic which they suggested could be
related to the formation of the chromosphere.
Summary
Although the observations of the present investigation
cannot alone establish precisely the site of or the
mechanism for the Ca II emission in AR Lac or the age or the
evolutional stage of AR Lac, they do allow the system to be
assigned to a general evolutional category by supporting the
observations of others.
The layer of AR Lac (and the other RS CVn stars) in
which the Ca II emission arises is undoubtedly the lower
chromosphere, as evidenced by solar analogy and by
measurements of (1) the radial velocity of the emission and
(2) the thickness of the emitting layer in AR Lac. Radial
velocity measurements favor an emitting layer attached to
the star(s) rather than some external emission site such as
a gas stream.
The behavior of the Ca II emission reveals that it is
not restricted to only one surface position on the stellar
components. Measurements of the changes in Ca II emission
with phase indicate that within that emitting layer some,
though not all, of the emission from AR Lac arises at the
tips of the tidal bulges. The entire stellar surface is
responsible for a distributed background of Ca II emission.
Sudden, non-periodic changes in emission are produced either
by (1) flares or prominences or by (2) eclipse and rotation
around the limb of isolated large emission regions.

171
The underlying emission agent is apparently a
temperature increase, which probably results from the
collision of opposing streams of material within the star.
Normal collision already present in a star may be enhanced
by currents, streams, or whirlpools (vortices) of material
within the stars being induced by (1) the close binary
association of the stars, (2) differences in gravitational
acceleration over the stellar surfaces, and (3) sunspot-like
activity, flaring, or prominences. Alternatively, this
collisional chromospheric heating might perhaps be effected
by acoustic energy transport as a result of enhanced tidal
coupling as the RS CVn stars expand toward the giant stage.
On an atomic level, the question of whether the
mechanism of Ca II emission in AR Lac is ordinary excitation
or is the final step in a fluorescence cascade has
apparently not been discussed since the late 1940's and is
perhaps still uncertain. The Ca II emission might also
possibly result from a selective excitation by emission from
atoms of another element with a strong emission line
coincident in energy with the H and K lines.
The formation of and changes in other spectral lines (H
emission, Fe, and Ce) in AR Lac can apparently be explained
by gas streams, bombardment by extra-component particles, or
a turbulent vortex.
Radio emission is probably not produced by thermal
bremsstrahlung from circumstellar material, a more likely
source being magnetobremsstrahlung from relativistic

172
electrons. The radio source is much larger than the system
stars themselves.
By inference based on the association of solar magnetic
fields with sunspots and with strong Ca II emission, there
are possibly magnetic fields associated with the starspots
in AR Lac. No measurements of the Zeeman effect have been
attempted, however.
Irregular light-curve variations indicate that the
surface luminance of the AR Lac primary is less uniform than
that of the primary. The intrinsic variability of the
primary is not caused by pulsation, but may be generated by
starspots, flares, or prominence activity.
(1) Pre- and post-primary-eclipse Ca II-emission
depressions and light-curve depressions and (2) metal
deficiencies are attributed to enhanced absorption by a
circum-secondary envelope of material resulting from mass
ejection from the secondary. Infrared and ultraviolet
excesses and symmetry of the Balmer emission also result
from the presence of this circumstellar envelope.
Pulsation, a tilted ring of circum-secondary material,
gas streams, tidal effects, and the reflection effect have
all been ruled out as mechanisms for the photometric
distortion wave in RS CVn stars. The photometric distortion
wave and its changes in rate of motion and in amplitude are
best explained by the presence of a group of large starspots
which migrate in longitude, drift in latitude, and change
with latitude in size, number, migration rate, and drift

173
rate on a differentially rotating star, much as sunspots
do. It is assumed that the starspot drift is driven by a
pole-equator temperature differential (poles hotter). The
spots are apparently convection cells extending throughout
the convection zone, the depth of which governs their size:
the deeper the zone, the larger the spots. Because the RS
CVn stars have deep convective shells, but are not
completely convective, the spots would be moderately large,
be restricted to latitudes away from the polar regions, and
would produce large-amplitude periodic brightness changes as
the spots rotate around the limb and are eclipsed. RS CVn
stars might evolve through three spot-migration and
spot-position categories, each rooted in the depth of the
convective zone. Fast differential rotation and tidal
effects due to the presence of the companion star might
enhance the magnetic field-line breakthrough effect,
generating more and larger spots than on the sun.
Photometric and spectroscopic evidence exists
demonstrating the observability not only of large groups of
starspots but also of large individual spots on the AR Lac
components. When the spot groups face earthward, the
photometric distortion wave minimum and the Ca II emission
maximum are observed. Although one theoretical model
contends that individual spots would not produce a
sufficient variation in magnitude to be observable, the
differential magnitudes in the observations indicating
individual spots exceeded the minimum theoretical detectable

174
differential magnitude by at least a factor of 100. It is
concluded, then, that large individual spots were observed.
Abrupt period changes undergone by AR Lac cannot be
explained by intrastellar instabilities, faster-than-
synchronous rotation of the fainter component, apsidal
motion, orbital motion about a third body, or mass transfer
by the Biermann-Hall mechanism. Some type of mass ejection,
by (1) eruptive prominences or (2) more-or-less-continuous
ejection of material (like the solar wind), both associated
with a migrating spotted region (either bright or dark--the
question remains), correlates well with the observation of
period increases and decreases when the spotted region is on
the following and leading hemisphere of the star,
respectively. The mass loss is apparently enhanced by
component interaction in AR Lac.
The epoch of the (1) Ca II emission maximum, (2) the
photometric distortion wave minimum, and (3) period changes
are unquestionably correlated in RS CVn, UX Ari, and Z Her.
Apparently the tri-fold relationship obtains in AR Lac also,
the relationship between the latter two quantities having
been almost definitely established and the relationship
between the former two quantities having been tentatively
established for AR Lac.
Correlations of photometric behavior with infrared and
radio behavior in UX Ari and V711 Tau, respectively, offer
some basis for the supposition that such relationships may
exist in other RS CVn stars. The possibility of an infrared

175
correlation has not been investigated for AR Lac, and
results of attempts at radio correlation have so far been
null.
AR Lac obeys the Wilson-Bappu relation and Gratton's
period-luminosity relationship for late-type binaries with
Ca II emission.
The evolutionary status of AR Lac is decidedly not
pre-main sequence. The overwhelming majority of the
evidence places the RS CVn stars in a post-main sequence
stage, the more massive component having evolved to the base
of the giant branch and the less massive component having
evolved to a point just before or just after core-hydrogen
exhaustion. Slow, not rapid, mass exchange (by a stellar
wind) has been, and possibly still is, occurring, perhaps
generating a situation (in AR Lac, at least) in which the
components see-saw back and forth evolutionally. Evidence
for such a stellar wind in RS CVn stars is their enhanced
chromospheric activity and their period changes. Based on
the extreme strength of their Ca II emission, their lack of
Li absorption, their galactic positions and velocities,
their orbital characteristics, their physical character¬
istics, and their population count, the RS CVn stars can
almost certainly be fixed firmly in a long-lived post-main
sequence stage of evolution, at an age somewhere between 1 X
10® and 3 X 10^ years.

SECTION VI
FUTURE INVESTIGATIONS
Introduction
There are several valuable spectrogram analyses,
necessary equipment modifications, and desirable
observations which suggested themselves during this
investigation.
Spectral Analysis
Series of spectra of three RS CVn systems other than AR
Lac (UX Ari, Z Her, V711 Tau) were obtained as a part of
this investigation. UX Ari and Z Her are eclipsing members
of this group; V711 Tau is a non-eclipsing member. A
complete analysis of these spectrograms would supplement the
analysis already performed herein for AR Lac. Results of
such an analysis would allow a comparison (though incomplete
due to the
lack of data) of
the
behavior
of
the
Ca II
emission in
eclipsing members
of
the group
to
that
of a
non-eclipsing member.
A series of high time-resolution and high
grating-resolution spectra of RS CVn were obtained in 1974
by Oliver at KPNO. Preliminary scanning microdensitometer
tracings of these spectrograms revealed that the H and K
emission of this system exhibits short-term changes. Such
variations are indicative of a high level of chromospheric
activity (such as turbulence) or of occultation of a
176

177
localized emission area (Weiler, 1967; Naftilan and Drake,
1977; Struve, 1952; Weiler, 1978), Construction of line
profiles and complete measurement of these profiles would
contribute to the understanding of the structure of the
stars in this system and similar systems.
Analyses of the data for these four systems were not
included as a part of this dissertation for two reasons:
(1) The coverage of the phase cycles was so incomplete that
no valid conclusions could be drawn regarding the
behavior of the Ca II emission either during eclipse
phases or during other parts of the cycles. (The
primary culprit which prevented observations was the
weather.) Many additional data in combination with
those already obtained are necessary to make a
significant contribution to the body of knowledge of
these systems.
(2) Failure of part of the electronics of the scanning
microdensitometer forced the postponement of further
data reduction until substantial equipment
modifications could be completed.
Equipment
Several deficiencies in the available equipment
rendered the procedure for obtaining the data and performing
its subsequent analysis cumbersome to say the least. The
observation-and-data-reduction system is at present most
severely limited by its data-analysis capabilities.

178
Exposure times for the spectrograph were as much as
a factor of 10 times longer than those for similar
spectrographic systems at other observatories (Oliver,
1976a). A factor of approximately 4 can be accounted for by
the degraded reflectivity of the 76-cm primary just prior to
its scheduled time for resurfacing. The remaining factor of
about 2.5 can presumably be attributed to low grating
efficiency, because this is- the only unknown in the entire
telescope-spectrograph system. Boiler and Chivens offered no
specifications for the grating efficiency (Oliver, 1976).
Ray tracings revealed no deficiencies in the apertures or
the optical design of the system, and calculations of light
losses at the collimator and within the spectrograph camera
could not account for this large a factor.
Another effect on the exposure time (which was
accounted for) was the order of the blaze of the grating.
Because the gratings in the present spectrographic system
are blazed in the third-order blue, the dispersion is
increased by a factor of approximately 3 over that of a
first-order blaze (a desirable effect); but the exposure
time is also increased by a factor of 3 (an undesirable
effect) because the light intensity decreases as order
increases.
In order to remedy both problems (inefficiency and low
light intensity) simultaneously, the present gratings should
be replaced by a high-efficiency grating blazed in the
first-order blue. As a suggested replacement, a grating

179
(available from Boiler and Chivens: Wheeler, 1973) ruled at
1200 lines/mm, blazed at 4000 A in the first-order blue
(very near the K line, 3934 A), with a blaze angle of 14°,
would provide nearly 2.5 times the dispersion and resolving
power as the present grating, yet allow about 7 times as
much energy to be incident on the plate at that wavelength.
In order to achieve the same plate density, the exposure
time would therefore be reduced by a factor of about 7.
In order to attain a more accurate assessment of the
correct plate exposure (which is determined by the intensity
of light received and the length of time of the exposure),
the exposure meter could be reassembled using a more
sensitive photomultiplier tube, thereby allowing
discrimination between a bright sky and a faint star. The
resulting elimination of "guestimation" of exposure times
would in turn eliminate plates too thin to show emission
reversals and plates too overexposed to be measurable.
The imprecise sensitometry procedure could also be
greatly improved. At present the stellar spectra are
obtained and developed under one set of conditions, whereas
the sensitometry plates are a different set of plates
exposed and developed under a different set of conditions.
Such a situation is not conducive to the production of
sensitometry plates which are to be used as standards for
absolute spectral plate emulsion density comparisons of the
highest precision. This imprecision could be eliminated by

180
(1) modification of the spectrograph camera system so that
the sensitometry spots are applied directly to the
stellar plate simultaneously while the spectrum is
being obtained, or
(2) construction of an auxiliary sensitometry box in which
the stellar plate would receive the same exposure time
in the same wavelength region immediately after the
spectrum is obtained. (Plans for construction of such
a box were being drawn up by Fitzgibbons, 1980.)
The tedious and time-consuming procedure of plate
analysis could be greatly improved by extreme modification
of the equipment used in the intermediate steps of
digitization of the spectral data. At present it is a
multistep process involving the scanning microdensitometer,
the transmission densitometer, and much manual work
constructing characteristic curves and converting
deflections into emulsion densities, which are in turn
converted into intensities, which are finally numerically
integrated over the line profile to produce an equivalent
width. This lengthy process could be eliminated by
modifying the scanning microdensitometer to digitally record
density and/or deflection data directly from the spectrum
and from the accompanying sensitometry spots. A computer
program could be designed to perform the analysis of the
digitized data. Oliver (1980) planned and has completed
(1982) such a modification, which would employ the PET
computer directly linked to the scanning microdensitometer.

181
Other necessary additions to the microdensitometer are
wavelength markers which are recorded during tracing (or
noted during digitization) and/or a means of tracing (or
recording digitally) the comparison spectrum simultaneously
with the stellar spectrum.
Radical modification of the photometric sensitivity of
the microdensitometer is also necessary. Under naked-eye or
microscopic examination many under- or overexposed spectra
exhibit emission reversals. The range of densities over
which the instrument can operate, however, is so limited
that only plates which are like the baby bear's porridge
(juuust right) can be traced. (This investigator has long
suffered the frustration of the "Goldilocks Syndrome.") A
system which is not even as sensitive a discriminator as the
human eye is somewhat less than adequate for probing the
secrets of the universe. In order to remedy this situation,
the electronics of the densitometer could be altered to
allow it to measure low total and differential light
levels. This modification would increase the capability of
the system in two ways:
(1) Spectra which are widened only one-third to one-half of
the minimum the present system can accommodate (because of
the low level of light transmitted) could be measured,
therefore allowing (a) the analysis of spectra of this
description which have already been obtained and (b) the
future reduction of exposure times by a factor of 2 or
3. This enhancement of time resolution would be of great

182
value in the observation of short-lived phenomena such as
partial phases of eclipses of binary stars, flares, and
formation and dissolution of starspots.
(2) Spectra with high fog levels or spectra which are very
thin could be measured. (Both are cases which result in
very small differences between spectrum density and fog
density.) This augmented capability not only would allow
the use of many previously obtained plates which cannot be
analyzed with the present system but also would relieve the
present restriction on the allowable range of measurable
densities.
The foregoing modifications of the spectrographic and
data analysis systems will produce data of higher precision
and allow almost on-the-spot data reduction (rather than
forcing years of waiting for results).
The problems of emulsions and the microdensitometer
will be circumvented completely by the completion of the
spectrum scanner with its direct video display and disc
storage system (Oliver, 1983b).
Observations
In the present investigation a number of spectra were
obtained of the non-eclipsing RS CVn binary V711 Tau. This
system has an eighth-magnitude visual companion which shares
the same right ascension; consequently the alignment of the
visual system is along the spectrograph slit, and the visual
companion is included in the exposure. Although the
contribution of this companion is faint, it does render the

183
resulting spectrum a composite, which would be extremely
difficult to separate into the components contributed by
each part of the visual system. It is mechanically
possible, however, to rotate the slit of the spectrograph
90° to eliminate the light from the visual companion. V711
Tau could then be trailed along the slit in declination
rather than in right ascension, thereby obtaining a spectrum
of the RS CVn system alone.
Emission in the sodium D lines (5890A and 5896A,
produced by neutral sodium) has been searched for in some
stars (Young and Koniges, 1977). Obtaining a series of
spectra at these wavelengths would allow the construction of
a light curve at the D lines similar to the one constructed
at the K line in the present investigation. If the image
tube (see Section II) which was used in an attempt to obtain
spectra of the D lines can be redesigned to function under
ambient conditions, such spectra can be obtained.
The Li I 6708 line has been sought, but not observed,
in AR Lac (Naftilan and Drake, 1977; Young and Koniges,
1977). Measurements of the strength of this line in AR Lac
might yield some supplementary data which would establish
even more definitely the age and the evolutional stage of
the system. A strong Li I 6708 line is the mark of a very
young system (Wallerstein and Conti, 1969). All young stars
observed by Conti (1970) had considerable amounts of Li, a
characteristic which he considered to be an almost certain
indicator that the stars are not evolved.
The presence of

184
Li does not, however, provide incontrovertible evidence of
youth or of an unevolved stage, because there are some old
stars which exhibit this line (Wallerstein and Conti,
1969 ). On the other hand, the absence of the line does
automatically indicate with reasonable certainty that the
system is old or evolved (Conti, 1970). The presence of a
strong Li line in AR Lac would indicate that it might be a
youthful system, and the absence of the Li line would lend
further credence to the precept that AR Lac is evolved.
Many investigators have repeated Gratton's (1950)
assertion that the Ca II emission in binary stars is much
stronger than that in normal single stars; however no
conclusive evidence to support this statement has ever been
presented. (Perhaps Gratton misread or misunderstood
Struve's (1945) statement that the number of Ca II-emitting
binaries,
not
the strength of
the i r
emission, is greater
than that
of
single stars.)
Very
crude comparisons (as
stated by the observers involved) have been made of Ca II
emission strength in hundreds of stars and systems (Adams
and Joy, 1931; Joy and Wilson, 1949; Wilson and Bappu, 1957;
Young and Koniges, 1977); however, no one has performed a
study specifically for the purpose of establishing whether a
disparity in emission strength exists between single stars
and binaries. Also, of a total of 734 stars observed in
these investigations there were only 54 binary systems
(explicitly listed as such) represented. Further, the
authors used various relative criteria to judge the emission

185
strengths; as a result the spectra were not all measured to
the same standard. Because of the paucity of data based on
the same standard of comparison, a program of great interest
would be a precision survey of large numbers of single and
binary stars which exhibit Ca II emission. The single stars
should be observed during an entire rotation so that any
variabi1ity
in their
emission
due
to
rotation
can be
observed.
The binary stars should
be
observed at all
phases
and for several epochs
in order
to
take
into account any
variability
in their
emission
due
to
eclipses
and/or
migration and rotation of emission regions. The absolute
intensities of the
Ca
II emission of
all spectral
and
luminosity classes
of
Ca II-emitting
stars should
be
compared to determine what relationship exists among all of
these factors (duplicity, surface temperature, absolute
magnitude). Determinations of distributions and sizes of
the emitting areas could be made in some single and binary
stars, and a study of the rotation of single stars could be
made using the emission variations as a rotation indicator.
The data from these observations would also contribute to
the determination of the position (in latitude) of the
emission regions, the spot-position categories, the
migration categories, the resultant (possibly) evolution-
based categories, and the lengths of starspot cycles. For
the RS CVn stars in particular the ratio of the emission of
each component in a system relative to the continuum of the
cooler component could be compared to that for single

186
subgiant KO field stars. Because the RS CVn systems are
detached, it would be expected that these ratios would be
nearly equal, indicating that rapid mass transfer has not
taken place (Oliver, 1976b). The period variations in these
stars, however, imply that some mass transfer, though
slight, must have occurred; consequently an observation
program of this type would yield further information on the
evolutional stage of the RS CVn systems. Long- and
short-term variations in the emission of the RS CVn systems
indicate a dynamic chromosphere (Weiler, 1967; Naftilan and
Drake, 1977; Weiler, 1978). This observational program
would therefore also obtain information on the structure of
these stars.
The aforementioned series of observations of the RS CVn
systems (which would include the bright newly discovered
systems HR 5110 and HD 224085 — see Table 2) will allow the
behavior of the Ca II emission of the eclipsing members of
the group to be compared to that of the non-eclipsing
members. Unhampered by intervening eclipses, observations
of the non-eclipsing stars at all phases would indicate
whether the emission is localized, because emission would
disappear at phases when the emitting hemisphere is
anti-earthward. The non-eclipsing systems might also shed
further light on the mechanism of the emission. In RS CVn
eclipsing systems which exhibit emission in only one
component, good time-resolution spectrograms taken during
the partial phases of the eclipse of the emitting component

187
would allow examination of the brightness distribution of
the emitting region in as much detail as is possible.
For reduction of the data, simultaneous U-photometric
observations would be necessary in order to establish the
absolute intensity of the U continuum of the stars at the
times of the spectrographic observations.
All of the suggested observations necessitate time
resolution of 20ra or better, a requirement which should be
easily achievable with the modified equipment.
Epilogue
A span of eighty years of observation has yielded a
profound lack of satisfactorily corroborative results among
observers of AR Lac. This circumstance demands the
establishment of a regular coordinated program of further
extensive simultaneous observations in all regions of the
spectrum.

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BIOGRAPHICAL SKETCH
Sara Witherow Hoffman was born in the South and has
spent most of her life in the South, having lived in Memphis
since she was a child. She began her career in astronomy
early, collecting astronomical information on planets and
stars from about age four.
After graduating from high school as a Merit
Scholarship Finalist, she received her undergraduate
education from Southwestern At Memphis, where she was
awarded two National Science Foundation grants for research
in physics and an assistantship to teach the introductory
physics laboratory for physics majors. She also received
the French Government Book Award for the most outstanding
scholastic achievement in French I. She was elected to
membership in Sigma Pi Sigma Physics Honor Society and Chi
Beta Phi Honorary Science Fraternity. She was also a
reporter for the college newspaper, The Sou'wester, and a
member of the Southwestern Singers. She earned enough hours
for majors in both physics and mathematics, and elected to
receive her degree in physics. She was graduated from
Southwestern as the first girl to receive the degree of
Bachelor of Science with Honors in Physics. The degree
"with Honors" is not equivalent to the usual cum laude (with
honors) designation, at the low end of the hierarchy of
197

198
honor degrees granted by most institutions. To the
contrary, the degree "with Honors" was, at the time of the
author's graduation, the highest honor which Southwestern
conferred on its graduating students. To be awarded this
honor degree required not only a high grade-point average
and exceptionally high scores on the four comprehensive
examinations required for graduation but also a year of
enrollment in Honors Research, culminating with a thesis.
Her Honors Thesis was entitled "The Infrared Spectral
Reflectivities of Ice, Snow, and Solid Carbon Dioxide."
Her acceptance into the doctoral program in physics at
the University of Tennessee at Knoxville was accompanied by
the award of a graduate assistantship by the Department of
Physics. An interest in teaching coupled with the lucrative
offer of a (tax-free!) two-year Ford Foundation grant
enticed her to become a participant in the non-terminal
Master of Arts in College Teaching in Physics program, which
is an enriched Master of Science degree program requiring
sixty hours of coursework in graduate physics, graduate
mathematics, and teaching seminar (rather than the usual
forty five hours in physics alone for an M.S.), plus two
years of practical teaching experience being an instructor
of the three-quarter sequence of five-credit-hour college-
level physics lecture and laboratory courses. During her
sojourn at UT, she was active in organizing the Knoxville
Astronomy Club. She was graduated with a non-thesis MACT in
Physics with a minor in mathematics.

199
While at the University of Florida pursuing her Ph.D.
in astronomy with a minor in physics, she held a graduate
assistantship in the Department of Physics and Astronomy,
was an instructor in the undergraduate astronomy laboratory
program, served for two years as the Coordinator of that
program, contributed much of the material for the astronomy
laboratory manual (which was later published), and was the
designated substitute for professors in the introductory
astronomy lecture sections. The research presented in her
dissertation constitutes the first UF dissertation in the
field of stellar spectroscopy. Further, her record-breaking
longevity as a graduate student in astronomy at UF qualifies
her as the most nearly tenured graduate student in the
department. . . Her extracurricular activities included
being instrumental in the founding of the RHO Sunshine Club
and the Florida Astronomical Society, having held office as
secretary, vice-president for publicity, and president in
the latter organization. In addition to those posts, she
has been the editor-in-chief and the principal journalist
for the FAS publication, the ASTROLOG, and has been
interviewed on numerous local radio and television programs
for the purpose of promoting astronomy to the general
public.
Currently a tenured academic faculty member in the
Natural Sciences Area at Santa Fe Community College, she
instituted the present SFCC astronomy program, which
includes courses that have become extremely popular, but at

200
the same time have been maintained at a rigorously demanding
college level of difficulty (ask her former students!). She
has also contributed considerably to the construction of new
courses in physical sciences and the restructuring of other
courses in physics and physical sciences. She is a member
of the Florida Astronomical Society, the Astronomical
Society of the Pacific, the Planetary Society, and the
Southeastern Geological Society.
The author's immediate plans include publication of the
results of her dissertational research in an astronomical
journal, execution of the spectroscopic research proposed in
her dissertation, and continuation in her capacity as the
astronomer-physicist at SFCC. In the near future she
intends to complete, from her previously conceived outlines,
several writing, video-tape, visual-aid, and research
projects in astronomy, physics, and grammar. She will
continue her formal education by enrolling in classes in
geology, meteorology, physics, mathematics, and dancing.
She also intends to shift her career emphasis from classroom
instruction to writing and research, and tentatively plans
to apply for a position as an astronaut-specialist, possibly
for a Mars mission.

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
^ig r-A , ,M L,. â–  i'^J
Frank Bradshaw Wood, Chairman
Professor of Astronomy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree (of Dcof Philosophy.
JjZrhn P. Oliver
Associate Professor of Astronomy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
/
z
TV
Howard L. Cohen
Associate Professor of Astronomy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Alex G. &mitn
Professor of Astronomy

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Charles F. Hooper,
Professor of Physic^
This dissertation was submitted to the Graduate Faculty of
the Department of Astronomy in the College of Liberal Arts
and Sciences and to the Graduate School, and was accepted
as partial fulfillment of the requirements for the degree
of Doctor of Philosophy.
August, 1983
Dean for Graduate Studies
and Research

UNIVERSITY OF FLORIDA
3 1262 08554 0770




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