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
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xv, 200 leaves : ill. ; 28 cm.
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English
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Hoffmann, Sara Witherow
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Astronomical spectroscopy   ( lcsh )
Eclipsing binaries -- Spectra   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

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

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University of Florida
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aleph - 000440926
notis - ACK1490
oclc - 11272217
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Full Text












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



















t- O




**..
----,s>- N 2_____________________




eono




a, > 4



3



*.. o >








0 0
z3o 2















I II











SN3 3AII
.I0.








o o a0


0 IC0 e 0



--N ----- i ----*- ___ __
S 2 2 "L~- o 3
() H11 lN -Vin3 3 ll -3








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.