Citation
A photometric study of RS Canum Venaticorum including critical analyses of the distortion wave and period variations

Material Information

Title:
A photometric study of RS Canum Venaticorum including critical analyses of the distortion wave and period variations
Creator:
Ludington, Elwyn Whit, 1949-
Publication Date:
Language:
English

Subjects

Subjects / Keywords:
Amplitude ( jstor )
Astronomical magnitude ( jstor )
Comparison stars ( jstor )
Datasets ( jstor )
Eclipses ( jstor )
Light curves ( jstor )
Orbitals ( jstor )
Structural deflection ( jstor )
Sunspots ( jstor )
Variable stars ( jstor )

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Elwyn Whit Ludington. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
5086309 ( OCLC )
0022801558 ( ALEPH )

Downloads

This item has the following downloads:


Full Text








A PHOTOMETRIC STUDY OF RS CANUM VENATICORUM
INCLUDING CRITICAL ANALYSES OF
THE DISTORTION WAVE AND
PERIOD VARIATIONS







By

ELWYN WHIT LUDINGTON



















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





UNIVERSITY OF FLORIDA

1978













Dedicated to the memory of my grandfather,

Elijah Whitfield Fisher.












ACKNOWLEDGEMENTS


I wish to express my appreciation to the many people who have

helped me accomplish the task of writing this dissertation.

First, I acknowledge my mother's years of love and encouragement.

While maintaining a secure home environment, she required of me a high

degree of independence which I feel has been invaluable in my pursuit of

higher education. Second, I thank Mr. and Mrs. Robert E. Ludington, my

uncle and aunt, for promoting my interest in amateur astronomy. Third,

the guidance of Dr. Frederick Decker during my undergraduate years must

be acknowledged. His advice was the beginning of my pursuit of astrono-

my as a career. Fourth, I thank Nancy A. Ludington for her encouragement

during my initial years of graduate study. I wish to express my undying

gratitude to Dr. John E. Merrill and Barbara M. Oliver for the words of

wisdom which they gave me during the most trying times of my graduate

student career. There are many others who deserve my thanks for their

personal involvement in my life: Charles Jackman, Karen Rockwell,

Charles H. Morgan, Jr., David Killian, and Mary Horn, to name a few.

Professionally, I would like to thank Dr. John P. Oliver for sug-

gesting the topic of this dissertation, and for his expert guidance

during the course of the research. The members of my supervisory commit-

tee are also thanked for their assistance. Of equal importance to the

successful completion of this work were the many graduate students with

whom I have had the pleasure of working. In particular, I would like to

thank David Florkowski, Gregory Fitzgibbons, Patricia Guida, Charles

iii








Jackman, David Killian, Norman Markworth, and Elizabeth Mullen for our

many discussions which greatly stimulated my endeavors.

Steven Gladin and John Young are thanked for their kind and

very helpful assistance with computer programming.

Finally, I would like to thank Karen P. Rockwell for her assis-

tance with the reduction of the chart recordings and her help with this

manuscript.







































iv













TABLE OF CONTENTS


ACKNOWLEDGEMENTS . . . . . . . . . .... iii

TABLE OF CONTENTS . . . . . . . . . . . . v

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

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

ABSTRACT . . . . . . . . . . . . . . x


Chapter

I. INTRODUCTION . . . . . . . . .. . . 1

Topic of Current Research . . . . . . .... 1
Historical View . . . . . . . . . .. 2
Scope of Dissertation . . . . . . . . . 44

II. INSTRUMENTATION . . . . . . . . . . . 45

The Basic Equipment . . . . . . . . . .. 45
Amplifier Calibration . . . . . . . . . 48

III. PROCEDURE AND DATA REDUCTION . . . . . . . . 51

Observational Procedure . . . . . . . . . 51
PHRED . . . . . . . . . . . . 54
DEXTOR . . . . . . . . . . . . . 65
Data Reduction . . . . . . . . . . . 67

IV. DATA ANALYSIS PROCEDURE . . . . . . . . . 74

Introduction . . . . . . . . . . 74
Outline of WAVE Procedure .. . . .......... 74
The WINK Program . . . . . . . . . . 78
The ROMC Program . . . . . . . . . . 81
The FOURFIT Program . . . . . . . . . .. 81
The LCPLOT Program . . . . . . . . . .. 82
Detailed WAVE Procedure . . . . . . . . .. 82

V. ANALYSIS AND SOLUTION . . . . . . . . . . 87

Introduction . .. . . . . . . . . . 87
The Data Analyzed . . . . . . . . . .. 87


v








The Analysis . . . . . . . . . . . . 91
The Final Solution . . . . . . . . . . 99
The Distortion Wave . . . . . . . .... ... 102
Period Changes . . . . . . . ... .... 104

VI. DISCUSSION . . . . . . . ... .. . . .139

Introduction . . . . . . . ... . . 139
The Distortion Wave . . . . . . . . 139
Orbital Period Variations . . . . . . .... 147
Conclusion . . . . . . . ... . ... . 149

APPENDIX . . . . . . . . .. . . . . . . 153

LIST OF REFERENCES . . . . . . . . . . . . 167

BIOGRAPHICAL SKETCH . . . . . . . ... .... . 173





































vi














LIST OF TABLES


1. JOY'S ABSOLUTE DIMENSIONS . . . . . . . . . 5

2. POPPER'S RESULTS FOR RS CVN . . . . . . . . . 13

3. LIST OF RS CVN BINARIES . . . . . . . . . 24

4. LUDINGTON-OLIVER FORMAT . . . . . . . .. .. 56

5. DIFFERENTIAL MAGNITUDES AND COLORS OF CHECK STAR . . . .. 71

6. WINK PARAMETERS . . . . . . . . . . . 78

7. ASSUMED PARAMETER VALUES . . . . . . . . . 80

8. SOURCE OF DATA . . . . . . . . . . . 88

9. SUMMARY OF RS CVN SOLUTION . . . . . . . . .. 92

10. FINAL VALUES OF WINK PARAMETERS . . . . . . .. . 100

11. FINAL VALUES OF EPOCH-DEPENDENT PARAMETERS . . . . .. 101

12. NORMAL POINTS FOR 1921 DATA . . . . . . . . .. 117

13. NORMAL POINTS FOR 1963 DATA . . . . . . . . .. 119

14. NORMAL POINTS FOR 1964 DATA . . . . . . . . .. 121

15. NORMAL POINTS FOR 1965 DATA . . . . . . . . .. 123

16. NORMAL POINTS FOR 1966 DATA . . . . . . . . .. 125

17. NORMAL POINTS FOR 1975v DATA . . . . . . . .. 127

18. NORMAL POINTS FOR 1976v DATA . . . . . . . .. 129

19. NORMAL POINTS FOR 1975b DATA . . . . . . . .. 131

20. NORMAL POINTS FOR 1976b DATA . . . . . . . .. 133

21. NORMAL POINTS FOR 1975u DATA . . . . . . . .. 135

22. NORMAL POINTS FOR 1976u DATA . . . . . . . .. 137

23. TIMES OF MINIMA AND CHARACTERISTICS OF THE DISTORTION WAVE . 141


vii













LIST OF FIGURES


1. 1975 Visual Light Curve of RS Canum Venaticorum . . . .. 29

2. Schematic Diagram of Instrumentation . . . . . .... 47

3. Fine-Gain Stability . . . . . . . . . . . 49

4. Coarse-Gain Stability . . . . . . . . . . 49

5. JCL Cards for PHRED . . . . . . . . . . . 59

6. Differential Magnitudes of Check Star . . . . . .. 70

7. Outline of Basic WAVE Procedure . . . . . . . .. 75

8. Sample Plot from LCPLOT Program . . . . . . . .. 77

9. The WAVE Procedure . . . . . . . . . . . 83

10. Input Stream which uses the WAVE Procedure . . . . .. 85

11. 1921 Light Curve of KO Star in RS CVn . . . . .. . 106

12. 1963 Light Curve of KO Star in RS CVn . . . . . .. 107

13. 1964 Light Curve of KO Star in RS CVn . . . . . .. 108

14. 1965 Light Curve of KO Star in RS CVn . . . . . .. 109

15. 1966 Light Curve of KO Star in RS CVn . . . . . .. 110

16. 1975v Light Curve of KO Star in RS CVn . . . . . .

17. 1976v Light Curve of KO Star in RS CVn .. . ....... 112

18. 19756 Light Curve of KO Star in RS CVn . . . . . . 113
18. 1975b Light Curve of KO Star in RS CVn .............. ..113

19. 1976b Light Curve of KO Star in RS CVn . . . . . .. 114

20. 1975u Light Curve of KO Star in RS CVn . . . . . .. 115

21. 1976u Light Curve of KO Star in RS CVn . . .. . . 116

22. Distortion Wave Amplitude . ... ... . . . . 142



viii







23. Phase of Distortion Wave Minimum . . . . . . 143

24. Shape of Spotted Region ...................... .146

25. Photoelectric 0-C Diagram . . . . . . . ... 148
















































ix














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


A PHOTOMETRIC STUDY OF RS CANUM VENATICORUM INCLUDING
CRITICAL ANALYSES OF THE DISTORTION WAVE
AND PERIOD VARIATIONS

By

Elwyn Whit Ludington

December 1978

Chairman: John P. Oliver
Major Department: Astronomy

Photoelectric data in the UBV system were obtained by the author

in 1975 and 1976 at Rosemary Hill Observatory. These data of RS Canum

Venaticorum were analyzed together with the published Catania data. The

analysis included the use of a modified version of D. B. Wood's (A.J. 76,

701) computer program WINK. A truncated Fourier series representation

of the distortion wave was subtracted from the observed light curve so

improved elements could be determined from the difference by use of the

WINK program. This process was not at all like the usual rectification

procedure; it was an iterative procedure which greatly improved the

confidence in the determination of the elements of RS CVn. With the

single exception of the effective temperature of the KO III star, the

eclipsing elements are consistent for all epochs and colors studied.

Using these elements, it was possible for the distortion wave to be

isolated; therefore, it will now be possible for theories of its origin

and structure to be tested more critically. The results are consistent


x









with a spotted surface for the KO star. However, the sunspot analogy

does not accurately describe the nature of the spots.

















































xi














CHAPTER I
INTRODUCTION


Topic of Current Research

The eclipsing binary star RS Canum Venaticorum (RS CVn) is the

prototype of a very interesting, but poorly understood, group of stars.

It has been chosen for further study because it has the most complete

observational record of this group, and because it is sufficiently

bright to allow observations with the available equipment. The RS CVn

binaries (also known in the literature as RS CVn systems, RS CVn-type

binaries, RS CVn stars, etc.) have been recently reviewed by Hall (1976).

He concludes that the group is best defined by systems in which (1) the

hotter star is of spectral type F or G and luminosity type V or IV,

(2) strong Ca II emission is present in the H and K lines, and (3) the

orbital period of the binary system is between approximately a day and

2 weeks. There are other characteristics which are common to many of the

systems listed by Hall, but which were deemed unnecessary for the purpose

of classification. Some of these characteristics would be mass ratios

near unity, cooler components near spectral class KO III, and photo-

metric distortions superimposed on the normal eclipse phenomena (if it

exists). It is the complications caused by the last of these characteris-

tics to which this dissertation is addressed.

A new set of observations of RS CVn will be presented which

will extend the basic astronomical knowledge of the system and confirm

the earlier observations. A new technique of solution is developed

1





2

which circumvents the previous problems encountered when deriving ele-

ments from a light curve with unexplained light variations. A natural

result of this technique is to isolate the unexplained light variation

(referred to as a 'distortion wave' in this work) so that it may be

studied independently. It is also hoped that the times of minima can

be improved with this technique so that a better representation of the

period variations can be obtained.

In the remainder of this chapter the literature on RS CVn and

RS CVn binaries will be reviewed and the scope of the dissertation will

be outlined. In the chapters to follow the new photoelectric data will

be presented, starting with the instrumentation and procedure used.

Following this will be a discussion of the distortion wave and period

variations. The dissertation will conclude with a summary of the

results, interpretation as to their meaning, and suggestions for future

research.


Historical Review

The review of the literature shall start with a chronological

history of the research on RS CVn. When this review reaches the early

1970's,it will be more convenient to speak in terms of the RS CVn

systems, rather than RS CVn itself.

RS Canum Venaticorum from 1914 to 1972

RS CVn was first reported as a variable star by L. Ceraski in

1914. She reported that the star was observed to be fainter, on

photographic plates read by M.S. Blazko, on 7 April 1896 (by 1m5),

15 May 1907 (by 1I0), and 3 May 1911 Cby l0O). Numerous observers

studied th.is system during the following 16 years. The results of





3


these observations culminated in the solution of the light curve presented

by Sitterly (1930). Sitterly summarized the considerable observa-

tional material obtained between 1914 and 1928 by Townley (1915),

Hoffmeister (1915, 1919), Maggini (1916), Gadomski (1926), Schneller

(1928) and others. He presented the times of minima that these various

observers had collected up to 1928 and discussed the period changes.

He noted that the period steadily increased during the interval 1900

to 1928. This can easily be verified from the times of minima as plotted

on the 0-C diagram (Observed time of minima minus the Calculated time of

minima from a linear ephemeris). He had accumulated 710 visual estimates

using the 23-inch Princeton refractor and 351 photographic estimates from

Harvard plates. The visual estimates were obtained during the years 1920

to 1922 (mostly in 1921), while the photographic estimates covered a much

longer time (from 1892 to 1922). The visual light curve showed asymmetry

outside eclipse and in primary eclipse. The photographic light curve, on

the other hand, showed no asymmetry outside eclipse, nor did it show a

secondary eclipse. In retrospect, this can be understood in terms of a

moving distortion wave averaging out the asymmetry over the much longer

interval of time during which the photographic estimates were made. This

process would, of course result in a much larger standard error for points

of the photographic light curve, but this would be expected in any case

because of the lower precision of this technique. Except for the asymme-

try outside eclipse, Sitterly's visual light curve solution was in good

agreement with the photographic light curve. The solution was complicated

by a small secondary eclipse, only 0.03 deep, which compares with a depth
of 0?2 by modern photoelectric photometry. Sitterly determined a depth of





4


1 27 for primary eclipse, which is in reasonable agreement with a modern

value of 1T1. He attempted a solution in which the following sides of

both stars were more luminous than the advancing sides. This was neces-

sary in order to explain the outside eclipse asymmetry, which amounted

to a peak to peak difference of 0 13 between the portion of the light

curve preceding and following primary eclipse. This gave much better

residuals than the other solutions but it was discarded because it

seemed so physically inexplicable, particularly since it required the

fainter star to have a difference in brightness from one side to the

other of 55%1 The solution which was finally adopted as the best

representation of the true values was obtained by solving the visual

light curve without any rectification. The resulting elements were:

Uniform disks assumed,

k = 0.30, i = 79.9 degrees,

rl = 0.289 r2 = 0.0867,

Lb = L2 = 0.690, Lf = L1 = 0.310,

where the subscript b (or 2) refers to the brighter star, and the sub-

script f (or 1) refers to the fainter star. The estimated probable

error for a visual observation was + 0.0364, while the estimated

probable error for a photographic observation was + 0.09. It is there-

fore wise that he chose to base the solution on the visual light curve.

The comparison star used was BD+360 2345, and the differential magni-

tudes were originally given as comparison minus variable.

In the same year, Joy (1930) published spectroscopic data on

RS CVn. He used the results of Sitterly's photometric solution along

with his own spectroscopically determined radial velocities to arrive






5

at absolute dimensions. A summary of Joy's results is given in Table 1

(the subscripts have the same meaning as noted above).

TABEL 1
JOY'S ABSOLUTE DIMENSIONS
K1 = 91.6 km/s m1sin3i = 1.79 M

K2 = 99.0 km/s m2sin3i = 1.66 M

y = -8.9km/s m2/ml = 0.93

a sin i = 6.04 x 106 km rb = 1.6 R

a2sin i = 6.53 x 106 km rf = 5.3 Ro

mb = 1.85 Mo mf = 1.71 Mo


Joy concluded from the spectroscopic absolute magnitude and from

the spectral class that both stars are dwarfs. However, the size and

brightness of the fainter star were in direct conflict with this. Joy

ended his article by saying, ". . the secondary star is certainly pecul-

iar and cannot readily be classified among other stars for which we know

the physical characteristics" (p. 45). Joy agreed with Sitterly's inter-

pretation that the fainter secondary star is "a sort of 'subgiant.'"

C. Payne-Gaposchkin (1939) made a study of the period changes and

light curve asymmetries of RS CVn as a part of a paper on variable stars.

She collected approximately 4000 photographic estimates of the brightness

from Harvard plates exposed between the years 1892 and 1938. From the

data, 17 times of minima were computed and plotted. In addition, a light

curve was made by combining individual points into normals. In primary

eclipse each normal was made up of 10 individual points, while outside

eclipse each normal was comprised of 100 individual points. The

normal points were computed after each individual point





6


was corrected for the change in period, as she had estimated it. The

resulting light curve agreed with Sitterly's in its general characteris-

tics. However, it did not agree with the asymmetry that Sitterly had

observed from his visual light curve. Recall that Sitterly had pre-

sented a visual and photographic light curve for RS CVn, but his photo-

graphic light curve failed to show a secondary minimum or any asymmetry

outside eclipse. Payne-Gaposchkin, on the other hand, found a shallow

secondary eclipse in her photographic light curve (of depth 0o06), and

a difference in the height between the two maxima of only a few hun-

dredths of a magnitude. She noted, however, that when the light curve

is made from points taken about the same time as those of Sitterly, a

somewhat larger difference was found. In an effort to summarize the

differences in magnitude between the two maxima, she presented a table

of these differences at four epochs of minima. She noted that if the

difference is assumed to be a periodic phenomena, then the period would

be approximately 8000 days (22 years) or 1670 orbital periods, i.e., the

approximate period of the orbital period changes. She estimated that

an absolute orbital radius of 2 x 109 km would be necessary to explain

the period changes as a light-time effect. Further, she determined

that if thisweredue to a third body, then the required mass of 4 M

would seem larger than could possibly go undetected photometrically.

This represented the first convincing evidence that the period changes

were of an unusual nature, and the first time that the differences in

heights of maxima were ascribed to be of a possibly periodic nature.

The most significant aspect of this paper was that the differences in

the height of the two maxima were ascribed to the redder (and fainter)






7


of the two stars. This was based on her realization that the size of the

asymmetry was greater in the visual light curve than in the blue photo-

graphic light curve.

W. A. Hiltner (1947) noted that a define group of stars existed

which showed Ca II emission. In this short note he collected the

scattered data on the 13 systems known to him at that time (RA Eri, SS Cam,

AR Mon, RU Cnc, RS Cnc, RW UMa, RS CVn, SS Boo, WW Dra, Z Her, AW Her,

RT Lac and AR Lac). Hiltner found from his study of RS CVn the same

characteristics reported by other observers whose data he had collected

together. The emission was noted to be usually from the fainter of

the two stars in the eclipsing system and the emission was apparently

. . not situated uniformly around the parent-star" (p.481). In fact

he stated that the emission approached invisibility only at the secondary

eclipse when the fainter star is partially covered by the brighter, but

smaller star. This led him to agree with Struve (1946) and others that

the Ca II emission in these stars originates from a tidally extended re-

gion above the photosphere of the fainter star. The emitting region was

isolated at the extremes of this tidal bulge along the line joining the

two stars. Struve's and Hiltner's papers could be considered the first

recognition that there was a group of stars (today referred to as

RS CVn binaries) which warranted consideration as a group.

Gratton (1950) studied 19 systems which showed H and K lines of

Ca II emission in the last section of a paper published just a few years

after Hiltner's. This list included the 13 stars in Hiltner's paper

plus six others which were not eclipsing binaries, but were of a binary

nature. These six stars were primarily more luminous and of longer periods





8


than those in Hiltner's list. Gratton attempted to give additional

evidence that the tidal bulge proposed by Struve and Riltner was the

proper mechanism for the explanation of the H and K emission.

Briefly, Gratton's analysis followed these lines. By assuming

that all stars with a tidal distortion above some lower limit would

show emission lines, it was then expected that the giant stars which

show emission would have longer orbital periods. This condition led

to the relation
> kI,
aI + a >

where it was assumed that the variation in mass could be neglected, R

was the radius of the star, al and a2 were the relative orbital radii,

and k1 was a constant. Since the stars being studied were of approxi-

mately the same spectral type (and therefore had the same surface bright-

ness), the radius was proportional to the square root of the luminosity.

In addition, the sum of the relative orbital radii was proportional to

the period (P) to the two-thirds power. Therefore the period and the

absolute magnitude CM) for the binaries showing H and K emission lines

were above a line 0.3 M + log P = constant.

Gratton plotted the absolute magnitude versus log P for 13 of

the 19 stars in the list. The binaries SS Cam, Z Her, 56 Peg, AW Her,

AR Lac, and RU Cnc were excluded because of the lack of data. Gratton

stated, "It is seen that there is a definite correlation between M and

P; we may tentatively take the limiting line 0.3 M + log P = 2.5" (p. 40).

Stars above the line 0.3 M + log P = 1.0 are practically in physical

contact; for these stars the distortion would be too great and might

cause instability.





9


It seems to the present writer that the assumptions which led to

this conclusion are reasonable, with the possible exception of the cor-

relation between the emission and the degree of tidal distortion. More

recently, Young and Koniges (1977) have investigated this relationship;

this will be discussed later.

Keller and Limber (1951) used an unfiltered 1P21 photomultiplier

tube to obtain a light curve of RS CVn during the spring of 1949. They

used BD+350 2421, BD+350 2422, and BD+350 2418 as comparison stars, with

the differential luminosity expressed relative to 80+350 2422. Inside

eclipse, individual points were tabulated, but outside eclipse only the

normal points were given. From an expanded plot of these data around

the primary minimum Keller and Limber noticed a systematic difference in

luminosity. They found that this variation in the depth of primary was

most probably due to intrinsic variability of the fainter star. They

also noted the same asymmetry outside eclipse observed by Sitterly and

Payne-Gaposchkin. It is important to note that the observations of

Keller and Limber were taken over only a three-month interval, so that

the normals they produced outside eclipse were not affected as much by

variations in the asymmetry as was the case for the observations of

Sitterly (mostly one year of data) or Payne-Gaposchkin (nearly 47 years

of data). The asymmetry observed by Keller and Limber was of the same

general character as that of the previous observers; it had a higher

maximum after primary eclipse than prior to primary eclipse. The dif-

ference in the two maxima was 0O04. The rectified light curve was

solved using a limb darkening coefficient of 0.8 with the aid of the

Merrill (1950) tables. The elements so determined were:





10


Lb 0.726, L = 0.274,

k = 0.365, rf = 0.265,

i = 82?5 + 005.

From the luminosity and radius of each component they computed

the ratio of surface intensities. This ratio, approximately 20, could

not be reconciled with the value of 5.5 they computed on the basis of

the energy distribution of the stars Ccorrected for the effects of the

Balmer discontinuity, atmospheric transmission, and the response of

the instrumentation). This, of course, was the same problem Joy had

commented upon.

Keller and Limber very crudely estimated the polytropic index

of the fainter star to be 2.9-5. They used an 0-C diagram made from all

the available times of minima, and an orbital eccentricity determined

from a single estimate of the time of secondary minimum based on their

own data.

While it is obvious that their observations are the best of any

available at that time, it is equally obvious Cas can be seen from the

light curve in their paper) that the time of secondary minimum is

greatly complicated by the asymmetry of the light curve. It was there-

fore wise of them to state, "It is not possible to obtain the phase of

the secondary with much precision" (p. 647).

Bidelman C1954) published a list of stars which were known to

show emission lines and whose spectral types were later than B. The

list for stars showing Ca II emission, which are also spectroscopic

binaries, continues to be referenced today. RS CVn as well as all of

the other stars in Hiltner's paper were among the 72 stars in Bidelman's

table.








Popper (1961) observed RS CVn in an effort to improve the

quality of the spectroscopic orbit and to add photoelectric observations

on a standard system to the body of existing data. He obtained 12 spec-

trograms between the years 1954 and 1958 which showed the same general

features previously observed by Joy (1930) and Hiltner (1947). The only

major difference between his spectrograms and those of the previous

observers was the sharpness of the absorption lines due to the brighter

component of spectral class F4. Joy had designated the spectral type as

F4n, which would mean that the lines were "nebulous." Popper noted the

bright H and K emission lines of Ca II from the cooler (fainter) compo-

nent, as well as the variable emission intensity of the H line. The

solution of Popper's radial velocity curve was compared with Joy's.

Both observers assumed a circular orbit. Popper's results gave slightly

smaller masses for both stars. In addition, he believed that the differ-

ence in the systemic radial velocity of 6 km/s was probably a real

(but unexplained) phenomenon. The photometry was done during the summer

of 1956, in January 1958, and in January 1959. No attempt was made to

cover the entire light curve. The comparison star was HD 114778

(BD+350 2420), i.e., the same star used later by Chisari and Lacona

(1965), Catalano and Rodono (1967) and the present writer. The photom-

etry- of this star from the three seasons resulted in the following

magnitudes:

V = 8.42, B-V = +0.46, and U-B = -004.

This star was OT03 fainter in 1956 than it was during the 1958-59

observing seasons. Popper was not sure whether this difference was due

to a real variation, to the difference in the zenith angles involved,

or to the difference in the set of standard stars used.






12


As expected, primary eclipse was observed to be deeper for

shorter wavelengths, and secondary minimum was observed to be deeper in

the yellow than it was in the blue. Surprisingly, the depth of primary

eclipse was 0o3 different in 1956 than it was in 1958-59. This must be

attributed to the fainter star, since this eclipse is a total one. No

such variation was found in the system's brightness outside eclipse; so

the intrinsic variation of the fainter star was not uniform over its sur-

face. A similar, but a much smaller, difference existed between the

other observed primary minima. The observed difference in depth of

primary could be explained by a change in the radius of the fainter star.

Unfortunately, there were insufficient data to determine if this was the

case. Another possible explanation would have been a change in the color

of the fainter star. The data available to Popper indicated a change in

color of the proper sense but of insufficient size to account for the

observed difference. Also, since the variations outside eclipse had the

same color as the fainter star it was very reasonable to expect this star

to be the source of the variation. These two effects (variation in the

depth of eclipse and the variations outside eclipse) could have been due

to a combination of pulsation and "spottedness" of the fainter star,

according to Popper. He pointed out that the depth of secondary eclipse

as observed by Keller and Limber (1951) was greater than expected from

their values of k and the depth of primary minimum. This led him to

believe that there was a large uncertainty in the value of k. Popper

also found a discrepancy in the ratio of surface brightness as calcu-

lated from the spectral types and that obtained from the light curve. He

noted, however, that the discrepancy was probably not as large as that

found by Keller and Limber. For reference, the results of Popper are





13


summarized in Table 2.
TABLE 2
POPPER'S RESULTS FOR RS CVN

a sin i = 16.7 Ro (B.C.)f = -0m3

Mb sin3 i 1.32 Mo Mb = 1.32-1.36 Mo

Mf sin3i = 1.38 Mo Mf = 1.38-1.42 Mo

i = 82-90 Rb = 1.5-2.0 Ro

a = 16.7-16.85 Ro Rf = 3.3-4.6 Ro

rb = 0.09-0.12 Lb = 3.7-7.8 Lo

rf = 0.20-0.27 Lf = 5.0-9.1 Lo

(B-V)b = 0.39-0.44 (Mbol)b = 2.5-3.4

(B-V)f = 0.91 (Mbol)f = 2.4-3.0

Tb(eff) = 65000-68000K (Mr)b = 2.5-3.4

Tf(eff) = 47000K (Mr)f = 2.7-3.3

(B.C.)b = 0 0

Plavec, Smetanova, and Pekny (1961) showed by their calculations

that the periodic term in the period variation could not possibly be

due to a third body (unless this third body greatly violated the mass-

luminosity relation). They found that in the extreme case, the mass of

the third body would have to be of the same order as that of the stars

in the system. A similar conclusion was reached earlier by Payne-

Gaposchkin (1939). Their calculations were based on the much more

reliable data of Keller and Limber (1951) and Popper (1961). Popper's

data were used by them to make a new estimate of the effects of apsidal

motion, and here again the results indicated that this hypothesis could

not be responsible for the periodic term of the period variations.





14


Chisari and Lacona (1965) observed RS CVn from the S. Agata Li

Battiati station using a 30 cm (12 inch) Cassegrain telescope in 1963

and 1964. Their effective wavelength was stated to be 5150 A, which is

slightly bluer than that for the standard V filter. The bandwidth was

not given, but the EMI 6256A photomultiplier tube was filtered with a

yellow Galileo G 1-26 filter. They used the same star as Popper for a

comparison (HD114778 = BD+350 2420). However, they did not correct the

observations for the effects of atmospheric extinction, because they

considered the closeness of the comparison to the variable sufficiently

small to make correction unnecessary. After rectification of the light

curve they solved the 1964 observations to obtain the following elements:

Initial epoch (Julian Date) = 2438467.1282,

Period = 4d797660,

x = 0.8, i = 84,

k = 0.46, L1 = 0.269,

rl = 0.244, L2 = 0.731,

r2 = 0.112, e = 0.0 (assumed).

They found the period to be decreasing in the same sense as

Keller and Limber (1951) had found, but not by the amount predicted

by observations obtained prior to 1936. They concluded that the system

was semi-detached and that the material one would expect in such a

system was leaving the larger star. Thus a cloud would be formed which

would cause the anomalous light variations in the light curve. This

does not agree with subsequent research.

Plavec (1967) studied the properties of Algol-like close

binaries with double-line spectra. RS CVn was among the stars studied

and was found to be detached by a significant amount. Several other





15


stars were noticed to have similar properties which were different from

genuine Algol binaries. RS CVn, WW Dra, Z Her, AR Lac, and SZ Psc were

considered by Plavec to form a well-defined sub-group. It is significant

that except for SZ Psc all of these stars were in Hiltner's list of 13

systems showing Ca II emission.

Catalano and Rodono (1967) presented additional photoelectric

observations of RS CVn taken with the same equipment Chisari and Lacona

had used in 1963 and 1964. However, it may be of importance to note

that the observations were not all taken at the same site. The data for

1965 were apparently obtained from the same place as those of Chisari

and Lacona, but the equipment was then moved to Serra La Nave. The

subsequent data taken in 1966 were from this site using the same tele-

scope and equipment. All of the observations used the same comparison

star as Popper, Chisari and Lacona, and the present writer; namely

BD+350 2420. They also observed a check star (BD+350 2422), which

showed, contrary to Popper's earlier suspicions, that the comparison star

BD+350 2420 is of constant light. They made no attempt at a solution, in

the classical sense, to the new observations, but instead they pointed

out an important fact about the distortion wave in RS CVn.

The distortion wave was found to shift with respect to the

eclipses in the direction of decreasing phase, and completed one cycle

in 2400 orbital periods. To explain this phenomenon a model was

developed in which a ring of material circled the hotter star. This

was similar to the proposal of Chisari and Lacona, but the model

developed by Catalano and Rodono was much more detailed. In this model

a non-uniform ring of material was located around the smaller star of

the system. They assumed that the material would make Keplarian orbits





16


around this star and were therefore able to compute the distance

between the star and the ring. The period of the quasi-sinusoidal

distortion wave represented one orbit of a particle in the ring. The

results required that the material be outside the limiting Roche lobe

for the star. In this case the ring would be unstable, but they proposed

that the material lost from the system be replaced by material from the

larger star. If the primary star is inclined to the orbital plane, its

axis would be expected to precess with a period which they computed to

be about the same as that of the retrograde period of the distortion

wave. The quasi-sinusoidal shape would then be due to the non-uniform

distribution of material in the ring, but there was no exlanation for

the persistence of this particular distribution over the time scale of

the observations (1963 to 1966). The 1965 light curve showed no appre-

ciable variations beyond those already known, but the data for 1966 in-

dicated that the depth of primary eclipse was not the same for all

nights during which this portion of the light curve was observed. The

phenomenon was earlier reported by Keller and Limber and by Popper.

Whether this was real or a result of the new observatory site, in the

case of Catalano and Rodono's data, is not known.

Nelson and Duckworth (1968) reported, in an abstract, on the

observations they had obtained of RS CVn from 1965 to 1967. Their

observations were not given, but they reported that the light curves

show variations in the depth of primary and secondary eclipses of up

to a quarter of a magnitude in the violet, and similar but smaller

variations in the other colors. They also reported that the data showed

changing shapes for the eclipses and the portions of the light curve

outside eclipse, over the three years they observed the system.





17

Catalano and Rodono (1968) summarized several aspects of their

observations of RS CVn in a more widely accessible forum than their

previous publication. First, they found additional evidence for the

distortion wave's retrograde shift. From the observations of Keller

and Limber, Popper, Chisari and Lacona, their own published data for

1965 and 1966, and new unpublished data for 1967 and 1968,they were

able to more accurately determine the period of the retrograde shift.

Unfortunately, for their previous model, the results were incompatible

with the theoretical procession rate of 2400 orbital periods. They

found that the distortion wave retrograde shift period was of the order

of 800 orbital periods or less. The new data for 1967 and 1968 were ob-

tained on the standard UBV system, which allowed them to determine the

color of the system outside eclipse. From the graph of the color index

and outside eclipse variation, it was obvious that the color index in-

creased with decreasing intensity of the distortion wave. Since the

color of the distortion wave became bluer as it became fainter, they

suggested that the investigations of Mergentaler (1950) could be a

possible explanation. They reported that Mergentaler proposed that

systems which show such a color change can be explained by a gas of

negative hydrogen ions of different optical thicknesses. Catalano and

Rodono noted that this would require that the gas be in an equilibrium

configuration in order to maintain the shape of the distortion wave as

they had observed it. Variations in the depth of primary minimum had

been observed in the past, but their more consistent and more extensive

observations were able to confirm this phenomenonand to show that it was

correlated with the position of the distortion wave. Since the primary

eclipse was total, only the secondary (larger, cooler star) of the system





18


was visible at that time, thus this star was probably responsible for

the distortion wave phenomenon. It is not clear to the present writer

if Catalano and Rodono were referring to the secular (:800 orbital period)

shift of the distortion wave across the primary eclipse as the source of

variations in its depth or to some sort of flaring activity on the larger

star. In the former case it would be difficult to explain changes in

depth of primary eclipse which have been observed on much shorter time

scales. Nevertheless, their conclusion was in complete agreement with

the earlier conclusions of Payne-Gaposchkin (1939), Keller and Limber

(1951), and Popper (1961) regarding the source of the light variations

(in eclipse and/or out of eclipse).

The period variations had been well known previously, but there

had been significant evidence that the variations were due to apsidal

motion (Keller and Limber 1951; and Plavec and Smetanova 1959). However,

more recent studies of Plavec, Smetanova and Pekny (1961) have cast

considerable doubt on the appropriateness of apsidal motion to explain

the period variations. Catalano and Rodono showed that the existence of

a moving distortion wave made the measurement of photometric eccentricity

highly questionable. In fact they stated, ". .. the displacement of

secondary minimum resulting from our observations is incompatibly smaller

than the orbital period variations" (p. 440).

Finally, the Catania astronomers concluded the article with some

notes on the spectroscopic peculiarities in RS CVn. They had observed

the same emission lines of Ha, and Ca II as Hiltner (1947), Joy (1930),

and Popper (1961). Unlike Hiltner they were unable to notice the disap-

pearance of the H and K lines at secondary eclipse.






19


In a theoretical presentation, Hall (1972) discussed an alterna-

tive model for RS CVn. This model attempted to explain the following

characteristics of the system:

1. The existence of the distortion wave

2. The migration of the wave to decreasing phase

3. The anomalous depth of secondary eclipse

4. The non-uniform migration rate of the distortion wave

5. The variable depth of primary minimum as a function of time

6. The displacement of secondary minimum from a position mid-way

between adjacent primary minima

7. The variable amplitude of the distortion wave

8. The changes in orbital period

The model that was proposed by Hall, by analogy with the sun, was

that of spots on the cooler component of the system. It was well known

that the sun has dark spots on its surface from time to time. Starting

from this, Hall felt that it was reasonable to expect that other stars

would have similar spots. In the case of RS CVn, he anticipated that the

spot or spots would cover between 30% and 60% of the facing stellar disk

of the KO star. This spotted region was, for whatever reason, confined

to one hemisphere and to the equatorial region between about + 300. Hall

reasoned that the star would be rotating differentially, again by analogy

with the sun. The equatorial region would rotate faster than the polar

regions, as is the case in the sun (which also has a convective envelope).

The stars of the system were expected to be in synchronous rotation, but

the latitude at which the rotation was synchronized with the orbit was

expected to be of the order of + 300. Again relying on the analogy with

the sun, he assumed that the spot activity would be periodic, with a





20


cycle of 1800 orbital periods. Further, he assumed that the spots on

the cooler component of RS CVn would form at higher latitudes at the

beginning of each spot cycle, and proceed to form at lower and lower lati-

tudes as the cycle progressed.

With this model the existence of the distortion wave is easily

explained. Differential rotation of the star explains why the distortion

wave moves to decreasing phase. Since the surface of the cooler star is

not of uniform brightness, the depth of primary eclipse will vary depend-

ing on the location of the spotted hemisphere at the time of this eclipse.

Furthermore, the location of the spotted region can cause the location of

the minimum during the secondary eclipse to be shifted to either side of

phase 0.5. Since the model assumes that the spot activity is periodic in

a fashion similar to the sunspot cycle, and that the star rotates differen-

tially, then the migration rate of the distortion wave will vary depending

on the latitude of the spotted region and the amplitude of the distortion

wave will vary in a similar fashion.

Hall presented very convincing evidence to support this model.

The spotted region would only have to be 10000K cooler than the surround-

ing photosphere in order to account for the typical amplitude of the

distortion wave. This was of the proper value to also explain the anoma-

lous depth of secondary eclipse, if it was assumed that the spotted re-

gion was eclipsed at secondary minimum. Hall noted that this implies that

as the spotted region migrates, due to differential rotation, around the

star, the depth of secondary eclipse should vary accordingly. This has

not been confirmed.

Catalano and Rodono (1968) had shown the correlation between the

position of the distortion wave and the depth of primary minimum. Hall's





21


model provided an explanation for this. The deepest primary minima

occurred during times when differential rotation brought the spotted

region to the hemisphere facing the earth. The displacement of secon-

dary eclipse from the mid-point of the light curve had been explained by

Catalano and Rodono (1968) as a consequence of the migration of the dis-

tortion wave. Hall's model clarified this in terms of the location of

the spotted region during the secondary eclipse. If the spotted region

was located so that it faced the earth at quadrature, then the loss of

light during secondary eclipse would be asymmetric. From a plot of the

available estimates of the amplitude of the distortion wave as a function

of epoch, Hall was able to represent the variation with the periodic

function

AV(max-min) = -0T12 007 sin ((E+450)/1800).

He used the linear ephemeris of Schneller (1928) to calculate the value

of E. Note that this function can be used to predict the value of the

amplitude of the distortion wave at any time. Hall also presented

another graph which allowed the prediction of the distortion wave migra-

tion rate. In Fig. 2 of his paper he plotted the orbital phase of the

minimum of the distortion wave as a function of epoch (E). From this

graph one was able to see that the discontinuities in the migration rate

occur at the minimum of the spot cycle. This was the result expected

from the analogy with the sun and differential rotation. Arnold and Hall

(1973) later made corrections to the model without changing the substance

of the results.

In the remainder of the paper Hall attempted to explain the

period variations as the result of mass ejections from the spotted active

region. The required mass loss rate was rather high (of the order 106





22



solar masses per year). The conclusion he reached on the evolutionary

status of RS CVn was not decisive, but he considered the star to be most

likely in a pre-main-sequence state of evolution.

RS CVn Binaries

The early stages in the development of the definition of this

group of binary stars have been discussed in the preceeeding paragraphs.

Certainly, the research results of Struve (1946) and Hiltner (1947) were

the first clues to the existence of a group of stars which are different

from the classical binary and significantly different from other peculiar

systems. The research effort over the subsequent 30 years (Gratton 1950;

Plavec 1967; Popper 1967, 1970; Oliver 1971, 1973, 1974; and Hall 1976)

slowly developed a clearer picture of the physical and observational

characteristics of these stars which separates them from any other group

which has been classified.

Popper (1967, 1970) listed approximately 20 systems which he

believed to be of special interest because of their spectroscopic charac-

teristics, light variations, and unique placement in the H-R diagram.

Oliver (1974) was the first to undertake a comprehensive study of these

stars as a group. This research led Oliver (1971, 1973, 1974) to list

the criteria for inclusion in the group and to propose a list of stars

which would therefore be members. To date, the best review of the RS CVn

binaries is the recent paper by Hall (1976). In the paragraphs to follow,

the current understanding of the RS CVn phenomenon will be discussed.

Since the most characteristic observational property of the group is

strong H and K emission, the discussion will begin with the spectroscopic

characteristics. Variations in the observed light of the systems are an

observational property of many of the systems in the group. The discus-





23


sion of these variations will be followed by a short report on ultraviolet

and infrared excess. Period variations have also been noticed in many of

the RS CVn binaries; the short and long-term variations will be reviewed.

The recent discovery of radio and soft X-ray emission from several of the

RS CVn binaries has been very exciting. The report here will attempt to

summarize these observations and the resulting implications. Finally,

this section will conclude with a review of the proposed evolutionary

status of these stars. However, before beginning, it will be useful to

state the properties of RS CVn binaries which Hall (1976) proposed as

the defining characteristics. They are as follows:

1. Orbital period between 1 day and 2 weeks

2. Strong H and K emission seen outside eclipse

3. The hotter star is F or G, IV or V

The list of members in this group which has been developed over the last

few years is given in Table 3. This list is derived from Hall's (1976)

review paper and new discoveries.

Spectroscopic characteristics

The existence of strong H and K emission in the RS CVn binaries

has been well documented by Struve (1946), Hiltner (1947), Eggen (1955),

Popper (1967, 1970), Oliver (1974) and Weiler (1978a). The emission is

strong in the sense that it is usually significantly above the continuum.

In no case is this H and K emission to be confused with the normal emis-

sion core reversal in late-type single stars which gives rise to the

Wilson-Bappu effect.

Struve (1946) studied the variation in the strength of the H and

K lines as a function of phase angle in several stars. It was his con-

clusion that the maximum strength was at the quadrature points (O025 and





24


TABLE 3

LIST OF RS CVN BINARIES

Name V Orbital Spectral Type Masses (a,c)
fa Period(b) hot + cool(b) hot + cool

UX Ari 6.5 6.438 G5V + KOIV 0.63 + 0.71
CQ Aur 9.0 10.621 GO
SS Boo 10.3 7.606 dG5 + dG8 1.00 + 1.00
SS Cam 10.0 4.824 dF5 + gG ... ...
RU Cnc 10.1 10.173 dF9 + dG9
RS CVn 8.4 4.798 F4V-IV + KOIV 1.35 + 1.40
AD Cap 9.8 6.118(d) G5 0.5: + 1.1:
UX Com 10.0 3.642 G5-9 0.95 + 1.12
RT CrB 10.2 5.117 GO 1.27 + 1.34
WW Dra 8.8 4.630 sgG2 + sgKO 1.4 + 1.4
Z Her 7.3 3.993 F4V-IV + KOIV 1.22 + 1.10
AW Her 9.7 8.801 G2IV + sgK2 1.38 + 1.36
MM Her 9.5 7.960 G8IV 1.20 + 1.24
PW Her 9.9 2.881 GO 1.4 + 1.6
GK Hya 9.4 3.587 G4 1.2: + 1.3:
RT Lac 9.0 5.074 sgG9 + sgKl 0.6 + 1.5
AR Lac 6.9 1.983 G2IV + KOIV 1.30 + 1.30
RV Lib 9.0 10.722 G5 + K5 2.2 + 0.4
VV Mon 9.4 6.051 GO .
LX Per 8.1 8.038 GOV + KOIV 1.23 + 1.32
SZ Psc 7.3 3.966 F8V + KlV-IV 1.33 + 1.65
TY Pyx 6.9 3.199 G5 + G5 1.20 + 1.22
RW UMa 10.2 7.328 dF9 + K1IV 1.50 + 1.45
RS UMi 10.1 6.2(e) F8(e) .
HR 1099 5.9 2.8(e) G5(e) 0.18 + 0.23
HR 5110 5.0 2.613 F2IV + KIV 0.02 + 0.005
HD 5303 ... 1.840(f) G2V + FO(f)
HD 224085 7.6(g) 6.724(g) K2-3IV-V(g)
W92 11.7(h) 0.745(h) KOIVp(h)


Notes for Table 3.

a Unless otherwise noted values from Popper and Ulrich (1977).
b Unless otherwise noted values from Hall (1976).
c M sin3 i.
d Popper and Ulrich (1977) list as 3.0 days.
e Popper and Ulrich (1977).
f Hearnshaw and Oliver (1977).
g Rucinski (1977).
h Walker (1978).





25


075). Oliver (1974) summarized the existing data by saying that the

emission was usually at a minimum during the secondary eclipse, but not

in all cases, nor at all times. Hiltner (1947) had found a disappearance

of the H and K emission lines at secondary eclipse in RS CVn. This led

him to believe that the emission originated from localized sources at

the extremities of a tidal bulge along the line joining the two stars.

Struve (1946) had earlier offered a similar explanation for the origin

of the emission in similar cases. Catalano and Rodono (1968) were

unable to confirm the disappearance of the Ca II emission lines at

secondary minimum, thus raising some doubt as to the validity of

Hiltner's tidal bulge hypothesis. More recent studies by Weiler (1975a,

1978a)find that the emission is associated with the larger star, but the

emission is not localized. Furthermore, Weiler does not find the

strengthening at the quadriture points or the tendency for the emission

to weaken at secondary minimum.

The existence of Ca II emission is indicative of chromospheric

activity (Young and Koniges 1977; Weiler 1975a; Naftilan and Drake 1977;

and Weiler 1978a). This emission must originate from the larger (cooler)

component because the emission lines have velocities which agree well

with the absorption lines for this component (Popper 1961; Oliver 1974).

In addition, the width of the emission lines is of the proper amount to

be explained by the synchronous rotation of the larger star (Popper

1970).

The emission lines of Ca II are not the only emission lines which

have been reported. Weiler (1978a)studied 6 RS CVn systems and found

H to be in emission in all 6. Naftilan (1975) found H to be in emis-

sion (weakly) in RS CVn itself. The H emission in AR Lac has been
a





26


associated with the cooler star by Naftilan and Drake (1977). The H

emission in the six systems studied by Weiler (1975a, 1978a) was variable

to a significant degree in four of them. Similar emission in the H line

has been reported by Bopp (1978) for the systems HR 1099 and UX Ari.

However, it was noted that these were the only two stars from a survey

of about 30 stars which showed persistent H emission. Three other stars

showed sporadic H emission at the resolution used. Weiler (1978b)

points out that at higher resolution it is possible that all RS CVn

binaries may show some filling in of the H line by emission.

The H and H and K emission in several RS CVn binaries has shown

correlation with the phase position of the distortion wave and the phase

of greatest emission (Bopp 1976; Herbst 1973; and Weiler 1975b, 1978a).

In addition Weiler finds the distortion wave more pronounced the greater

the correlation. This is strongly suggestive of a physical relationship

between the causes of the two phenomena. Weiler (1978a) suggests that

the emission is due to an active photosphere which in turn drives an

active chromosphere in the region of the photospheric activity. Young

and Koniges (1977) attribute this to tidal coupling which increases the

density scale height and thereby changes the acoustic-wave power spectrum.

These investigators feel that the results support Hall's (1972) model

for a spotted surface on the cooler component in RS CVn, and possibly

other stars with similar characteristics.

Oliver (1974) found a variation in the absorption line strengths

but the correlation with light curve variations was weak.

The abundance of metals in binary systems was studied by Miner

(1966). In the systems he studied, an underabundance of metals was

found in eclipsing binaries. The underabundance does not appear to be





27

as great in the 3 RS CVn systems which were included in the project as

for the other eclipsing systems. The sub-giant components of 12 Algol-

like binaries were observed by Hall (1967) and found to have an under-

abundance of heavy elements. Naftilan (1975) found the cooler stars in

RS CVn and RW UMa to be underabundant in iron and chromium, which he

noted is in contradiction to a pre-main-sequence state of evolution.

The cooler component of AR Lac was also found to be deficient in metals

by Naftilan and Drake (1977). Anderson and Popper (1975) concluded that

from the observed radius and temperature of the stars in TY Pyx there is

an indication of an abundance (or opacity) anomaly in both stars. This

would seem to indicate that RS CVn binaries are not very young. Naftilan

and Drake (1977) have concluded from their research that the anomalously

low metal abundance is not due to free-free emission filling-in the metal

lines in AR Lac, nor is it due to a circumstellar shell. Recent soft

X-ray emission from UX Ari has led Walter, Charles, and Bowyer (1978) to

conclude that the heavy element depletion in this system is real, because

they do not observe an Fe emission line at 0.85 KeV as was seen in the

X-ray spectrum of Capella.

Lithium (Li) has not been detected in several RS CVn binaries;

this supports the view that these stars are not very young (Naftilan and

Drake 1977; Young and Koniges 1977; and Conti 1967). On the other hand,

Rucinski (1977) has found a weak Li line in HD 224085. This system was

recently added by Hall (1978) to the list of RS CVn type binaries.

As has been mentioned previously, a correlation between chromo-

spheric Ca II emission and tidal coupling has been found by Gratton

(1950), Young and Koniges (1977), and Glebocki and Stawikowski (1977).

The investigators do not agree, however, as to the cause of the emission.





28


Young and Koniges believe that this is evidence that when a star's outer

atmosphere is affected by gravitational attraction of a close companion

the result is a change in the density scale height. This shifts the

acoustic-wave power spectrum to lower frequencies, which results in a

large increase in the dissipation of energy into the chromosphere.

Gratton believed that the tidal distortion would produce localized

regions of emission in accordance with Hiltner's model. However, the

latter interpretation was excluded by Struve (1948) when he was unable

to find the expected degree of linear polarization from such a localized

region. Weiler (1978a)was also unable to find the variation in the H

and K emission lines as a function of phase that would be expected from

the tidally distorted bulge. He concluded that the emission may well be

somewhat localized, but not at the extremities of a tidal bulge formed

along the line joining the two stars. Glebocki and Stawikowski believe

that their study of H and K emission supports the tidal bulge hypothesis,

while Weiler feels that his research clearly points to an active chromo-

sphere. Time may resolve the dispute.

Photometric anomalies

The light curves of many (if not all) of the RS CVn binaries show

various anomalies. The most common and striking light curve anomaly is

a quasi-sinusoidal wave that distorts the normal eclipse phenomenon as

can be seen in Figure 1. This wave-like distortion has been referred to

as the "distortion wave" by Oliver (1974); this term will be used

throughout this dissertation. There are, however, other phenomena which

are abnormal in the light curves of these binaries. Several of the sys-

tems show season-to-season changes in the system brightness, while a few

have exhibited increases in brightness over very short time scales. The

















1.50



1.25 IS I *
I-

U) +
Z 1.00 t
Lw +
Z 4
z
0.75 +
+


0.50 -



0.25 I I II I
0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.1 0.2 0.3 0.4 0.5 0.6
PHASE


Fig. l.-The 1975 visual light curve of RS Canum Venaticorum.





30

short time scale variations have been referred to as flare-like activity

by some observers. These irregular changes in the light of the system

cannot be explained by changing parameters of the distortion wave, and

are therefore discussed as separate (but perhaps related) phenomena.

Besides the variations in the light of the system, the light curves of

these binaries have two additional anomalies which warrant mention.

First, the depth of the primary eclipse in several systems has shown

variations, which are not associated with changes in system brightness.

Second, the secondary eclipse for many systems has shown variations in

its position and depth.

The distortion wave in RS CVn was first noted by Sitterly (1930)

as a difference in the heights of the maxima. This observation was noted

by several researchers before the true picture was developed by the

Italian astronomers at Catania. Following the advice of Popper (1961)

the Catania astronomers (Chisari, Lacona, Catalano, and Rodono) started

a long-term program of photoelectric observations of RS CVn. This work

produced the remarkable discovery that the difference in the heights of

the maxima was changing, and the changes could be explained by a migrating

quasi-sinusoidal wave superimposed on the light curve. Chisari and

Lacona (1965) and Catalano and Rodono (1967, 1968) showed very convincing

evidence for the existence of this wave, and for the slow migration to

decreasing phase angle from season-to-season. They referred to the slow

shift of the distortion wave to decreasing phase as a "retrograde migra-

tion." Oliver (1974) has shown that this property is very common in the

RS CVn binaries which he studied. It is commonly held that the existence

of the distortion wave and the retrograde migration are properties that

all RS CVn binaries share. The evidence is not complete for all the





31


systems considered to be of the RS CVn binary type, but many systems have

shown this phenomenon (Bopp, Espenak, Hall, Landis, Lovell, and Reucroft

1977; Oliver 1974; Hall 1972, 1977; Popper 1974; Chambliss 1976; Milone

1968; Nelson and Duckworth 1968; Hall, Henry, Burke, and Mullins 1977;

Hall, Montle, and Atkins 1975, Blanco and Catalano 1970; Landis, Lovell,

Hall, Henry, and Renner 1978; Hearnshaw and Oliver 1977; and Rucinski

1977). Many of the above investigators reported migration rate changes,

and variations in the amplitude of the distortion wave from season-to-

season. Perhaps significantly, Eaton (1977) has found the distortion wave

to be moving to increasing phase in the system SZ Psc. The retrograde

migration in SS Boo has apparently reversed itself according to Hall

(1978). The color dependence of the distortion wave amplitude is very

interesting. For most of the systems (reported in the aforementioned

publications) the amplitude is greater in the V band than in the B band.

However, there are notable exceptions to this: WW Dra (Oliver 1974),

RT Lac (Milone 1968), UV Psc (Sadik 1978), and SZ Psc (Eaton 1977).

In addition to variations in the amplitude of the distortion

wave within a system, the size of the amplitude varies a great deal from

system to system. The largest amplitude appears to be about 0.2 for

RS CVn (in the V band), and the smallest appears to be about 0 02 for

several other systems. Recently, information as to the actual shape of

the distortion wave has become available. Rucinski (1977) noted an inter-

esting change in the shape of the light variations for HD 224085, and the

present writer (Ludington 1978) has noted changes in the detailed shape of

the distortion wave in RS CVn. Hall, Montle, and Atkins (1975) noticed a

change in the shape and/or amplitude of UX Ari from their UBV and JHKL

photometry in 1972. The significance of these variations is not clear,

but they would seem to point to dynamic structures on the stellar surfaces.





32

Popper (1967) and Oliver (1974) have noted that the RS CVn sys-

tems show small irregular variations in the system brightness. Wood (1946)

was perhaps the first to observe these irregular variations in the system

AR Lac. More recently, Bopp et al. (1977) have found evidence for irreg-

ular variations of 0T02 in the output of HR 1099. Larger variations

have been discovered in the brightness of UX Ari by Hall (1977) and

Landis et al. (1978). The latter group also detected a flare-like event

of JD 2443054.76 which lasted for approximately one hour, and increased

the system brightness by 0O15.

The irregular variations discussed in the last paragraph refer

to the total system brightness. Light variations have been reported

during the primary eclipse by Wood (1946) and Keller and Limber (1951)

for AR Lac and RS CVn, respectively. Similar changes during primary

eclipse have been noted by Popper (1961) for RS CVn; Milone (1977) for

RT Lac; Nelson and Duckworth (1968) for RS CVn; and Oliver (1974) for

SS Boo, WY Cnc, RS CVn, Z Her, AR Lac, RT Lac, and SZ Psc. It should

be noted that several of these systems have total (occultation) primary

eclipses. Therefore, if the variation is seen during this total phase,

it is expected that the variation is due to intrinsic variability of

the larger (cooler) star only. In the case of AR Lac, this is not the

case. The total portion of primary eclipse was seen to have small or

no variation (Kron 1947). Kron found that the variation occurredduring

the ingress and egress branches of the eclipse.

Since the primary eclipse in RS CVn is total, then the secondary

eclipse will be annular. Thus, since the larger star is still visible,

it is not surprising that this eclipse also shows anomalous behavior.





33


Keller and Limber (1951) found that from the depth of the eclipse the

ratio of intensities was much less than would be expected for stars of

the spectral types which make up RS CVn. Popper (1961) found the same

inconsistency with the system, but also found the discrepancy to be less

severe. In addition, Keller and Limber reported a small eccentricity

from the displacement of secondary eclipse. Neither the spectroscopic

orbit of Joy (1930), nor the orbit of Popper C1961) showed anything but

a circular orbit. The distortion wave discovered by the Catania ob-

servers supplies the explanation for both the changing depth of primary

minimum and for the displacement of the secondary eclipse from the 0?5

position. The variation in brightness at the total phase of primary

eclipse and the displacement of secondary eclipse are correlated with the

migration of the distortion wave. Hall's C1972) model took the distortion

wave explanation one step farther. If the spotted region that Hall pre-

dicts does indeed exist, then the anomalous depth of secondary eclipse

is explained by the variation of the surface brightness of the larger

star. Hall's spot model also explains the displacement of secondary

eclipse in more concrete terms.

Optical and radio polarization

The polarization of the electromagnetic radiation from RS CVn

binaries was first searched for by Struve (1948). In this study he

attempted to locate the linear polarization which would result from

the tidal bulge proposed by Hiltner (1947).as the origin of the Ca II

emission. The H and K lines of AR Lac showed no evidence of linear

polarization. Struve placed an upper limit of 10% on the polarization

from this star. In a survey of unevolved and evolved main-sequence

binary systems Pfeiffer and Koch (1977a) found that the unevolved





34


systems showed no significant linear polarization. The evolved binaries

showed intrinsic linear polarization if the log S was greater than or

approximately equal to 1.0. Here the 'S' represents the separation of

the stellar photospheres in units of solar radii. They further stated

that the incidence of polarization in this group does not depend on mass-

ratio, total system mass, fractional component size, rotational velocity,

the stage of evolution (Case A or Case B), or the detached or semi-

detached state of the system. It was their belief that this was evidence

for the necessity of sufficient "free" volume to allow more material and/

or greater asymmetry to produce the linear polarization.

Three RS CVn binaries have been reported to have some degree of

polarization. RS CVn was reported to display variable linear polariza-

tion by Pfeiffer and Koch (1973). The variation was cyclic with orbital

period and showed random short-term variation. This was suggestive to

them of electron and/or Rayleigh scattering in an active circumstellar

envelope. Only an upper limit could be set by Pfeiffer and Koch (1977b)

for the linear polarization in the visual band for HR 1099 (less than

0.02%). At radio wavelengths no significant linear polarization has been

detected for HR 1099 or UX Ari, but a significant degree of circular

polarization has been detected (Owen et al. 1976; and Spangler 1977).

The degree of circular polarization was found by them to be a function

of wavelength, and was only detected during outburst activity. This was

suggestive of microwave bursts like those observed from the sun.

Pfeiffer (1978) recently reported on some very detailed polariza-

tion studies of RS CVn. He concludes that the polarization is due to

scattering in a large cloud which engulfs the system. He also comments

that RS CVn itself is the only RS CVn binary in which he has been able





35


to detect linearly polarized light, as of the time of his presentation.

Ultraviolet and infrared excess

Oliver (1974) has done the most comprehensive study of ultra-

violet (UV) excess in the RS CVn binaries. It was his conclusion that

an ultraviolet excess was a common occurrence in the U-B color index of

the cooler component. Since few of the stars have UBV data available,

it is conceivable that virtually all the systems have a cooler component

with a UV excess. Recently, Rhombs and Fix (1977) presented data which

confirmed very clearly the UV excess in RS CVn, AR Lac, and UX Ari. They

also were able to show that the cooler component was responsible in each

case. Hall (1972) suggested that the excess could possibly be analogous

to the excess in T Tauri stars. Rhombs and Fix, on the other hand, con-

cluded that free-free emission from a hot circumstellar gas was the best

explanation.

Infrared (IR) excess, like the ultraviolet excess, appears to be

a common characteristic of nearly all RS CVn binaries. The problem of

the infrared excess has been discussed by several authors (Atkins and

Hall 1972; Hall, Montle, and Atkins 1975; Hall 1976; and Milone 1976a,

1976b). There is general agreement that at least the majority of RS CVn

binaries display some degree of infrared excess, but the source of the

excess is controversial. Milone (1976b) found an IR excess in 10 of 14

systems showing light curve asymmetries, which were chosen at random for

study. Of this group, 5 systems are classed by Hall (1976) as RS CVn

binaries. Three of these were definitely found by Milone to have an

infrared excess. He cautioned, however, that the other two stars (SS Boo

and WW Dra) may well show the excess because the spectral type and light

ratios were taken from the literature and could cause a mis-evaluation of





36


the excess. Atkins and Hall (1972) found an infrared excess in 5 or 6

systems for which they had sufficient data to make an adequate evaluation.

Milone (1976a,b) considers the IR excess to be due to a circumstellar gas

around the more massive component of the system. Atkins and Hall (1972)

did not consider a circumstellar cloud a possible explanation for the

JHKL photometry they had obtained. This question remains unsettled, but

in light of the polarization data of Pfeiffer (1978) it would seem that

a circumstellar cloud may be the correct explanation at least in the

single case of RS CVn itself.

Period variations

The period variations in many of the systems listed by Hall (1976)

are very pronounced. He noted that a linear ephemeris in some cases can

lead to errors of about a quarter of an orbital cycle in only 10 years or

so. Hall suspects that virtually all of the systems have these large

period variations, because about a third are known to, and the rest have

insufficient data.

Since th.e RS CVn binaries are detached systems, the period changes

are not due to the same mechanism as in the semi-detached Algol-type

binaries. In the previous section on the history of RS CVn it became

apparent that the period changes are also not due to apsidal motion or

light-time effects of orbital motion. Therefore, it is very clear that

the mechanism responsible is rather unusual.

Flare-type mass ejection from one hemisphere has been proposed

as an explanation for the short-term period changes CHall 1972; Arnold

and Hall 1973; Hall 1975b; and Hall 1976). In this model the brighter

hemisphere is ejecting matter by a high-velocity impulse-type mechanism.

This results in a correlation between the observable short-term period





37

changes and the observable phase of the distortion wave minimum. The

mass loss rate required to account for the period variations is rather

large: 10- Mo/year. In the latest version of this model, Hall (1976)

suggests that the effective moment arm is some Alfven radius so that the

required mass loss rate is reduced.

Several aspects of this model have been criticized. Catalano and

Rodono (1974) objected to ejection of material from the brighter hemi-

sphere on the grounds that one would expect flare-type mass ejection from

the active spotted hemisphere. They also pointed out that the measurement

of the time of minimum was affected by the deformation of primary eclipse

by the distortion wave. This effect would have the same sense as the

correlation of distortion wave minimum with period change. Hall (1975b)

was able to show that, while it was true that the effect had the same

sense, the magnitude of the 0-C variations by deformation of primary

eclipse were 25 times too small.

In the case of AR Lac it has been possible to use a modification,

for this specific system, of the model to explain the long-term period

changes (Hall, Richardson and Chambliss 1976). The long-term period

variations in the other systems have not been adequately explained.

Further research, both observational and theoretical, is greatly to be

desired in this area.

The possibility of an enhanced stellar wind in RS CVn binaries

has been proposed by Oliver (1974), Ulrich and Popper (1974) and Popper

and Ulrich (1977). This is a conceivable source of period changes and

deserves further investigation as pointed out by Hall (1976).





38


Emission at radio wavelengths

The detection of an RS CVn binary at radio wavelengths by Gibson

and Hjellming (1974) was believed by them at first to indicate mechanisms

similar to those for known Algol-like flares. The spectral index of the

flare was definitely non-thermal as was the case for the Algol-like

flares. Later work by Gibson, Hjellming, and Owen (1975) showed that

the flares were non-thermal in UX Ari but that an evolving synchrotron

source was a more likely mechanism than the infall of matter.

Gibson et al. (1975) compared the flare from UX Ari with those

of UV Ceti stars, and found that there was little similarity. The spec-

tral index for a UX Ari flare was about +0.2, while typical values for

UV Ceti stars range from -3 to -5. Even at the end of the flare observed

on 11, 12 August 1974 the spectral index of UX Ari only reached -0.6.

Therefore, the type of flare is different from those in UV Ceti stars.

This was supported by the decay time-scales in the 2 types of

flares. Gibson et al. (1975) found that a UX Ari flare decayed on a

time-scale of days. This was about 100 to 200 times the decay rate of

a flare in a typical UV Ceti star.

Circularly polarized emission has been detected at radio wave-

lengths by Spangler (1977), and Owen, Jones, and Gibson (1976) from

2 RS CVn binaries (UX Ari and HR 1099). The level of polarization was

about 5% (for UX Ari) to 20% (for HR 1099) at 1400 MHz, about 8% (for

HR 1099) at 8085 MHz, and less than 2% (for HR 1099) at 2695 MHz. The

detection of circular polarization in these stars contrasts sharply with

the lack of circularly polarized emission from Algol.

No linear polarization has been detected at radio wavelengths

from any RS CVn binary at the time of this writing. Owen et al. (1976),





39


however have put an upper limit of 2-3% at 2695-8085 MHz for the linearly

polarized emission from HR 1099.

No correlation has been found between optical and radio variability

as reported by Chambliss (1976) and Spangler (1977). This is not a sur-

prising result if the flare-like activity is similar to the typical solar

microwave flare. In these solar flares the energy output in the radio

region is much greater than in the optical region.

Radio binaries tend to be of late spectral type (G and K), and

they tend to be above the main-sequence according to Owen and Spangler

(1977). This may be part of the explanation for the high frequency of

radio emitters among RS CVn binaries. On the other hand, and perhaps

more likely, the statistics may be biased by the selection of RS CVn

binaries as candidates for radio emission surveys. More data are required

to establish this point more clearly either way.

Owen and Spangler (1977) were unable to detect any change in the

observed flux from AR Lac at 4585 MHz during any eclipse. This is a good

indication, as they pointed out, that the source is not a compact region

between the two stars. They computed that the radius and brightness

temperature of a source located in this region would be limited by

r > 3 x 1011 cm, and Tb > 4 x 109 K.

Gyrosynchrotron radiation has been suggested as the source of the

radiation (Gibson et al. 1975; Owen et al. 1976; Spangler 1977; and

Owen and Spangler 1977). These authors have found that this mechanism

explains the radio flare observations better than other alternatives they

have considered. It accounts for the observed non-thermal spectral index,

the circularly polarized emission during flare events, and the absence of

linear polarization (if reasonable assumptions are made about the physical
properties of the emitting region).





40


A magnetic field of about 30 Gauss and an electron density of

about 2.4 x 1010 cm- would be indicated by Spangler's (1977) calcula-

tions. Spangler et al. (1977) felt that this model compliments Mullan's

(1974, 1976) theory, and therefore would also seem to support the star-

spot hypothesis of Hall (1972, 1976).

Soft X-ray emission

A most exciting discovery has been the recent detection of soft

X-ray emission (0.2 to 2.8 KeV) from many RS CVn binaries. As of June

1978, Liller (1978) reported that 11 of the RS CVn binaries had been

identified as X-ray sources. This compares with two or three identifica-

tions reported by Charles (1978) in April 1978. This discovery, along

with the previously known radio emission, gave additional credence to the

solar analogy of highly active regions in the atmosphere of the sub-giant

component as proposed by Hall (1972, 1976).

Cash, Bowyer, Charles, Lampton, Garmire, and Riegler (1978) were

able to fit a solar abundance plasma at about 107 OK to the soft X-ray

spectrum of Capella. This star was included as a related system to the

RS CVn binaries in Hall's (1976) discussion. It is not a "classical"

RS CVn binary, so the importance of the above paper is clear only when

subsequent soft X-ray data are reviewed. The soft X-ray spectrum of the

"classical" RS CVn binary UX Ari was fit with a plasma of 107 OK, but it

could not be fit with a plasma of solar abundance (Walter, Charles, and

Bowyer 1978a). This gives additional evidence for an underabundance of

heavy metals in RS CVn systems. This result was confirmed in two other

"classical" systems, RS CVn itself and HR 1099, by Walter, Charles, and

Bowyer (1978b). The spectra of these two stars could not be fit as nicely





41


as was the case for UX Ari, but the authors found that the results were

consistent with a 107 K thermal spectra in both cases.

Walter et al. (1978a) felt that the soft X-ray spectra of RS CVn

binaries was consistent with an active spotted region. In this model

they saw the active region as associated with flare-like activity, which

in turn would continuously supply sufficient energy to power a 107 OK

corona. At this temperature they computed the velocity of the ions

to be sufficient to rapidly deplete the matter. However, they noted

that a magnetic field of only 50 Gauss would be enough to bottle up the

hot plasma.

In addition to the above, Walter et al. (1978a) noted three inter-

esting facts about the new information obtained from the X-ray detectors.

First, they noted that if UX Ari is anything like a typical RS CVn binary,

then from the space density of 10-5 pc-3 the RS CVn binaries contribute

a full 10% of the soft X-ray background at low galactic latitudes. Second,

they computed the mass loss rate from their emission measure. The value

they obtained (10-10 M /year) is in reasonable agreement with that pro-

posed by Ulrich and Popper (1974). Third, they reported that White,

Sanford, and Weiler (1978) have detected a flare in the X-ray spectrum

of HR 1099 which was coincident with a radio flare.

The evolutionary status

The evolutionary status of the RS CVn binaries has been an

especially difficult problem. The mass of the components is generally

of the order 0.5 to 1.5 M This is for both stars and therefore, with

few exceptions, the mass ratio is very close to unity. The picture that

has developed over the last 10 or 15 years regarding binary star evolu-

tion has, in general, shown that mass ratios near unity should be the





42

exception. RS CVn binaries are much too numerous to be an exceptional

case. Thus a problem appears; either the binary evolutionary scheme is

wrong or the RS CVn systems do not exist. Obviously, this is much too

"black-and-white" a statement. More to the point, it would be expected

that the theory needs some adjustment in order for the large number of

systems with unity mass ratio to be explained. It is important to real-

ize that the binary evolutionary theory referred to above explains the

evolution after the existence of the binary pair on the main sequence.

The evolution prior to this point is not well understood, and could very

easily be the key to the unity mass-ratio puzzle.

The similarity of the characteristics of the cooler component of

RS CVn to those of T Tauri stars led Hall (1972) to conclude that RS CVn

was in pre-main-sequence evolution. This was in contradiction to the

earlier investigation by Field (1969), who found that RS CVn as well as

AR Lac were not in pre-main-sequence contraction. The age of the RS CVn

binaries as determined by Montle (1973) supported the pre-main-sequence

evolutionary picture.

Eventually, a clearer case arose for the post-main-sequence

evolutionary status for the RS CVn binaries. This process started with

Oliver's (1974) evaluation of the evolutionary status and his suggestion

of a slow mass transfer by means of a strong stellar wind. Ulrich and

Popper (1974) proposed that by allowing for such a stellar wind it would

be possible for the evolutionary status of these stars to be explained on

the basis of normal single star models.

The pre-main-sequence status for binaries of the RS CVn type was

almost conclusively eliminated as a possibility by Hall (1975b), and

Biermann and Hall (1976). Hall (1975b) found that the visual companion of





43


the eclipsing RS CVn binary WW Dra was a normal F8 V star. The most

important thing about is was the estimate of its mass. It was less

massive than either star in the WW Dra system. This clearly would indi-

cate that the stars in WW Dra could not be in pre-main-sequence contrac-

tion. Hall also showed that there was sufficient evidence of binary

motion for the possibility of an optical pair to be insignificant.

Biermannand Hall (1976) gave very convincing arguments to exclude

the pre-main-sequence evolutionary status. They concluded by a process

of elimination that the RS CVn binaries were the result of the fission

of a single star as it leaves the main-sequence.

At the time of this writing, the consensus is that the evolu-

tionary picture as presented by Popper and Ulrich (.1977) is the closest

to reality. They presented the following circumstantial evidence of

post-main-sequence evolution of RS CVn binaries:

1. They are not associated with regions of known star formation

2. For the mass and radius range the post-main-sequence life-time is

100 times longer than the pre-main-sequence life-time

3. The larger radius is associated with the more massive component

4. WW Dra and HR 1099 have dwarf companions of lower luminosity

In addition, they recalculated the age of the RS CVn binaries using

Montle's (1973) value for the velocity dispersion and Wielen's (1974)

calibration. The results indicated that the RS CVn binaries are about

3x109 years old Ci.e. about the same age as similar main-sequence stars).

In fact, they felt that the age is very slightly greater than a main-

sequence star, and that the RS CVn binary phenomenondevelops when stars

of this general nature reach the Hertzsprung gap. In some cases they

proposed that it would be necessary to modify simple single star evolu-





44

tionary processes by a slow stellar wind (-5 x 10o11Mo/year) in order to

account for the system's current position on the H-R diagram.

Scope of Dissertation

The intent of this dissertation can be summarized by two goals:

1. To obtain two new light curves of RS CVn in (at the minimum) two

colors, separated in time by approximately one year; however, the data

for each must be obtained within a three month term in order to minimize

the effect of a migrating distortion wave;

2. To determine the elements of the eclipsing system for RS CVn by a

new technique which eliminates the problems introduced by the photometric

distortion wave.

In meeting these two goals, several others will, by necessity,

result:

3. The constancy of the comparison star BD+350 2420 will be confirmed.

4. The distortion wave will be isolated so that it may be studied in a

future research effort.

5. The radial pulsation model for the photometric distortion wave will

be refuted.














CHAPTER II
INSTRUMENTATION


The Basic Equipment

The instrumentation used in collecting the data presented in this

dissertation may appear to some in the avant-garde of instrumental

development as antiquated. This sentiment is partially due to the

enormous technological development during the past decade. In addition,

this attitude reflects a prevailing view that innovation is superior.

Snobbery and high technological advance aside, the important point is

that the data presented here of RS CVn are of the highest quality.

The 46 cm telescope used in this investigation is located at

Rosemary Hill Observatory, 6.5 km from Bronson, Florida. The optics,

telescope tube, equatorial fork mount, and pier were built by R. E.

Brandt. The electrical drive, slow motion controls, secondary mirror

mount, finder scope, counter weight, and setting circles were installed

by the staff at the University of Florida (primarily, John P. Oliver,

E. Whit Ludington, and Eli Graves). The optical system is an f/10.5

Ritchey-Chritien design. The mirrors of the system are aluminized and

Beral overcoated.

The photometer has been described by Chen and Rekenthaler (1966).

Four diaphragms are available; they are small circular openings of

0.500, 0.2500, 0.079 and 0.039-inch diameters on a rotatable disk.

The smallest opening was used in all of the photometry presented here;

this corresponds to a diameter of 42.5 arc seconds on the sky.

45






46


There are three filters which the user may select. The light

passes through only one filter at a time, and the observer must manual-

ly move the slide on which the filters are mounted to the desired filter

before a reading is taken. The ultraviolet filter (u) is made from

Corning 9863, the blue filter (b) is made from Corning 5030 and Schott

GG13 in combination, and the yellow (or visual) filter (v) is made from

Corning 3389. These filters, in union with the same instrumentation used

in this photometry of RS CVn, have been found by Markworth (1977) to

match closely the standard UBV system. The photomultiplier tube used in

this work was an EMI 9781, operated at 900 volts.

A DC electrometer amplifier designed by Oliver (1976) was used

to amplify the current from the photomultiplier tube. This amplifier,

called PA-10, has many different gains which may be selected by rotary

switches. This allows an amplification from 0 to 105. The amplifier

was used with a time constant of second.

All of the data were recorded on a Heath chart recorder with a

fiber-tip pen operated by a servo-type motor. The observer may select

from a wide range of speeds on this chart recorder. In all the record-

ings of RS CVn, speeds of either 1 inch/min or 0.5 inch/min were used.

The data from 5, 6 March 1976 onward were also recorded manually

from a digital integrator. This instrument, referred to as DA-10, was

designed and built by John P. Oliver. It integrates the signal by

counting the pulses from a voltage-to-frequency converter in the PA-10

amplifier. The observer has the option of many integration times from

1 second to 100 seconds. The integrations are started manually,

but are stopped and displayed by the internal electronics.






47






46 cm Ritchey- Chritien
telescope




r- - ~ -42.5 arc second
/ diaphragm


EMI 9781 and
ubv filters

HIGH VOLTAGE
SUPPLY
900 v

PA-10
OC
AMPLIFIER









CHART
RECORDER
DA-IO
DIGITAL
INTEGRATOR







Fig. 2.-Schematic diagram of the instrumentation used to obtain
the photometric data of RS CVn at Rosemary Hill Observatory during
the years 1975 and 1976.





48



A schematic diagram of the instrumentation appears in Fig. 2.

From MJD 42469 to MJD 42492, inclusive, the attachment of the

photometer to the telescope required the use of a glass-prism diagonal.

The glass in the prism is opaque to the ultraviolet region of the spec-

trum; for this reason only the v and b filters were used. Since no u

data were obtained during this time, it was impossible to compute the

u-b color. This explains the absence of values for these dates in the

tabulation in the appendix.

Amplifier Calibration

It is desirable that the amplifier be linear and stable for

high quality photometry. The linearity of the PA-10 has been demon-

strated by Oliver (1976). The stability can be demonstrated by the

nightly calibrations obtained during the course of this research.

Usually at the beginning and end of each night of observing,

a calibration sequence was obtained. A calibration sequence consisted

of a set of deflections with the input to the amplifier disconnected

and the internal calibration source as the input current. The calibra-

tion consisted of four steps:

1. Establish the value of true zero.

2. Measure the relative gain of adjacent settings on the
rotary switch that selects the smaller gain increments
(called the fine-gain switch).

3. Measure the gain of each setting on the rotary switch
that selects the larger gain increments (called the
coarse-gain switch) relative to the "CAL" setting.

4. Check the zero value.

The results of the above measurements were then used in the data reduc-

tion (see Chapter III).









S0.52.
z
( 0.51
<: + io t ++ + + + ++ 4 o 0
0.50

z 0.49
< 0.48 ** ** I I I : .*
S 0 0 0 0 0 0 0 0 0
C\ D O O N (D O(

TIME (MJD 42450)
Fig. 3.-Fine-gain stability. The start and the end of a night calibration is indicated by o and + .

2 .7 0 . .* ..* a .* .a
z

< 2.606 0o + + + + o +
S2.605 +

Z 2.55

( 2 .5 0 ..A.... .i -.a
0 0 0 0 0 0 0 0 0 0
c (O CO 0 N q (D O

TIME (MJD- 42450)
Fig. 4.-Coarse-gain stability. The start and the end of a night calibration is indicated by o and +.





50


In Figures 3 and 4, the relative gains for settings of the

fine-gain and coarse-gain switches are presented, respectively. From

inspection of these figures, it is clearly evident that the short-term

stability and the long-term stability of the amplifier are very good.

In Fig. 4 a difference in the level of the coarse-gain is evident from

1975 to 1976. This is of no significance in differential photometry

such as that presented here on RS Canum Venaticorum.













CHAPTER III
PROCEDURE AND DATA REDUCTION


Observational Procedure

The accuracy that can be achieved with modern photoelectric

photometers is limited by the earth's atmosphere more than by any

other factor. The earth's atmosphere is not completely transparent;

it does not even have the same transparency at all wavelengths of

light. The problem of measuring the intensity of stars is further

complicated by the random and unpredictable fluctuations in the trans-

parency of the atmosphere as a function of time, and the somewhat pre-

dictable change as a function of airmass.

There are means of reducing the effects of a real atmosphere

on the measurement of a star's light. The most important is to measure

the light differentially. By this it is meant that a star of constant

brightness, called the comparison star, is chosen as a reference. The

brightness of the program star, called the variable star, is measured

under the same atmospheric conditions as the brightness of the compari-

son star. If the atmospheric conditions are exactly the same when the

brightnesses of the two stars are measured, and the comparison star is

indeed of exactly constant brightness, then any variation in the ratio

of the variable star brightness to the comparison star brightness is

due solely to the variable star.

Of course, it is not possible in practice to guarantee that the

atmospheric conditions are exactly the same during the measurement of

51





52

both stars. The best way to insure that these conditions are as nearly

identical as possible is to choose a comparison star which is very near

in the sky to the variable star, and then to measure their brightnesses

in as short a time span as possible. The nearness in the sky of the

comparison star to the variable star and the nearness in time of measure-

ment of their respective brightnesses are the two most important factors

in high accuracy differential photoelectric photometry. Other criteria

which will help improve the accuracy of the differential measurement

are the following:

1. The comparison star should be nearly the same color as the
variable star.

2. The comparison star should be of nearly the same brightness
as the variable star.

3. The amount of atmosphere through which the measurements
are taken should be kept to a minimum.

4. The amount of scattered light from the background sky
(which cannot be avoided) should be measured and minimized.

For the observations presented here, these conditions have been

quantitatively met by the following procedures:

1. The comparison star is only 71 arc minutes from the variable
star in the sky.

2. The typical sequence used to obtain the intensity measure-
ment and the time required are given schematically on the
following page:





53

1975 time required (sec) 1976 time required (sec)

45 45
C 3 x 30 C 3 x 30
30 30
SC 3 x 30 SC 3 x 30
30 45
C 3 x 30 V 3 x 30
45 30
V 3 x 30 VS 3 x 30
30
VS 3 x 30
30
V 3 x 30
total time: 750 ~ =12 min) 510 (=8 min)

Where C represents the measurement of the comparison star's
brightness in three colors (v,b,u), CS is the three-color
measurement of the sky near the comparison star, V is the
three-color measurement of the variable star, and VS is the
three-color measurement of the sky near the variable star.
The integration time for each color measurement was always
30 seconds, the time to set the telescope on the comparison
star or the variable star was usually about 45 seconds, and
the time to move the telescope to a region of the sky near
a star (or back again) devoid of visible stars was typically
30 seconds.

3. The colors of the comparison and variable stars are:

Variable (RS VCn) B-V = 0.56 and U-B = 0.05 (Oliver 1974)
BD+350 2420 B-V = 0.47 and U-B = 0.03 (Oliver 1974)

4. In no case was a differential measurement made through
more than two air masses.

5. Typically the sky brightness was measured at least every
half hour, or after the measurement of each star, if the
sky brightness was changing rapidly. To minimize the sky
contribution to the signal, the smallest diaphram available
on the photometer was always used (42.5 arc seconds in dia-
meter)

6. To determine if the comparison star was indeed of constant
light, a check star was observed occasionally.

The above discussion assumes that the instrumentation is linear

and stable to within the requirements of differential accuracy. If

this is the case and the above criteria are met, then all that remains

is the calculation of the ratio of the variable star brightness to the





54


comparison star brightness. In making these calculations it will be

possible to correct, in part, for the atmospheric extinction which has

been minimized, but not eliminated by the proper choice of a comparison

star.

It was pointed out in Chapter II that the majority of the data

exists in two forms: chart records and tabulations manually recorded

from the DA-10 digital integrator. The chart records made prior to 5,

6 March 1976 were read and recorded in a tabulation form exactly like

that used on and after 5, 6 March 1976. The keypunch shop of the

Northeast Regional Data Center was engaged to punch these data on stan-

dard computer cards, in a format called the "Ludington-Oliver" format

(see Table 4). A computer program called PHRED (PHotoelectric

REDuctions) was written to accept this format for the raw data and to

do the reduction to the instrumental system (except for the inclusion

of the effects of atmospheric extinction). The application of the ef-

fects of a real atmosphere to the partially reduced output of PHRED is

handled by a computer program called DEXTOR.


PHRED

Introduction

PHRED is a computer program that is written in the PL1 program-

ming language. It is a very versatile program for reducing photoelec-

tric observations to the instrumental system. It has far vaster capa-

bilities and fewer limitations than any other available reduction pro-

gram. It is limited by the size of the computer used rather than by

the observations. It can, for example, handle the observations of over

600 different objects in 200 different filters taken during one night

of observing. PHRED can be instructed to produce a plot for any object-





55

filter combination the user may desire. This can be very helpful in

evaluating the quality of the observations. In addition, the user can

instruct PHRED to calculate the principal extinction coefficients, the

outside-the-atmosphere magnitude and the standard errors of each.

Furthermore, the program is not restricted to variable star data. It

can also do the reduction of standard stars to the instrumental system.

PHRED does all normal reduction, except atmospheric extinction and the

reduction to the standard system. For example, it corrects for a zero

offset in the data-gathering system. It converts to heliocentric Modi-

fied Julian Date. It applies gains, unless the user is using a pulse

counting system, in which case the gains will be ignored. All in all,

the user has a great deal of control over the operation of the program,

and very few assumptions have been made about the way the data must be

taken, or the organization they must be in for reduction by this pro-

gram. Of equal importance to the user of PHRED is the detailed log of

the reduction and the warning messages to help the user gain the de-

sired results.

Program Control

The user instructs the program to do certain things by use of

Control Cards. These are records that start with an asterisk (*). The

asterisk is followed by one letter of the alphabet. This letter deter-

mines the option that is to be used or the type of parameter cards that

will follow it. Any characters after the first letter will not be re-

cognized by the program.

The first step in using PHRED is to have the data prepared on

cards in the Ludington-Oliver format. The outline of this format is

given in Table 4. Any item on which a deflection can be taken is de-

fined by the user with an object code. This includes sky deflections,





56

TABLE 4

LUDINGTON OLIVER FORMAT

ITEM COLUMN FORMAT EXAMPLE-COMMENTS

Object Code 01-02 A(2) CO,SC,S1,S2, etc.
Object Name 03-12 A(10) BO-15 1734, RS CVN, etc.
Modified JD(a) 13-17 F(5) 42451, 000, any 5 digits
Filter Code 1 18 A(1) V, Y, R, etc. (c)
UT 1 19-24 F(6) 043012, hhmmss
Gain 1 25-27 A(1), A(2) D04, 'D' is coarse gain,'04'
is fine gain
Defl 1 28-32 F(5) 00120, 00120, 98765, etc.
Filter Code 2 33 A(1) B, I, K, etc.
UT 2 34-39 F(6) 105959
Gain 2 40-42 A(1), A(2) E04
Defl 2 43-47 F(5) 00001
Filter Code 3 48 A(1) U, S, B, etc.
UT 3 49-54 F(6) 001059
Gain 3 55-57 A(1), A(2) A02
Defl 3 58-62 F(5) 00000
Observer 63-65 A(3) EWL, JPO, REN, FBW, etc.
Telescope 66-68 A(3) 046, 300, dia. in centimeters
Photometer(b) 69-71 A(1),A(1),A(1) Codes for: amplifier, filter set,
photomultiplier tube
Observatory 72-74 A(3) RHO, FAS, MCD, etc.

Notes for Table 4:

(a) The Modified Julian Date of each deflection is calculated by the
following equation:
MJD(obs) = MJD(col 13-17) + DEC(UT)/24.
(b) The photometer code is divided into three subcodes. The first is
for the amplifier, the second is for the filter set used, and the
third is for the photomultiplier tube used.
(c) Each record has room for only three deflections. If there are more
than three deflections for each object code, these are then put on
the following cards with the proper filter code for each. All other
columns should be copied from the first card.





57

dark current, zero offset, variable star, standard star, etc. There

are two characters on the card for the object code. There are no re-

strictions on which of the 256 characters of the EBCDIC character set

may be used. The filter code is used in a like manner. There is room

on a card for three filters to be coded. If more are required, the

data are continued on the next card by copying the object code. The

gain is an instrumental setting that causes the input from the photo-

multipier tube to be amplified by a specific amount. This must be ac-

counted for in order to arrive at the true value before amplification.

The code that is used on the Ludington-Oliver format is comprised of

two parts. The first part is for a setting of a coarse-gain switch,

while the second is for a setting of a fine-gain switch. PHRED does

not make any distinction between the two. It reads the three characters

as a single code; therefore, the user must supply (in the control card

section) the value for this combination of coarse and fine-gain control

settings. The deflection that is recorded will of course include the

amplification indicated by the gain code. The deflection is restricted

to five digits. This should be sufficient for the most majority of the

photoelectric photometry. The deflection fields must not include em-

bedded blanks. A deflection is possible even when the signal current

from the photoelectric device is exactly zero. This is called the zero

offset and must be removed from other deflections if the proper results

are to be achieved. Therefore, PHRED will recognize an object code 'Zp'

as the zero reading. It will ignore the gain setting used and take the

average of all such readings for that night and substract that value

from all deflections before the gains are applied. The user must be

aware of the proper use of the time for each observation. The Modified





58

Julian Date (which was defined by the IAU in 1973) is recorded on each

card; this is actually the interger part of the Modified Julian Date.

The Universal Time (UT) is also recorded for each deflection. Six

columns are used for each UT. The first two digits are for the hours,

the second two digits are for the minutes, and the last two digits are

for the seconds.

PHRED has been designed to perform several tasks for the user.

PHRED can process one night or multiple nights of observations in a

single submission. The first night of observations begins with a set

of control cards; these might include the *LIBRARY, *FILTERS, *CODES,

*SORT, *VARIABLE, *PLOTS, *BEGIN, and *TITLE control cards. The last

two, however, have a special importance. The *BEGIN must be the first

card in the control section and the *TITLE must be the last control

card before the data. The other control cards may be in any order.

There are three additional control cards which are of special importance.

These are the *DATA, *ADD, and *END control cards. *DATA must follow

the title cards and proceed the data. *END must follow the data. *ADD

is used if the user wishes to add additional data, but does not wish

them to be considered as the original data. For example, the observer

may have neglected to take a comparison star deflection at the very be-

ginning of the night. While this will not prevent the normal operation

of PHRED, it will require extrapolation. To avoid this, the user can

add an artificial deflection with the *ADD control card. After the

original set of data has been ended with an *END card, the user inserts

the *ADD card followed by as many cards of additional data (in the

Ludington-Oliver format) as he desires. The additional data are also

ended with an *END card. The next night of observations will then





59

follow, beginning with the *BEGIN CARD. It is not necessary to re-

peat all control cards for the second night if they were already used

in the first night's control card section. That is, the second night

will be processed with the same instructions as for the first night,

unless the user changes them. For example, it is unlikely that the

gains will have exactly the same values from night to night. Therefore,

the *GAIN control card will probably be necessary in the second night's

control section. On the other hand, the stars that were observed and

the filters that were used will probably be the same; therefore, the

user does not need the *LIBRARY, *CODES and *FILTER control cards in

the control card section for the second night. Four of the control

cards work in a "flip/flop" fashion, i.e., they are "off" until they

appear for the first time, then they are "on" until they appear again,

and then they are "off", etc. These are *MAGNITUDES, *INTERPOLATE ALL

SKY, *SORT, and *VARIABLE.

In Figure 5 is a listing of the JCL cards for using PHRED.

Notice that this assumes the existence of a load module for PHRED.

//JOBLIB DD DSN=B0035001.S13.ATYLIB,DISP=SHR
//STEP1 EXEC PGM=PHRED
//SYSPRINT DD SYSOUT=A,DCB=BLKSIZE=120
//RAWD DD SYSOUT=A,DCB=BLKSIZE=120
//GRAPH DD SYSOUT=A,DCB=BLKSIZE=120
//LOG DD SYSOUT=A,DCB=BLKSIZE=120
//NSKY DD SYSOUT=A,DCB=BLKSIZE=120
//DECK DD SYSOUT=A,DCB=BLKSIZE=100
//DISK DD UNIT=SYSDA,DSN=&&DISK,SPACE=(TRK,(3,3),,CONTIG),
// DCB=(RECFM=F,BLKSIZE=80,DSORG=DA),DISP=(NEW,DELETE,DELETE)
//CARDS DD *,DCB=(RECFM=F,BLKSIZE=80,LRECL=80)

Fig. 5.- JCL cards for PHRED

Control Cards

Listed here are the control cards and their meanings:

*ADD -- Adds additional Data Cards to those already read and writes

them into the Raw Data file (RAWD). The additional data should be ended





60

with *END. The Ludington-Oliver format is used for additional data.

*BEGIN -- The card should appear at the beginning of each new

night of data. Each time this card is encountered, the previous night

is known by PHRED to be complete and is then processed.

*BOTTOM -- This card should be the last card in the input deck.

It will insure the processing of the last night of data.

*CODES FOR OBJECTS -- The following parameter cards define the

object codes. A blank code terminates object code input. The codes are

two characters long, left justified in a four-column field. For example,

V SV C SC K SK

is the default if no codes are defined. Any code used in the data but

not defined will cause a warning message to be printed in the LOG file,

and the data will be ignored. Any code that is defined, but for which

there are no data will not, of itself, cause an error. Note that

stellar codes should be odd (1st, 3rd, 5th, etc.), sky codes should be

even (2nd, 4th, 6th, etc.). The order of the codes is important if the

*VARIABLE option is used.

*DATA -- This card signals the beginning of the data card ob-

servations. The data should be ended with *END. The data will be writ-

ten into the Raw Data file (RAWD). The *DATA card must follow the last

title card (see *TITLE).

*END -- This card is used to end a group of data cards. Either

the original data or any and all additions to it are ended with *END.

*FILTER CODES -- The following parameter cards define the filter

codes. A blank code terminates the set. The codes are one character in

length, left justified in two-column fields. For example,

VBU
is the default if no codes are defined.






61

*GAINS -- The following parameter cards define the gain codes

and their values. A blank code and value terminates the set. The

codes are three characters in length, while the value can be as much as

12 columns long. The code and its value are separated by one space (an

equal sign or any other single character may be used). Therefore, to-

gether they comprise 16 columns. For example,

004=0.5049 E02=2.501234567 A06= -0.4989

is a valid gain code parameter card.

The default for this control card is to apply a gain of zero magnitudes

to all the data points. A message will be written into the LOG to indi-

cate this.

*HARDCOPY -- This card is included if a punched deck (or other

machine readable copy) is desired of the reduced data. The parameter

card can be used to control the contents of this output file. The

parameter card format is a six-character field in columns one through

six. There are, at the present, only three possibilities for the user

to choose from.

ALL
NONE
V/C

"ALL" will cause the total of the NSKY printed file to be put into the

DECK output file. "NONE" will cause nothing to be put into the DECK

output file, while "V/C" will cause only the variable minus comparison

data to be put into the DECK output file.

*INTERPOLATE ALL SKY -- Usually an observer will take deflections

on a star and on the nearby sky. This will allow him to subtract the

sky from the star deflection and be left with just the deflection due

to the star. If this card is inserted, the program will use any even





62

code interpolation of sky deflections. This means that if there are

sky observations only with the comparison and none for the variable,

the user must include this card. Without this card, the program sub-

tracts the interpolated value of an even code from the value from the

next smaller odd code. With this card, all even code values are com-

bined and.copied in place of the original even code values.

*JD OVERRIDE -- The following parameter card defines a five-

digit number that will override the integer Modified Julian Date on

the data cards. It must not have a decimal point or sign. For example,

42451

is a valid parameter card. The default is to use the integer Modified

Julian Date on the data cards. Note that the integer Modified Julian

Date coded on each card is used to compute the time for each of the

deflections on the card. Therefore, the use of this control card op-

tion will cause all the cards to have the same Julian Date, even if the

original data cards for a single night contained more than one Julian

Date. The default is reestablished at the beginning of a new night of data.
*K-EXTINCTION COEFF -- If the user wishes to have extinction

coefficients calculated, he may specify on the following parameter

card(s) which star (or sky) and filter(s) he wishes used. There are

no limits to this combination of object code and filter code. The for-

mat for the parameter card is a four-column field with the object code

in the first two columns and the filter code in the third column (the

last column is blank). For example,

V6V SVV CV SCV

will produce extinction coefficients for the variable star, for the

sky readings next to the variable, for the comparison, and for the





63

comparison sky, all for the visual filter (assuming the object and

filter codes defined in the examples for *CODES FOR OBJECTS and

FILTERS). The default is to not calculate any coefficients.

*LIBRARY STARS -- The following parameter cards contain the

"vital statistics" on the stars being reduced. The format for these

cards appears below:

ITEM VALUE EXAMPLE COLUMNS FORMAT

Object code comp star C5 01-02 A(2)

name BD-1501734 BD-15 1734 03-12 A(1O)

RA 7h15m12s 7.2533333333 14-28 F(15,10)

Dec -15032'28" -15.541111111 29-43 F(15,10)

Note that when punched on the cards, the right ascensions and declina-

tions must be converted to hours and decimal hours and degrees and deci-

mal degrees. The last card must be a blank card to terminate the set.

If no library parameter cards are used, then the *K-EXTINCTION COEFF

control card option should not be used.

*MAGNITUDE -- If this card is used, the output will be in

magnitudes instead of intensity units. The default is output in in-

tensity units.

*N FULL SCALE -- The following parameter card will give the

fullscale value expected for the data. This value will then be used to

normalize all the deflections. This means that before anything else,

the values punched on the data cards will be divided by this number.

The number is read in from the first six columns of the parameter card

using an F(6) format. For example,

100000

10000

1000





64

are all valid full-scale values. The default value is 10000.

*OBSERVATORY -- The following parameter card is used to read

in the longitude, latitude, and (optionally) the station code for the

observatory at which the data were taken. For example,

+82.586666666 +29.377777777 RHO

is the default and/or the parameter card for Rosemary Hill Observatory.

It is read by (F(15,10),F(15,10),X(5),A(3)) PL1 format.

Longitude is a number between -180.0 and +180.0.

*PLOTS -- The following parameter cards are used exactly like

the one for *K-EXTINCTION COEFF. They specify which object-filter

combinations the user wants plotted. The codes and formats are the

same as for the *K-EXTINCTION COEFF parameter cards, The plots are in

magnitudes as a function of local time. No plot is the default.

*SORT -- This card, when used, will cause the sorting of every

object-filter combination into time order. Sorted data are necessary

for proper functioning of PHRED.

*TITLE -- This card signals the beginning of the title cards.

The first of these cards will be used as a heading on all pages per-

taining to this night of data. The rest (and there is no limit) will

be printed on the heading of the RAWD print file. There must be a

*TITLE card and at least one card following it. the *DATA card must

then follow the last title card.

*VARIABLE -- If the data are arranged for it, the user can

have the data treated as "variable star data." In this case the com-

parison star will be "removed" from the variable (to get relative

brightness). This is done by dividing the variable star's reduced in-

tensity by the interpolated comparison star's reduced intensity. If

*MAGNITUDE has been used, the process will be the difference of the





65

reduced magnitudes. The object codes must be listed after the *CODES

FOR OBJECTS control card in this order: variable star, sky variable,

comparison star, sky comparison, another star, another sky, etc.

*X TIME OFFSET -- The following parameter card can have up to

a 15-digit number (read by F(15,14)). This number is added to the

Julian data computed for each deflection. Its units must therefore be

days.

DEXTOR

Program Outline

DEXTOR is a program written in PL1 which applies differential

extinction coefficients to a dataset like that produced by PHRED.

If the instrumental system is nearly the same as the standard

UBV system, a simple linear set of equations can accurately describe

the effects of a real atmosphere. The equations normally used are

(la) v = v-k'X,

(Ib) (b-v)o = ((b-v)-kl-X)/(1+k;X), and

(Ic) (u-b)o = ((u-b)-k2 X)/(1+k X),
where the superscript "o" indicates the outside-the-atmosphere color

or magnitude of the star, X is the airmass, v,b, and u are the magni-

tudes of the star as viewed through the visual, blue, and ultraviolet

filters, respectively, and k, k1, ki, k2, and k2 are the extinction

coefficients. For a detailed development of the above equations see

Hardie (1962).

The above equations apply to the measurement of one star, but

the data can better be reduced differentially, rather than as in-

dividual magnitudes of the variable and comparison stars. In order to

do this, it is necessary to develop a set of equations which describe

the differential extinction computations. Start by defining a difference





66

operator D(...) which is equal to the variable minus the comparison
in magnitudes. The above equations can then be defined for the vari-
able star and for the comparison star. It can be shown that equations
(1) above become,
(2a) D(v) = D(v)-k.D(X),
(2b) D(b-v) D(b-v)-k 1D(X)-ki.D(X.(b-v)) and
(1+k4.Xv) (1+kl.Xc)

(2c) D(u-b)o = D(u-b)-k2-D(X)-k2.D(X.(u-b))
(1+k2'Xv) (1+k-Xc)
where the symbols have the same meanings as for equations (1), with
the additions of Xv equals the airmass of the variable star, and Xc
equals the airmass of the comparison star.
The equations (2) above are the ones which are used by DEXTOR
in computing the instrumental differential magnitudes of the variable
star. The extinction coefficients must be computed separately and
supplied to the DEXTOR program via control cards.
In the computations performed by DEXTOR, a simplifying assump-
tion has been made about the values of D(X.(b-v)) and D(X.(u-b)). It is
assumed that the differences can be replaced by the approximations,
(3a) D(X.(b-v)) = Xv
2 D(b-v), and

(3b) D(X.(u-b))= Xv + X
2 D(u-b).
The error introduced by this approximation is small if D(X) is
small. For D(X) = 0.01 the error in D(b-v)o is only 0O0004 for typical
extinction coefficients. No error was introduced in the reduction of the
RS CVn data for 0(u-b)o, because a value of zero was adopted for k2.





67

Extinction Coefficients

An average value for each of the extinction coefficients was

determined by the method of weighted least squares. The data used

were those from the comparison and check stars. The evaluation of the

coefficients was based on equations similar to equation (la). The

evaluation of these primary extinction coefficients was performed in

the PHRED computer program for each night of data. The results of

PHRED's computations were then weighted according to the precision of

PHRED's least squares determination, and the final extinction coef-

ficients were obtained by an additional application of the method of

least squares. The values adopted for application by DEXTOR to all the

data (1975 and 1976) were:

k = 0.308,

k = 0.174,

k = -0.03,

k2 = 0.667, and

k2 = 0.0.

The values for k1 and k2 were adopted based on the closeness of the

computed values to the expected values given by Hardie (1962).

The details of the computations are not critical to the quality

of the results. The effects of differential extinction are small.

In fact, the average value of the correction on a typical night was

0.001 magnitudes in the D(v)o value.


Data Reduction

PHRED Run

After the data were punched onto computer cards, the cards were

collected for processing by PHRED. It was necessary to first punch all





68

of the control cards for PHRED and verify that all the supplemental

data transferred to the program via the control section were correct

and in proper sequence.

When the above conditions were satisfied, the PHRED portion

of the reduction was complete. The computer listings are not included

here because they are bulky and do not easily conform to the required

format. Copies are, however, available to interested investigators.

Correction of Errors

Since there were a large number of data, it was impossible to

verify all numbers in the tabulations, reduction and printout. However,

it was important to investigate all significant human errors so that

they would not propagate through the remaining reduction.

The first step to reduce human errors was taken during the

keypunching. The tabulated data were punched and then verified by

the keypunch staff. Second, a program was written to scan the punched

cards and to flag changes in the deflection value that were obviously

too large or were changes in time sequence. This would locate many

transpositions of digits in the tabulation process, or keypunch errors.

The program was only partially successful. Third, the reduced data

were converted by use of the equation

(4) MJD = 41825.042 + 4.797855E,

to a common phase cycle and the light curve plotted. The linear

ephemeris above is due to Catalano and Rodono (1974). Any datum

which was obviously discrepant was carefully checked for errors in

tabulation, keypunching, or data reduction. Fourth, to check the re-

duction process performed by PHRED, a sample set of calculations was

performed manually with an HP-45 hand-held calculator. The sample






69

calculations, in every respect, agreed with the values from the PHRED

program to within the expected accuracy.

The majority of effort was devoted to the third method,

described above, for detecting errors. More than 60 individual

data were carefully checked in detail (requiring 10 full days of the

writer's undivided attention). The majority of the errors detected

occurred at the time the data were tabulated for keypunching. The cor-

rections could easily be made and the data adjusted. In a few

cases it was possible to identify the source of the error (miss-identi-

fication of star, clouds, telescope drift, etc.), but the information

necessary to correct these errors was not available. In these few

cases it was necessary to remove the offending data from the collection

in order to avoid contamination of the results by these known errors.

In only one case was a datum removed without an explanation that was

completely satisfactory to this writer. The first star deflections

(v,b,and u) were all significantly too high and the first variable star

deflections (v,b and u) were significantly low on the night of 1, 2

April 1976. For the remainder of the night the data were very good,

therefore these first measurements were removed from consideration.

Check Star Data

The ratio of the check star (BD+3502422) intensity to the

comparison star intensity should not be time dependent if the stars

are both of constant brightness. This allows the observer to have a

'check' on the assumption that the brightness of the comparison star is

constant, and therefore that the variable-to-comparison ratio is a true

measure of the variation in the variable star's brightness only.

Occasionally during the course of the observing program,

measurements of the check star brightness were obtained. In Fig. 6 a










0.05 .. 1 I I
V
S* .
0.15- *


0.25 0 -.15
B
: 0.25
0 .

0.20 0.35
U
0.30 *
*0 0 ii
.
0.40 I I I I I I
0.00 0.05 0.10 0.15 0.80 0.85 0.90 0.95 1.00

TIME ((MJD-42450]/500)

Fig. 6.-A plot of the differential magnitudes of the check star BD+350 2422. The left panel is for
the time of the 1975 observations, while the right panel corresponds to the 1976 observational
program. In most cases more than one differential measure was made on each night. All of the
individual points are plotted here. The average values for the differential magnitude and color of
BD+350 2422 are v = 0144 0l009, (b-v)o = Oml06 0 016, and (u-b) = 0m073 + 0.029.





C-





71

TABLE 5
DIFFERENTIAL MAGNITUDES AND COLORS OF CHECK STAR
HELIO. MJD D(v) D(b-v)o D(u-b)o
42469.33188 0.159
42469.40479 0.141 0.1033
42478.31961 0.150 0.0869
42480,34465 0.151 0.0904
42480.42243 0.144 0.1019
42491.32879 0.129 0.1084
42491.41073 0.148 0.1046
42508.06754 0.158 0.1111 0.0439
42508.23996 0.145 0.0933 0.0857
42508.24524 0.143 0.1536 0.0221
42508.41600 0.144 0.1086 0.1082
42508.42114 0.148 0.1297 0.0865
42515.38021 0.145 0.1058 0.0518
42515.38403 0.137 0.1050 0.0328
42515.41264 0.117 0.0995 0.1458
42518.12401 0.148 0.1143 0.0848
42518,31901 0.157 0. 1046 0.0644
42519.10308 0.154 0.1259 0.0311
42519.18606 0.141 0.1317 0.0521
42519.39703 0.130 0.1117 0.0801
42843.30877 0.121 0.1308 0.0426
42843.38933 0.136 0.0912 0.1122
42855.22996 0.143 0.1042 0.0518
42855.43218 0.145 0.1254 0.0814
42886.22183 0.141 0. 1059 0.0654
42886.29107 0.154 0.0966 0.0754
42895.25505 0.146 0.1038 0.0499
42896.10202 0.153 0.0872 0.0866
42896.15872 0.142 0.0890 0.0982
42896.28953 0.141 0.0954 0.0719
42896.36839 0.147 0.1124 0.0712
42917.17889 0.142 0.1022 0.0715
42917.31388 0.157 0.0793 0.0898
42923.12296 0.149 0.0929 0.1160





72
plot of the instrumental differential magnitudes is presented as a

function of Modified Julian Date. Notice that the plot is not con-

tinuous in time; this is because the observing was carried out only

during the spring months of 1975 and 1976. The data plotted in Fig. 6

appear in tabular form in Table 5.

Variable Star Data

The data for RS CVn obtained with the instrumentation des-

cribed in Chapter II, during the 1975 and 1976 observing seasons

from March to May, and reduced by PHRED and DEXTOR, appear in tabular

form as instrumental differential magnitudes in the appendix.

Transformation to Standard System

The goals of this research do not require transformation to the

standard system. Differential measurements with the same comparison

star and subsequent use of WINK in the analysis (see Chapters IV and V)

relaxes the requirements for standardization in the data. For these

reasons, only a small effort was made to obtain transformation coeffi-

cients.

The standard stars used were observed on two nights during the

course of the observing program. The transformation equations that

apply are given as follows:

(5a) B-V = A1 + A2(b-v)o

(5b) U-B = A3 + A4(u-b)o

(5c) V-v0 = A5 + A6(b-v)o

The values for the A's in equations (5) were computed by the

method of least squares using the data obtained from the photometry of

nine standard stars and the comparison star. The data for RS CVn has

not been transformed with these coefficients because the accuracy is so





73

very low. The transformation coefficients to the UBV system are

as follows:

Al = 0.89 0.01

A2 = 1.06 0.01

A3 = -2.02 0.32

A4 = 1.06 0.15 (the estimated errors are
standard errors)
A5 = 7.97 0.03

A6 = 0.0 0.1

More accurate transformations can be found in Markworth's (1977)

dissertation. His photometry used virtually identical instrumentation.














CHAPTER IV
DATA ANALYSIS PROCEDURE


Introduction

The analysis of the data was carried out on an AMDAHL 470 com-

puter at the Northeast Regional Data Center located on the Gainesville

campus of the University of Florida. The processing was accomplished

with several programs written in FORTRAN IV. One program (WINK), which

was written by D. B. Wood (1971, 1972), models an eclipsing binary system.

The remaining programs were written by the author except for the least

square subroutine (used in the Fourier program) which was written by

H. L. Cohen. The details of the operation will be discussed after an

outline of the WAVE procedure is discussed.


Outline of WAVE Procedure

A simplified outline of the procedure appears in Fig. 7. The

details of these computations are eliminated so that the process is

clearer. The procedure that this figure represents was used as an

in-stream procedure and was called WAVE. This term will be used in the

remainder of this dissertation to refer to this sequence of computer

programs which was used to analyze the data. The WAVE procedure starts

basically with the WINK program which both improves the eclipsing binary

elements and produces a theoretical light curve. The input data set to

WINK (which it attempts to solve) is called OROBS. This term refers to

the Old Revised OBServations.from a previous WAVE run or to observations



74





75


PREVIOUS PLOTS
AND
PRINTOUTS




PROGRAM
OROBS -- WI NK --CONTROL
(USER)


CALCM



CALC
OBS -- ROMC Bss



OMC


FOMC
FOURFIT OMC
TOMC
ROSS



ROBS



PLOTS AND o LCPLOT





Fig. 7.-0Outline of basic WAVE procedure





76

themselves when the procedure is initiated. In addition to the OROBS

the user also supplies a set of control parameters to WINK. After five

WINK iterations or after convergence (whichever comes first) the WINK

program produces a dataset called CALCM. This is the theoretical light

curve for the elements at the conclusion of the solution portion of

WINK. The term (CALCM) refers to the fact that it is necessary to pro-

duce the calculated light curve in magnitudes in order to include the

Quadriture Magnitude (QM) parameter in the values produced. This data-

set and the observations (OBS) are used in the ROMC program which is

next in the sequence. ROMC converts the magnitudes of the CALCM dataset

to intensities and subtracts them from the OBS dataset. The result is

the OMC dataset, which is a representation of the distortion wave. In

addition, ROMC produces a CALC dataset which is the converted CALCM

dataset. CALC is used later for plotting purposes. Next in the sequence

is the program FOURFIT. It uses the OMC dataset to determine the coef-

ficients of a truncated Fourier series, by the method of least squares,

which represents the distortion wave. The Fourier representation is

then subtracted from the OBS dataset. The result of the subtraction is

a light curve of RS CVn as it would appear if it did not have the photo-

metric complication. This dataset is called ROBS (Revised OBS). FOUR-

FIT does additional computations which are used for plotting purposes.

It computes a dataset from the truncated Fourier series at closely

spaced phases. This dataset is called FOMC. Lastly, FOURFIT calculates

the difference between the OMC dataset and the Fourier representation of

it. This is called TOMC.

The last significant program in the WAVE procedure is called

LCPLOT. This program plots the datasets produced in the previous steps






77




= a', L
** \ .w" *

9 ,





























a. 8 sanop pl fo progmredOd 6% a r in (
la o p mar eip
In.0 (b) 5m00 0.5 0.10
































In (b) is an enlargement of primary eclipse.
Ip;o-.--i.c-----------------------------






9k *C






i.^M^ z^'~e *^*^ -/w



























In (b) is an enlargement of primary eclipse.





78

of the procedure for evaluation by the user. A sample of the plots

produced appears in Fig. 8.

The WINK Program

This program has been widely used to determine the elements of

eclipsing binary systems. The program was written by D. B. Wood (1971,

1972) and has been updated by eight status reports (private communications).

The model is that of triaxial ellipsoids. The parameters of the model

which are pertinent to this investigation, their WINK codes and meanings

are shown in Table 6.

TABLE 6

WINK PARAMETERS


WINK
Code Symbol Meaning

1 i orbital inclination
2 e sin w e is the orbital eccentricity and
3 e cos w w is the longitude of periastron
4 Tc time (or phase) of conjunction
5 UA linear limb darkening coefficient for star A
6 uB linear limb darkening coefficient for star B
9 wA reflection albedo of star A
10 wB reflection albedo of star B

11 QM quadrature magnitude
13 TA effective temperature of star A
14 TB effective temperature of star B
15 aoA radius of a sphere with a volume equal to that
of the triaxial ellipsoid of star A (equivalent
radius of star A)
16 k ratio of equivalent radii (aoB/aoA)
17 BA gravity exponent for star A
18 BB gravity exponent for star B
19 q mass ratio (star B to star A)
41 nA polytropic index of star A





79
TABLE 6 Continued


WINK
Code Symbol Meaning

42 nB polytropic index of star B
43 Xe effective wavelength of observations
45 log gA logarithm of surface gravity of star A
46 log gB logarithm of surface gravity of star B

For systems like RS CVn in which the stars are sensibly spheri-

cal the equivalent radii are useful parameters. On the other hand, they

have very little physical meaning and the ellipsoidal axes are to be

preferred. The reader is cautioned to remember that any set of param-

eters- (whether it's a spherical radius, a set of radii for a triaxial

ellipsoid, or 3 radii of a Roche lobe) is merely a way of conveying

quantitatively information about a natural phenomena, which most likely

does not actually conform (in detail) to any of the model parameters.

The WINK program as it was used here both improved the elements

by the method of differential least sqaures and produced a synthetic

light curve (the CALCM dataset referred to earlier). The integration

was performed using the 4x4 Gaussian quadrature option, which has an

accuracy of 0.6%. The model atmosphere used is that which was supplied

by Wood in Status Report #7.

The first 19 parameters (only 16 of which are used here) may,

by user selection, be improved by the differential least squares sub-

routine. These parameters, for the purpose of this research were div-

ided into 4 groups by the author: the first-order parameters are i,

k aoA, and TB. The second-order parameters are wA, wB, uA, and

uB. The third-order parameters are Tc and QM. The fourth-order param-

eters, are e sin w, e cos w, TA, q, BA, and BB. The other parameters





80
of the WINK model must be assigned by the user and cannot be improved

by the differential least squares routine.

In this dissertation the terms "free-parameter" and "adjustable-

parameter" will refer to a parameter from the above set which has been

designated by the user as a parameter to be improved by the differential

least squares routine. Likewise, the term "fixed-parameter" refers to

a parameter which has been assigned by the user a particular value and

not allowed to be changed by the WINK routines.

No third light was allowed, and only the linear limb darkening

law was used. Certain parameters were by necessity assumed at the out-

set and never altered. These parameters and their assumed values are

given in Table 7.

TABLE 7

ASSUMED PARAMETER VALUES


Parameter Assumed Value

e sin w 0.0
e cos w 0.0 i.e., a circular orbit
TA 67000K from Popper (1961)
q 1.045 from Popper (1961)
nA 3.5
nB 3.5
log gA 4.0 from Gray (1976)
log gB 3.5 from Gray (1976)

The program was modified to allow for up to 200 data to be read

or written, and to produce an additional page of output, which is merely

a summary of the least square iterations. In all other respects the

program is complete through Status Report #8. The version of the WINK

model used here was updated through Status Report #8.





81

The ROMC Program

This program is very simple. It reads the CALCM dataset pro-

duced by WINK and converts the magnitudes (m) to intensities (I) by the

relation
-0.4m
I = 10-4m

This conversion is performed for each successive record in the

CALCM dataset. At the same time a record from the OBS dataset is read.

The phase of the two records are checked to assure that they are the

same. If they are not the same,an error message is written and the

program continues. After the subtraction of the CALC record intensity

from the OBS record intensity the result is written to the OMC dataset

along with the phase from the OBS record. These calculations are re-

peated until all the records have been processed. It should be noted

that the CALC dataset is written for plotting by the LCPLOT program

later in the procedure.

The FOURFIT Program

This program reads all the records from OMC dataset and by the

method of least squares determines the coefficients of the following

truncated Fourier series which best represents the data in OMC.

I(0) = A0 + A1 cos e + A2 sin 0 + A3 cos 20 + A4 sin 20.

Since the data in and around secondary eclipse are confused by

the transit of the smaller star across the assumed non-uniform surface

of the larger star these points (from phase 0.43 to phase 0.57) are

excluded from the least squares process.

After the coefficients of the truncated series have been deter-

mined they are used to evaluate the expression at each value of phase in





82


the OBS dataset. The result of each evaluation is then subtracted from

the OBS intensity at that phase. The results are what one would expect

if RS CVn was not complicated by the non-uniform surface brightness of

the larger star. This is not true, however, for the secondary eclipse

because the photometric effects of the transit geometry cannot be so

simply removed. These effects do contain important information about

the surface brightness distribution on the larger star.

The other functions of FOURFIT are to produce two datasets for

plotting by LCPLOT. The first dataset, called FOMC, is the evaluation

of the truncated Fourier series at 240 phase points so that the plot of

this dataset will appear to be a continuous line. The second dataset,

called TOMC, is the difference between the intensity of a record in the

OMC dataset and the evaluation of the Fourier series at the phase for

that record. In other words, it is the difference between the "real"

distortion wave and the Fourier fit to it. These points, when plotted,

should be randomly displaced (by only a small amount) about a straight

line of slope zero if the elements of the eclipsing system are nearly

correct. Here again, the region of secondary eclipse is an exception.


The LCPLOT Program

This program is very complex and for the present purpose need

not be discussed in detail. It plots the datasets the user wishes as

a function of phase. It is a general purpose program and is not re-

stricted to use in the WAVE procedure.


Detailed WAVE Procedure

The detailed JCL WAVE in-stream procedure appears in Fig. 9. It

differs from the above only in the details of the procedure, but not in

the results.





83


//WAVE PROC ROMC='ROMC',WINKOUT='&&CALCM',CALCM=,WINKIN='&&OROBS'
//GENO EXEC PGM=IEBGENER,COND=(4,LT)
//SYSPRINT DD DUMMY
//SYSIN DD DUMMY
//SYSUT1 DD DDNAME=REVO
//SYSUT2 DD DSN=&&OROBS,DISP=(NEW,PASS),SPACE=(TRK,(2,1),RLSE),
// UNIT=SYSDA,DCB=(.RECFi=FB,LRECL 80,BLKSIZE-6400,DSORG=PS)
//GEN1 EXEC PGM=IEBGENER,COND=(4,LT)
//SYSPRINT DD DUMMY
//SYSIN DD DUMMY
//SYSUT1 DD DDNAME=PARA
//SYSUT2 DD DSN=&&PARMS,SPACE=(TRK,(2,1),RLSE),DISP=(NEW,PASS),
// DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DSORG=PS),UNIT=SYSDA
//GEN2 EXEC PGM=IEBGENER,COND=(4,LT)
//SYSPRINT DD DUMMY
//SYSIN DD DUMMY
//SYSUT1 DD DDNAME=DATA
//SYSUT2 DD DSN=&&OBS,SPACE=(TRK,(2,1)RLSE),DISP=(NEW,PASS),
// DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DSORG=PS) ,UNIT=SYSDA
//GEN3 EXEC PGM=IEBGENER,COND=(4,LT)
//SYSPRINT DD DUMMY
//SYSIN DD DUMMY
//SYSUT1 DD DDNAME=PRED
//SYSUT2 DD DSN=&&PRED,SPACE=(TRK,(2,1),RLSE),DISP=(NEW,PASS),
// DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DSORG=PS),UNIT=SYSDA
//GEN4 EXEC PGM=IEBGENER,COND=(4,LT)
//SYSPRINT DD DUMMY
//SYSIN DD DUMMY
//SYSUT1 DD DDNAME=STOP
//SYSUT2 DD DSN=&&STOP,SPACE=(TRK,(2,1),RLSE),DISP=(NEW,PASS),
// DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DSORG=PS),UNIT=SYSDA
//GEN5 EXEC PGM=IEBGENER,COND=(4,LT)
//SYSPRINT DD DUMMY
//SYSIN DD DUMMY
//SYSUT1 DD DSN=&&OBS,DISP=(OLD,PASS)
DD DSN=&&STOP,DISP=(OLD,PASS)
//SYSUT2 DD DSN=&&NORM,SPACE=(TRK,(2,1),RLSE),DISP=(NEW,PASS),
// UNIT=SYSDA,DCB=BLKSIZE=6400,LRECL=80,RECFM=FB,DSORG=PS)
//WINC EXEC PGM=WINK,COND=(4,LT)
//FTO5F001 DD DSN=&&PARMS,DISP=(OLD,PASS)
// DD DSN=&WINKIN,DISP=(OLD,PASS)
// DD DSN=&&PRED,DISP=(OLD,PASS)
// DD DSN=&&NORM,DISP=(OLD,PASS)
//FTO6F001 DD SYSOUT=A
//FTO7F001 DD DSN=&WINKOUT,SPACE=(TRK,(2,1),RLSE,DISP=(NEW,PASS),
// DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DSORG=PS),UNIT=SYSDA
//FTO8F001 DD SYSOUT=A
//OMCA EXEC PGM=&ROMC,COND=(4,LT)
//FT01F001 DD DSN=&&OBS,DISP=(OLD,PASS)

Fig. 9.-The WAVE procedure.











ppanuL4U03-'6 '5Li



ON3d //
0o=3ZISN8=a3G'al=inosAs aa zinsAs//
(313l3G0'00)=dSIQ'S9OM=NSG aa .TinSAS//
AwJna aa NISAS//
AwWnG 00 INIHdSAS//
(9l'7)=ONO3'b3N39a3I=W9d 33X3 H3Nnd//
(31330'010) dSI0')WOJl=NS a00 T00J6Tl//
(313130'010) dSIG'3WOI =NSO 00 T0038O1J //
(=3173G'010) dSIG'S8oaoO=NSG 00 TOOJLZTi//
(313073'aIo) dSIG'W3fIVXT NS0'W3OIVO a 00 TOOj9T1i//
(3133'o10) dSIGa'G3Rd=NSG 00 TOO9TSU//
(31330'0710) dSIG'SW~VdT=NSO 00 Taa oojtT//
(3313a'a10o) dSIG'dOlSL,=NS a 00G TOJT1J//
(313730'010) dSIO'WUONKg=NSO 00 T00JZTij//
(SSvd'lO) dSIG'SOgq=NwSa 00 TOOjTJl//
(313730'010) dSIG'OWO'W=NSG 00 TOOJOTrJ//
(313l30'010)=dSIG'3DVTV=NSO 00 T0036013//
(313730'o0o)=dSIO'sgOTM=NSO 00 TOOJ8Oi0//
SiOld=3WVNG0 00 TOOdSOid//
a=linOSAS 00aa TOOLOi//
AWWna aa To00d901//
(3S7I'(OT'9L)'NI))=:3VdS'OOt7z=3ZIS1:S=3 //
'(SSVd'OOW)=dSIo'VOSAS=INnf'iL3AO?=NS a00 iO33ASAS//
V=inOAS aa inOdSAS//
(i17')=ONO3'olqd7I=W9d 33X3 Id3l//
08=3ZISlI=SDo's=ilnosAs o ziLnsAS//
(SSvd'aO)=dSIO'owo'0=NSo 00 finsAs//
Awwna 00 NISAS//
AWwna 00aa NIdSAS//
(.l't)=aGN03'3N39a3I=W9d D3X3 Nnd//
(Sd=:9OSO //
'00t,9=3ZISNIS'08=133]'83=W03)=00'(3S"Ib(T'Z)"a)=33VdS //
'V0SAS=iINn'(SSVd'M3N)=dSIG'aNO.iL=NSO 00 TOOKTId//
V=inOSAS 00 Tood901d//
vasA=iINn'(Sd=9DOS]'OOt9=3ZISI'O8=I337'-1E=W=333)=:30 //
'(3sq '(T'0)'T)i)=30VdS'(SSVd'M3N)=dSIG'SO0 00=NS 0GG TI000Old//
(SSVd'o10)=dSIo'3wo =NSO 00 T00JoOiL//
(SSVd'700)=dSI'S9O0M=NSa aa TOMITOi.//
(17')=NOD'iIAUnof=Wg9d D3X3 fno0//
(Sd=9osa'oo179=3ZISNt1T''08=737'OA=8W333)=3(0'(3S7' (TI') //
'bi)=3DVdS'VOSAS=LINn'(SSVd'M3N)=dsIa'O7VD=NSG'WOVD G 00360id//
(SSVd'G10)=dSIO'LnOl)NIM =NSG 0a T0080LSO//
V=inOSAS 00 o00d90oi//
VOSAS=IINn'(Sd=SI OSG'OOiT9=3ZISIS'o08=7373-'a=00033a)=000 //
'(SSVd'M3N)=dSI(' (3S7 '(TI')'N L=3DVdS<'DWO=NSa aa T00dSOid//


tr8





85






//CALL EXEC WAVE
//GENO.REVO DD *

the OROBS dataset
phase and intensity read by (2F10.5)

/*
//GEN1.PARA DD *

the WINK parameters and
model atmosphere

/*
//GEN2.DATA DD *

the OBS dataset
phase and intensity read by (2F10.5)

/*
//GEN3.PRED DD *
-1.0
the "true-false" card (defines the free-parameters)
WINK
47 0.0
48 0.0
49 1.0
86 1.0
0 -100.0
/*
//GEN4.STOP DD *
-1.0
STOP
/*
//LCPT.PLOTS DD *

the LCPLOT control cards for the
generation of plots (see Fig. 8)

/*
//PLIT EXEC PLOT


Fig.10.-The input stream which uses the WAVE procedure. Note that a
partitioned load module library must be supplied with the necessary
programs in it.





86


The input stream which uses the WAVE procedure is given in Fig.

10 The missing datasets depend on the application of the procedure.













CHAPTER V
ANALYSIS AND SOLUTION


Introduction

The WAVE procedure was described in the preceding chapter. It

was developed to assist in the solution of the light curves of RS CVn

because previous techniques were inadequate. The WAVE procedure is not

capable of arriving at a satisfactory solution without the critically

important supervision of a knowledgeable human being. The human must be

capable of analyzing intermediate results and determining the subsequent

steps by which a better solution might be obtained. At this point, WAVE

has been used in the analysis of the light curves of RS CVn, and it has

not yet been determined whether the procedure can be applied to other

eclipsing or non-eclipsing systems. It is the opinion of the author that

WAVE will prove to be helpful in obtaining solutions,in either case,

where unexplained photometric complications exist. Therefore, in order

to assist with the implementation of WAVE in further research, a detail-

ed account of the process by which the present solution of RS CVn was

obtained will be presented.

The Data Analyzed

The light curves of RS CVn that have been analyzed with the use of

the WAVE procedure are listed in Table 8. These do not represent all of

the published data which are available, but they are a selection which

meets the requirements of the research effort undertaken as the topic of

this dissertation.


87





88

TABLE 8

SOURCE OF DATA



Publication MJD of observations Xe Name

Sitterly (1930) 22759.2 22898.2 5150A 1921
Chisari and Lacona (1965) 38109.9 38227.0 5150A 1963
Chisari and Lacona (1965) 38468.9 38572.0 5150A 1964
Catalano and Rodono (1967) 38871.8 38944.0 5150A 1965
Catalano and Rodono (1967) 39213.9 39316.0 5150A 1966
This Dissertation 42469.0 42534.3 5500A 1975v
This Dissertation 42469.0 42534.3 4490A 1975b
This Dissertation 42506.0 42534.3 3770A 1975u
This Dissertation 42843.3 42929.2 5500A 1976v
This Dissertation 42843.3 42929.2 4490A 1976b
This Dissertation 42843.3 42929.2 3770A 1976u



In Table 8 the last column is a "name" which has been given to

the data for easy reference in this present work. This "name" is also

the year (and color in some cases) in which the data were obtained. In

a few cases it will be convenient to group the 1963, 1964, 1965, and

1966 data into a set, and to refer to this set as the "Catania data."

The astronomers who published these data were all observers at the

Catania observatory.

All of the Catania data and the author's data of RS CVn were

obtained using BD+350 2420 as a comparison star. This greatly facili-

tates the comparison of the light curves from the different years,

because the differential magnitudes are in the same light units. The

difference in the effective wavelength used by the Catania observers and

that used by the author has the effect of changing (only slightly) the

effective light unit. Since the bandwidth of the filter used by the

Catania observers was not available, it was impossible to make allowances





89

for any differences in the two instrumental systems. Fortunately, to

some extent this difference does not cause a problem with the analysis

because the WINK model uses the effective wavelength as an input param-

eter. Thus, the majority of the WINK parameters that are subsequently

determined are independent of the wavelength.

In Table 8 the specific dates for the observations are given

because only portions of the published data were used for the 1921 and

Catania light curves. The migration of the distortion wave would

"wash-out" some of the detail in the light curve if the duration of the

observing season was too long. For this reason the data which produced

the light curves used in the WAVE procedure were limited to those points

taken over a period of less than 140 days. The data taken by the author

was deliberately limited to a short time span (65 days in 1975 and 86

days in 1976).

The modifications to WINK (see Chapter IV) extended the capacity

of the model from 100 points to 200 points. This would have allowed

light curves to be made with up to 200 normal points. However, such

light curves would have been prohibitively expensive to run on the

computing system available. Therefore, a compromise was made between

the cost of computing (which increases approximately as the square of

the number of normal points) and the desirability of a large number of

normals which would give a good resolution of the details in the light

curves. The compromised value was 150 normal points per light curve,

or as close to this value as was realistic.

The calculation of the normal points was carried out on the dig-

ital computer. In computing the normal points the first step was to

compute the phase for each individual differential magnitude from the




Full Text

PAGE 1

A PHOTOMETRIC STUDY OF RS CANUM VENATICORUM INCLUDING CRITICAL ANALYSES OF THE DISTORTION WAVE AND PERIOD VARIATIONS By ELWYN WHIT LUDINGTON A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1978

PAGE 2

Dedicated to the memory of my grandfather, Elijah Whitfield Fisher. ,-* -?'•'•* -niii---

PAGE 3

ACKNOWLEDGEMENTS I wish to express my appreciation to the many people who have helped me accomplish the task of writing this dissertation. First, I acknowledge my mother's years of love and encouragement. While maintaining a secure home environment, she required of me a high degree of independence which I feel has been invaluable in my pursuit of higher education. Second, I thank Mr. and Mrs. Robert E. Ludington, my uncle and aunt, for promoting my interest in amateur astronomy. Third, the guidance of Dr. Frederick Decker during my undergraduate years must be acknowledged. His advice was the beginning of my pursuit of astronomy as a career. Fourth, I thank Nancy A. Ludington for her encouragement during my initial years of graduate study. I wish to express my undying gratitude to Dr. John E. Merrill and Barbara M. Oliver for the words of wisdom which they gave me during the most trying times of my graduate student career. There are many others who deserve my thanks for their personal involvement in my life: Charles Jackman, Karen Rockwell, Charles H. Morgan, Jr., David Killian, and Mary Horn, to name a few. Professionally, I would like to thank Dr. John P. Oliver for suggesting the topic of this dissertation, and for his expert guidance during the course of the research. The members of my supervisory committee are also thanked for their assistance. Of equal importance to the successful completion of this work were the many graduate students with whom I have had the pleasure of working. In particular, I would like to thank David Florkowski, Gregory Fitzgibbons, Patricia Guida, Charles iii ^-,— -., -~.ii-^i,^a-^„

PAGE 4

Jackman, David ICillian, Norruan Marioiorth., and Elizabetii Mullen for our many discussions wiitcL greatly stimulated my endeavors, Steven Gladfn and John Young are thanked for their kind and very helpful assistance with computer programming. Finally, I would like to thank Karen P. Rockwell for her assistance with the reduction of the chart recordings and her help with this manuscript. IV -Tlh— .^*--V,-

PAGE 5

TABLE OF CONTENTS ACKNOWLEDGEMENTS iii TABLE OF CONTENTS v LIST OF TABLES vii LIST OF FIGURES viii ABSTRACT x Chapter I. INTRODUCTION 1 Topic of Current Research 1 Historical View 2 Scope of Dissertation 44 II. INSTRUMENTATION 45 The Basic Equipment 45 Amplifier Calibration 48 III. PROCEDURE AND DATA REDUCTION 51 Observational Procedure 51 PHRED 54 DEXTOR 65 Data Reduction 67 IV. DATA ANALYSIS PROCEDURE 74 Introduction 74 Outline of WAVE Procedure 74 The WINK Program 78 The ROMC Program 81 The FOURFIT Program 81 The LCPLOT Program 82 Detailed WAVE Procedure 82 V. ANALYSIS AND SOLUTION 87 Introduction 87 The Data Analyzed 87 — 1 -k. T j-F^ -..iu*)|u -^ e'r*^ ^ > *TV

PAGE 6

Th.e Analysis 91 The Final Solution 99 The Distortion Wave 102 Period Changes 104 VI. DISCUSSION 139 Introduction 139 The Distortion Wave 139 Orbital Period Variations 147 Conclusion 149 APPENDIX 153 LIST OF REFERENCES 167 BIOGRAPHICAL SKETCH 173 VI ---?— .r-^T-*—'-'-**"! "-— fr^iy-.-Nei../ s'itm^sri.-'lm

PAGE 7

LIST OF TABLES 1. JOY'S ABSOLUTE DIMENSIONS 5 2. POPPER'S RESULTS FOR RS CVN 13 3. LIST OF RS CVN BINARIES 24 4. LUDINGTON-OLIVER FORMAT 56 5. DIFFERENTIAL MAGNITUDES AND COLORS OF CHECK STAR 71 6. WINK PARAMETERS 78 7. ASSUMED PARAMETER VALUES 80 8. SOURCE OF DATA 88 9. SUMMARY OF RS CVN SOLUTION 92 10. FINAL VALUES OF WINK PARAMETERS 100 n. FINAL VALUES OF EPOCH-DEPENDENT PARAMETERS 101 12. NORMAL POINTS FOR 1921 DATA 117 13. NORMAL POINTS FOR 1963 DATA 119 14. NORMAL POINTS FOR 1964 DATA 121 15. NORMAL POINTS FOR 1965 DATA 123 16. NORMAL POINTS FOR 1966 DATA 125 17. NORMAL POINTS FOR 1975v DATA 127 18. NORMAL POINTS FOR 1976v DATA 129 19. NORMAL POINTS FOR 1975b DATA 131 20. NORMAL POINTS FOR 1976b DATA 133 21. NORMAL POINTS FOR 1975u DATA 135 22. NORMAL POINTS FOR ig75u DATA 137 23. TIMES OF MINIMA AND CHARACTERISTICS OF THE DISTORTION WAVE .141 vit (.. .- ,„.'--___.,

PAGE 8

LIST OF FIGURES 1. 1975 Visual Light Curve of RS Canum Venaticorum 29 2. Schematic Diagram of Instrumentation 47 3. Fine-Gain Stability 49 4. Coarse-Gain Stability 49 5. JCL Cards for PHRED 59 6. Differential Magnitudes of Check Star 70 7. Outline of Basic WAVE Procedure 75 8. Sample Plot from LCPLOT Program 77 9. The WAVE Procedure 83 10. Input Stream which uses the WAVE Procedure 85 11. 1921 Light Curve of KO Star in RS CVn 105 12. 1963 Light Curve of KO Star in RS CVn 107 13. 1964 Light Curve of KO Star in RS CVn 108 14. 1965 Light Curve of KO Star in RS CVn 109 15. 1966 Light Curve of KO Star in RS CVn 110 16. 1975v Light Curve of KO Star in RS CVn Ill 17. 1976V Light Curve of KO Star in RS CVn 112 18. 1975b Light Curve of KO Star in RS CVn 113 19. 1976b Light Curve of KO Star in RS CVn 114 20. 1975u Light Curve of KO Star in RS CVn 115 21. 1976u Light Curve of KO Star in RS CVn 116 22. Distortion Wave Amplitude , 142 VTU — tl-^— -^ti^J^-T f

PAGE 9

23. Pdase of Distortion Wave Mlnimuni 143 24. Sfiape of Spotted Region 146 25. Photoelectric 0-C Diagram ..... 148 IX

PAGE 10

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A PHOTOMETRIC STUDY OF RS CANUM VENATICORUM INCLUDING CRITICAL ANALYSES OF THE DISTORTION WAVE AND PERIOD VARIATIONS By Elwyn Whit Ludington December 1978 Chairman: John P. Oliver Major Department: Astronomy Photoelectric data in the UBV system were obtained by the author in 1975 and 1976 at Rosemary Hill Observatory. These data of RS Canum Venaticorum were analyzed together with the published Catania data. The analysis included the use of a modified version of D. B. Wood's (A.J. 76, 701) computer program WINK. A truncated Fourier series representation of the distortion wave was subtracted from the observed light curve so improved elements could be determined from the difference by use of the WINK program. This process was not at all like the usual rectification procedure; it was an iterative procedure which greatly improved the confidence in the determination of the elements of RS CVn. With the single exception of the effective temperature of the KO III star, the eclipsing elements are consistent for all epochs and colors studied. Using these elements, it was possible for the distortion wave to be isolated; therefore, it will now be possible for theories of its origin and structure to be tested more critically. The results are consistent

PAGE 11

with a spotted surface for the KO star. However, the sunspot analogy does not accurately describe the nature of the spots. XI f^l 1*^1 g -^ V -^ — — t -^— =t*tr>-tf i^i ^i.rt '-Ml rti-tr.
PAGE 12

CHAPTER I INTRODUCTION Topic of Current Research The eclipsing binary star RS Canum Venaticorum (RS CVn) is the prototype of a yery interesting, but poorly understood, group of stars. It has been chosen for further study because it has the most complete observational record of this group, and because it is sufficiently bright to allow observations with the available equipment. The RS CVn binaries (also known in the literature as RS CVn systems, RS CVntype binaries, RS CVn stars, etc.) have been recently reviewed by Hall (1976). He concludes that the group is best defined by systems in which (1) the hotter star is of spectral type F or G and luminosity type V or IV, (2) strong Ca II emission is present in the H and K lines, and (3) the orbital period of the binary system is between approximately a day and 2 weeks. There are other characteristics which are common to many of the systems listed by Hall, but which were deemed unnecessary for the purpose of classification. Some of these characteristics would be mass ratios near unity, cooler components near spectral class KO III, and photometric distortions superimposed on the normal eclipse phenomena (if it exists). It is the complications caused by the last of these characteristics to which this dissertation is addressed. A new set of observations of RS CVn will be presented which will extend the basic astronomical knowledge of the system and confirm the earlier observations. A new technique of solution is developed 1 .^^n"r-"*i r=--*^lKw-iiltr,.tHfcaklri*- ,•

PAGE 13

which circumvents the previous problems encountered when deriving elements from a light curve with unexplained light variations. A natural result of this technique is to isolate the unexplained light variation (referred to as a 'distortion wave' in this work) so that it may be studied independently. It is also hoped that the times of minima can be improved with this technique so that a better representation of the period variations can be obtained. In the remainder of this chapter the literature on RS CVn and RS CVn binaries will be reviewed and the scope of the dissertation will be outlined. In the chapters to follow the new photoelectric data will be presented, starting with the instrumentation and procedure used. Following this will be a discussion of the distortion wave and period variations. The dissertation will conclude with a summary of the results, interpretation as to their meaning, and suggestions for future research. Historical Review The review of the literature shall start with a chronological history of the research on RS CVn. When this review reaches the early 1970's,it will be more convenient to speak in terms of the RS CVn systems, rather than RS CVn itself. RS Canum Venaticorum from 1914 to 1972 RS CVn was first reported as a variable star by L. Ceraski in 1914. She reported that the star was observed to be fainter, on photographic plates read by M.S. Blazko, on 7 April 1896 (by 1^5), 15 May 1907 [by iTo), and 3 May 1911 [by iTo). Numerous observers studied th.is system during the following 16 years. The results of

PAGE 14

these observations culminated in the solution of the light curve presented by Sitterly (1930). Sitterly summarized the considerable observational material obtained between 1914 and 1928 by Townley (1915), Hoffmeister (1915, 1919), Maggini (1916), Gadomski (1925), Schneller (1928) and others. He presented the times of minima that these various observers had collected up to 1928 and discussed the period changes. He noted that the period steadily increased during the interval 1900 to 1928. This can easily be verified from the times of minima as plotted on the 0-C diagram (Observed time of minima minus the Calculated time of minima from a linear ephemeris). He had accumulated 710 visual estimates using the 23-inch Princeton refractor and 351 photographic estimates from Harvard plates. The visual estimates were obtained during the years 1920 to 1922 (mostly in 1921), while the photographic estimates covered a much longer time (from 1892 to 1922). The visual light curve showed asymmetry outside eclipse and in primary eclipse. The photographic light curve, on the other hand, showed no asymmetry outside eclipse, nor did it show a secondary eclipse. In retrospect, this can be understood in terms of a moving distortion wave averaging out the asymmetry over the much longer interval of time during which the photographic estimates were made. This process would, of course result in a much larger standard error for points of the photographic light curve, but this would be expected in any case because of the lower precision of this technique. Except for the asymmetry outside eclipse, Sitterly's visual light curve solution was in good agreement with the photographic light curve. The solution was complicated by a small secondary eclipse, only 0'.03 deep, which compares with a depth of 0T2 by modern photoelectric photometry. Sitterly determined a depth of nmi'tir+t^ •'iriifc^ "r ^ -*?^w- ---^ /.fejii*llirr^ii vi"^ -. i^^

PAGE 15

ll'z? for primary eclipse, which is in reasonable agreement with a modern value of ll'l. He attempted a solution in which the following sides of both stars were more luminous than the advancing sides. This was necessary in order to explain the outside eclipse asymmetry, which amounted to a peak to peak difference of oTl3 between the portion of the light curve preceding and following primary eclipse. This gave much better residuals than the other solutions but it was discarded because it seemed so physically inexplicable, particularly since it required the fainter star to have a difference in brightness from one side to the other of 55%I The solution which was finally adopted as the best representation of the true values was obtained by solving the visual light curve without any rectification. The resulting elements were: Uniform disks assumed, k = 0.30, i = 79.9 degrees, r^ = 0.289 r^ = 0.0867, Lj^ = L2 = 0.590, L^^= L^ = 0.310, where the subscript b (or 2) refers to the brighter star, and the subscript f (or 1) refers to the fainter star. The estimated probable error for a visual observation was + o'!'0364, while the estimated probable error for a photographic observation was + 0.09. It is therefore wise that he chose to base the solution on the visual light curve. The comparison star used was BD+36 2345, and the differential magnitudes were originally given as comparison minus variable. In the same year, Joy (1930) published spectroscopic data on RS CVn. He used the results of Sitterly's photometric solution along with his own spectroscopically determined radial velocities to arrive

PAGE 16

at absolute dimensions. A summary of Joy's results is given in Table 1 (the subscripts have the same meaning as noted above). TAB EL 1 JOY'S ABSOLUTE DIMENSIONS K^ = 91.5 km/s m^sin-^i = 1.79 M 1 ""•" """" '"r"' ^•'-' "0 2 = 99.0 km/s m^sin i = 1.65 M Y = -8.9km/s m2/m^ = 0.93 a^sin i = 6.04 x 10^ km r. = 1.6 R^ 1 bo a^sin i = 6.53 X 10 km r^ = 5.3 R m^^ = 1.85 Mg m^ = 1.71 M^ Joy concluded from the spectroscopic absolute magnitude and from the spectral class that both stars are dwarfs. However, the size and brightness of the fainter star were in direct conflict with this. Joy ended his article by saying, "... the secondary star is certainly peculiar and cannot readily be classified among other stars for which we know the physical characteristics" (p. 45). Joy agreed with Sitterly's interpretation that the fainter secondary star is "a sort of 'subgiant.'" C. Payne-Gaposchkin (1939) made a study of the period changes and light curve asymmetries of RS CVn as a part of a paper on variable stars. She collected approximately 4000 photographic estimates of the brightness from Harvard plates exposed between the years 1892 and 1938. From the data, 17 times of minima were computed and plotted. In addition, a light curve was made by combining individual points into normals. In primary eclipse each normal was made up of 10 individual points, while outside eclipse each normal was comprised of 100 individual points. The normal points were computed after each individual point "rt^'imn: iti".— !-*! rf*—-.

PAGE 17

was corrected for the change in period, as she had estimated it. The resulting light curve agreed with Sitterly's in its general characteristics. However, it did not agree with the asymmetry that Sitterly had observed from his visual light curve. Recall that Sitterly had presented a visual and photographic light curve for RS CVn, but his photographic light curve failed to show a secondary minimum or any asymmetry outside eclipse. Payne-Gaposchkin, on the other hand, found a shallow secondary eclipse in her photographic light curve (of depth 0.06), and a difference in the height between the two maxima of only a few hundredths of a magnitude. She noted, however, that when the light curve is made from points taken about the same time as those of Sitterly, a somewhat larger difference was found. In an effort to summarize the differences in magnitude between the two maxima, she presented a table of these differences at four epochs of minima. She noted that if the difference is assumed to be a periodic phenomena, then the period would be approximately 8000 days (22 years) or 1570 orbital periods, i.e., the approximate period of the orbital period changes. She estimated that g an absolute orbital radius of 2 x 10 km would be necessary to explain the period changes as a light-time effect. Further, she determined that if this were due to a third body, then the required mass of 4 M would seem larger than could possibly go undetected photometrically. This represented the first convincing evidence that the period changes were of an unusual nature, and the first time that the differences in heights of maxima were ascribed to be of a possibly periodic nature. The most significant aspect of this paper was that the differences in the height of the two maxima were ascribed to the redder (and fainter) f .-^IW n .r*.

PAGE 18

7 of the two stars. This was based on her realization that the size of the asymmetry was greater in the visual light curve than in the blue photographic light curve. W. A. Hiltner (1947) noted that a define group of stars existed which showed Ca II emission. In this short note he collected the scattered data on the 13 systems known to him at that time (RA Eri SS Cam, AR Mon, RU Cnc, RS Cnc, RW UMa, RS CVn, SS Boo, WW Dra, Z Her, AW Her, RT Lac and AR Lac). Hiltner found from his study of RS CVn the same characteristics reported by other observers whose data he had collected together. The emission was noted to be usually from the fainter of the two stars in the eclipsing system and the emission was apparently "... not situated uniformly around the parent-star" (p. 481). In fact he stated that the emission approached invisibility only at the secondary eclipse when the fainter star is partially covered by the brighter, but smaller star. This led him to agree with Struve (1946) and others that the Ca II emission in these stars originates from a ti dally extended region above the photosphere of the fainter star. The emitting region was isolated at the extremes of this tidal bulge along the line joining the two stars. Struve 's and Hiltner's papers could be considered the first recognition that there was a group of stars (today referred to as RS CVn binaries) which warranted consideration as a group. Gratton (1950) studied 19 systems which showed H and K lines of Ca II emission in the last section of a paper published just a few years after Hiltner's. This list included the 13 stars in Hiltner's paper plus six others which were not eclipsing binaries, but were of a binary nature. These six stars were primarily more luminous and of longer periods -tSftdWri.i't-Wlta<^P-tH^-.^-i. -'._-i^ uiii—Ui

PAGE 19

than those in Hiltner's. list. Gratton attempted to give additional evidence that the tidal bulge proposed by Struve and Hiltner was the proper mechanism for the explanation of the H and K. emission. Briefly, Gratton's analysis followed these lines. By assuming that all stars with a tidal distortion above some lower limit would show emission lines, it was then expected that the giant stars which show emission would have longer orbital periods. This condition led to the relation > k-, a-] + a^ 1 where it was assumed that the variation in mass could be neglected, R was the radius of the star, a-, and a^ were the relative orbital radii, and k. was a constant. Since the stars being studied were of approximately the same spectral type (and therefore had the same surface brightness), the radius was proportional to the square root of the luminosity. In addition, the sum of the relative orbital radii was proportional to the period (P) to the two-thirds power. Therefore the period and the absolute magnitude (.M) for the binaries showing H and K emission lines were above a line 0.3 M + log P = constant. Gratton plotted the absolute magnitude versus log P for 13 of the 19 stars in the list. The binaries SS Cam, Z Her, 56 Peg, AW Her, AR Lac, and RU Cnc were excluded because of the lack of data. Gratton stated, "It is seen that there is a definite correlation between M and P; we may tentatively take the limiting line 0.3 M + log P = 2.5'' (p. 40). Stars above the line 0.3 M + log P = 1.0 are practically in physical contact; for these stars the distortion would be too great and might cause instability. imeP-l*** ^^TTlf— ^iH---1 -^fm.^'T.-r^^^'r

PAGE 20

It seems to the present writer that the assumptions which led to this conclusion are reasonable, with the possible exception of the correlation between the emission and the degree of tidal distortion. More recently, Young and Koniges (1977) have investigated this relationship; this will be discussed later. Keller and Limber (1951) used an unfiltered 1P21 photomultiplier tube to obtain a light curve of RS CVn during the spring of 1949. They used B0+35 2421, BD+35 2422, and BD+35 2418 as comparison stars, with the differential luminosity expressed relative to BD+35 2422. Inside eclipse, individual points were tabulated, but outside eclipse only the normal points were given. From an expanded plot of these data around the primary minimum Keller and Limber noticed a systematic difference in luminosity. They found that this variation in the depth of primary was most probably due to intrinsic variability of the fainter star. They also noted the same asymmetry outside eclipse observed by Sitterly and Payne-Gaposchkin. It is important to note that the observations of Keller and Limber were taken over only a three-month interval, so that the normals they produced outside eclipse were not affected as much by variations in the asymmetry as was the case for the observations of Sitterly (mostly one year of data) or Payne-Gaposchkin (nearly 47 years of data). The asymmetry observed by Keller and Limber was of the same general character as that of the previous observers; it had a higher maximum after primary eclipse than prior to primary eclipse. The difference in the two maxima was 0^04. The rectified light curve was solved using a limb darkening coefficient of 0.8 with the aid of the Merrill (.1950) tables. The elements so determined were:

PAGE 21

10 L^ = 0.725, L^ = 0.274, k = 0.355, r^ = 0.265, i = 82?5 + 05. From the luminosity and radius of each, component they computed the ratio of surface intensities. This ratio, approximately 20, could not be reconciled with the value of 5.5 they computed on the basis of the energy distribution of the stars Ccorrected for the effects of the Balmer discontinuity, atmospheric transmission, and the response of the instrumentation). This, of course, was the same problem Joy had commented upon. Keller and Limber very crudely estimated the polytropic index of the fainter star to be 2.9.5. They used an 0-C diagram made from all the available times of minima, and an orbital eccentricity determined from a single estimate of the time of secondary minimum based on their own data. While it is obvious that their observations are the best of any available at that time, it is equally obvious Cas can be seen from the light curve in their paper) that the time of secondary minimum is greatly complicated by the asymmetry of the light curve. It was therefore wise of them to state, "It is not possible to obtain the phase of the secondary with much precision" (p. 647). Bidelman (1954) published a list of stars which were known to show emission lines and whose spectral types were later than B. The list for stars showing Ca 11 emission, which are also spectroscopic binaries, continues to be referenced today. RS CVn as well as all of the other stars in Hiltner's paper were among the 72 stars in Bidelman 's table.

PAGE 22

11 Popper (1961) observed RS CVn in an effort to improve the quality of the spectroscopic orbit and to add photoelectric observations on a standard system to the body of existing data. He obtained 12 spectrograms between the years 1954 and 1958 which showed the same general features previously observed by Joy (1930) and Hiltner (1947). The only major difference between his spectrograms and those of the previous observers was the sharpness of the absorption lines due to the brighter component of spectral class F4. Joy had designated the spectral type as F4n, which would mean that the lines were "nebulous." Popper noted the bright H and K emission lines of Ca II from the cooler (fainter) component, as well as the variable emission intensity of the H line. The solution of Popper's radial velocity curve was compared with Joy's. Both observers assumed a circular orbit. Popper's results gave slightly smaller masses for both stars. In addition, he believed that the difference in the systemic radial velocity of 5 km/s was probably a real (but unexplained) phenomenon. The photometry was done during the summer of 1956, in January 1958, and in January 1959. No attempt was made to cover the entire light curve. The comparison star was HD 114778 (BD+35 2420), i.e., the same star used later by Chisari and Lacona (1965), Catalano and Rodono (1967) and the present writer. The photometry of this star from the three seasons resulted in the following magnitudes: V = 8'!'42, B-V = +0l'46, and U-B = -0?04. This star was 0.03 fainter in 1956 than it was during the 1958-59 observing seasons. Popper was not sure whether this difference was due to a real variation, to the difference in the zenith angles involved, or to the difference in the set of standard stars used.

PAGE 23

12 As expected, primary eclipse was observed to be deeper for shorter wavelengths, and secondary minimum was observed to be deeper in the yellow than it was in the blue. Surprisingly, the depth of primary eclipse was 0™3 different in 1956 than it was in 1958-59. This must be attributed to the fainter star, since this eclipse is a total one. No such variation was found in the system's brightness outside eclipse; so the intrinsic variation of the fainter star was not uniform over its surface. A similar, but a much smaller, difference existed between the other observed primary minima. The observed difference in depth of primary could be explained by a change in the radius of the fainter star. Unfortunately, there were insufficient data to determine if this was the case. Another possible explanation would have been a change in the color of the fainter star. The data available to Popper indicated a change in color of the proper sense but of insufficient size to account for the observed difference. Also, since the variations outside eclipse had the same color as the fainter star it was yery reasonable to expect this star to be the source of the variation. These two effects (variation in the depth of eclipse and the variations outside eclipse) could have been due to a combination of pulsation and "spottedness" of the fainter star, according to Popper. He pointed out that the depth of secondary eclipse as observed by Keller and Limber (1951) was greater than expected from their values of k and the depth of primary minimum. This led him to believe that there was a large uncertainty in the value of k. Popper also found a discrepancy in the ratio of surface brightness as calculated from the spectral types and that obtained from the light curve. He noted, however, that the discrepancy was probably not as large as that found by Keller and Limber. For reference, the results of Popper are

PAGE 24

13 summarized in Table 2, TABLE 2 POPPER'S RESULTS FOR RS CVN ^ma sin i = 16.7 Ro (B.C,)^ = -0.3 3. M, sin-^i = 1.32 Mo M^ = 1.32-1.35 Mo M^ sin^i = 1.38 Mo M^ = 1.38-1.42 Mo i = 82-90 Rj^ = 1.5-2.0 Ro a = 15.7-16.85 Ro R^ = 3.3-4.6 Ro r, = 0.09-0.12 L. = 3.7-7.8 Lo b b r^ = 0.20-0.27 L^ = 5.0-9.1 Lo (B-V)j^ = 0.39-0.44 ^\olh = ^-^-^-^ (B-V)^ = 0.91 (M^^^). = 2.4-3.0 T^(eff) = 6500-6800K (M^)|^ = 2.5-3.4 T^(eff) = 4700K (M^)^ = 2.7-3.3 (B.C.)j^ = oTo Plavec, Smetanova, and Pekny (1961) showed by their calculations that the periodic term in the period variation could not possibly be due to a third body (unless this third body greatly violated the massluminosity relation). They found that in the extreme case, the mass of the third body would have to be of the same order as that of the stars in the system, A similar conclusion was reached earlier by PayneGaposchkin (1939). Their calculations were based on the much more reliable data of Keller and Limber (1951) and Popper (1961). Popper's data were used by them to make a new estimate of the effects of apsidal motion, and here again the results indicated that this hypothesis could not be responsible for the periodic term of the period variations.

PAGE 25

14 Chisari and Lacona (1965) observed RS CVn from the S. Agata Li Battiati station using a 30 cm (12 inch) Cassegrain telescope in 1963 and 1964. Their effective wavelength was stated to be 5150 A which is slightly bluer than that for the standard V filter. The bandwidth was not given, but the EMI 6256A photomul tipl ier tube was filtered with a yellow Galileo G 1-26 filter. They used the same star as Popper for a comparison (HDl 14778 = BD+35 2420). However, they did not correct the observations for the effects of atmospheric extinction, because they considered the closeness of the comparison to the variable sufficiently small to make correction unnecessary. After rectification of the light curve they solved the 1964 observations to obtain the following elements: Initial epoch (Julian Date) = 2438467.1282, Period = 4'?797660, X = 0.8, i = 84, k = 0.46, L^ = 0.259, r^ = 0.244, L2 = 0.731, r^ = 0.112, e = 0.0 (as They found the period to be decreasing in the same sense as Keller and Limber (1951) had found, but not by the amount predicted by observations obtained prior to 1936. They concluded that the system was semi-detached and that the material one would expect in such a system was leaving the larger star. Thus a cloud would be formed which would cause the anomalous light variations in the light curve. This does not agree with subsequent research. Plavec 0967) studied the properties of Algol -like close binaries with, double-1 tne spectra. RS CVn was among the stars studied and was found to be detached by a significant amount. Several other W*aWlWlO I ^ l, — ^-WY1K3,B^*,r^. ^_i

PAGE 26

15 stars were noticed to have similar properties which were different from genuine Algol binaries. RS CVn, WW Dra, Z Her, AR Lac, and SZ Psc were considered by Plavec to form a well-defined sub-group. It is significant that except for SZ Psc all of these stars were in Hiltner's list of 13 systems showing Ca II emission. Catalano and Rodono (1967) presented additional photoelectric observations of RS CVn taken with the same equipment Chi sari and Lacona had used in 1963 and 1964. However, it may be of importance to note that the observations were not all taken at the same site. The data for 1965 were apparently obtained from the same place as those of Chi sari and Lacona, but the equipment was then moved to Serra La Nave. The subsequent data taken in 1966 were from this site using the same telescope and equipment. All of the observations used the same comparison star as Popper, Chisari and Lacona, and the present writer; namely BD+35 2420. They also observed a check star (BD+35 2422), which showed, contrary to Popper's earlier suspicions, that the comparison star 3D+35 2420 is of constant light. They made no attempt at a solution, in the classical sense, to the new observations, but instead they pointed out an important fact about the distortion wave in RS CVn. The distortion wave was found to shift with respect to the eclipses in the direction of decreasing phase, and completed one cycle in 2400 orbital periods. To explain this phenomenon a model was developed in which a ring of material circled the hotter star. This was similar to the proposal of Chisari and Lacona, but the model developed by Catalano and Rodono was much more detailed. In this model a non-uniform ring of material was located around the smaller star of the system. They assumed that the material would make Keplarian orbits l''*ft^'T-*.—^T*'rte*=hf?-^Tl'W— r^tftilr *^.-t*rf

PAGE 27

16 around this star and were therefore able to compute the distance between the star and the ring. The period of the quasi-sinusoidal distortion wave represented one orbit of a particle in the ring. The results required that the material be outside the limiting Roche lobe for the star. In this case the ring would be unstable, but they proposed that the material lost from the system be replaced by material from the larger star. If the primary star is inclined to the orbital plane, its axis would be expected to precess with a period which they computed to be about the same as that of the retrograde period of the distortion wave. The quasi-sinusoidal shape would then be due to the non-uniform distribution of material in the ring, but there was no exlanation for the persistence of this particular distribution over the time scale of the observations (1963 to 1966). The 1965 light curve showed no appreciable variations beyond those already known, but the data for 1966 indicated that the depth of primary eclipse was not the same for all nights during which this portion of the light curve was observed. The phenomenon was earlier reported by Keller and Limber and by Popper. Whether this was real or a result of the new observatory site, in the case of Catalano and Rodono's data, is not known. Nelson and Duckworth (1968) reported, in an abstract, on the observations they had obtained of RS CVn from 1965 to 1967. Their observations were not given, but they reported that the light curves show variations in the depth of primary and secondary eclipses of up to a quarter of a magnitude in the violet, and similar but smaller variations in the other colors. They also reported that the data showed changing shapes for the eclipses and the portions of the light curve outside eclipse, over the three years they observed the system. iT-^,,--,,-, _, -, ^ -.*.TW. —.tfl.t

PAGE 28

17 Catalano and Rodono 0968) summarized several aspects of their observations of RS CVn in a more widely accessible forum than their previous publication. First, they found additional evidence for the distortion wave's retrograde shift. From the observations of Keller and Limber, Popper, Chisari and Lacona, their own published data for 1965 and 1966, and new unpublished data for 19.67 and 1968, they were able to more accurately determine the period of the retrograde shift. Unfortunately, for their previous model, the results were incompatible with the theoretical procession rate of 2400 orbital periods. They found that the distortion wave retrograde shift period was of the order of 800 orbital periods or less. The new data for 1967 and 1968 were obtained on the standard UBV system, which allowed them to determine the color of the system outside eclipse. From the graph of the color index and outside eclipse variation, it was obvious that the color index increased with decreasing intensity of the distortion wave. Since the color of the distortion wave became bluer as it became fainter, they suggested that the investigations of Mergentaler O950) could be a possible explanation. They reported that Mergentaler proposed that systems which show such a color change can be explained by a gas of negative hydrogen ions of different optical thicknesses. Catalano and Rodono noted that this would require that the gas be in an equilibrium configuration in order to maintain the shape of the distortion wave as they had observed it. Variations in the depth of primary minimum had been observed in the past, but their more consistent and more extensive observations were able to confirm this phenomenon and to show that it was correlated with the position of the distortion wave. Since the primary eclipse was total, only the secondary (larger, cooler star) of the system --.r.i^'.=. -_r

PAGE 29

18 was visible at that time, thus this star was probably responsible for the distortion wave phenomenon. It is not clear to the present writer if Catalano and Rodono were referring to thp secular (800 orbital period) shift of the distortion wave across the primary eclipse as the source of variations in its depth or to some sort of flaring activity on the larger star. In the former case it would be difficult to explain changes in depth of primary eclipse which have been observed on much shorter time scales. Nevertheless, their conclusion was in complete agreement with the earli;er conclusions of Payne-Gaposchkin (1939), Keller and Limber (1951), and Popper (1961) regarding the source of the light variations (in eclipse and/ or out of eclipse). The period variations had been well known previously, but there had been significant evidence that the variations were due to apsidal motion (Keller and Limber 1951; and Plavec and Smetanova 1959). However, more recent studies of Plavec, Smetanova and Pekny (1961) have cast considerable doubt on the appropriateness of apsidal motion to explain the period variations. Catalano and Rodono showed that the existence of a moving distortion wave made the measurement of photometric eccentricity highly questionable. In fact they stated, "... the displacement of secondary minimum resulting from our observations is incompatibly smaller than the orbital period variations" (p. 440). Finally, the Catania astronomers concluded the article with some notes on the spectroscopic peculiarities in RS CVn. They had observed the same amission lines of H and Ca II as Hiltner (1947), Joy (1930), and Popper (1951). Unlike Hiltner they were unable to notice the disappearance of the H and K lines at secondary eclipse.

PAGE 30

19 In a theoretical presentation, Hall (1972) discussed an alternative model for RS CVn. This model attempted to explain the following characteristics of the system: 1. The existence of the distortion wave 2. The migration of the wave to decreasing phase 3. The anomalous depth of secondary eclipse 4. The non-uniform migration rate of the distortion wave 5. The variable depth of primary minimum as a function of time 6. The displacement of secondary minimum from a position mid-way between adjacent primary minima 7. The variable amplitude of the distortion wave 8. The changes in orbital period The model that was proposed by Hall, by analogy with the sun, was that of spots on the cooler component of the system. It was well known that the sun has dark spots on its surface from time to time. Starting from this, Hall felt that it was reasonable to expect that other stars would have similar spots. In the case of RS CVn, he anticipated that the spot or spots would cover between 30% and 60% of the facing stellar disk of the KO star. This spotted region was, for whatever reason, confined to one hemisphere and to the equatorial region between about + 30. Hall reasoned that the star would be rotating differentially, again by analogy with the sun. The equatorial region would rotate faster than the polar regions, as is the case in the sun (which also has a convective envelope). The stars of the system were expected to be in synchronous rotation, but the latitude at which the rotation was synchronized with the orbit was expected to be of the order of + 30 Again relying on the analogy with the sun, he assumed that the spot activity would be periodic, with a

PAGE 31

20 cycle of 1800 orbital periods. Further, he assumed that the spots on the cooler component of RS CVn would form at higher latitudes at the beginning of each spot cycle, and proceed to form at lower and lower latitudes as the cycle progressed. With this model the existence of the distortion wave is easily explained. Differential rotation of the star explains why the distortion wave moves to decreasing phase. Since the surface of the cooler star is not of uniform brightness, the depth of primary eclipse will vary depending on the location of the spotted hemisphere at the time of this eclipse. Furthermore, the location of the spotted region can cause the location of the minimum during the secondary eclipse to be shifted to either side of phase 0.5. Since the model assumes that the spot activity is periodic in a fashion similar to the sunspot cycle, and that the star rotates differentially, then the migration rate of the distortion wave will vary depending on the latitude of the spotted region and the amplitude of the distortion wave will vary in a similar fashion. Hall presented very convincing evidence to support this model. The spotted region would only have to be 1000K cooler than the surrounding photosphere in order to account for the typical amplitude of the distortion wave. This was of the proper value to also explain the anomalous depth of secondary eclipse, if it was assumed that the spotted region was eclipsed at secondary minimum. Hall noted that this implies that as the spotted region migrates, due to differential rotation, around the star, the depth of secondary eclipse should vary accordingly. This has not been confirmed. Catalano and Rodono (1968) had shown the correlation between the position of the distortion wave and the depth of primary minimum. Hall's

PAGE 32

21 model provided an explanation for this. The deepest primary minima occurred during times when differential rotation brought the spotted region to the hemisphere facing the earth. The displacement of secondary eclipse from the mid-point of the light curve had been explained by Catalano and Rodono (1968) as a consequence of the migration of the distortion wave. Hall's model clarified this in terms of the location of the spotted region during the secondary eclipse. If the spotted region was located so that it faced the earth at quadrature, then the loss of light during secondary eclipse would be asymmetric. From a plot of the available estimates of the amplitude of the distortion wave as a function of epoch, Hall was able to represent the variation with the periodic function AV(max-min) = -0^12 o'!'07 sin ((E+450)/1800) He used the linear ephemeris of Schneller (.1928) to calculate the value of E. Note that this function can be used to predict the value of the amplitude of the distortion wave at any time. Hall also presented another graph which allowed the prediction of the distortion wave migration rate. In Fig. 2 of his paper he plotted the orbital phase of the minimum of the distortion wave as a function of epoch (E). From this graph one was able to see that the discontinuities in the migration rate occur at the minimum of the spot cycle. This was the result expected from the analogy with the sun and differential rotation. Arnold and Hall (1973) later made corrections to the model without changing the substance of the results. In the remainder of the paper Hall attempted to explain the period variations as the result of mass ejections from the spotted active region. The required mass loss rate was rather high (of the order 10

PAGE 33

22 solar masses per year). The conclusion he reached on the evolutionary status of RS CVn was not decisive, but he considered the star to be most likely in a pre-main-sequence state of evolution. RS CVn Binaries The early stages in the development of the definition of this group of binary stars have been discussed in the preceeeding paragraphs. Certainly, the research results of Struve (1946) and Hiltner (1947) were the first clues to the existence of a group of stars which are different from the classical binary and significantly different from other peculiar systems. The research effort over the subsequent 30 years (Gratton 1950; Plavec 1967; Popper 1967, 1970; Oliver 1971, 1973, 1974; and Hall 1976) slowly developed a clearer picture of the physical and observational characteristics of these stars which separates them from any other group which has been classified. Popper (1967, 1970) listed approximately 20 systems which he believed to be of special interest because of their spectroscopic characteristics, light variations, and unique placement in the H-R diagram. Oliver (1974) was the first to undertake a comprehensive study of these stars as a group. This research led Oliver (1971, 1973, 1974) to list the criteria for inclusion in the group and to propose a list of stars which would therefore be members. To date, the best review of the RS CVn binaries is the recent paper by Hall (1976). In the paragraphs to follow, the current understanding of the RS CVn phenomenon will be discussed. Since the most characteristic observational property of the group is strong H and K emission, the discussion will begin with the spectroscopic characteristics. Variations in the observed light of the systems are an observational property of many of the systems in the group. The discus-

PAGE 34

23 si on of these variations will be followed by a short report on ultraviolet and infrared excess. Period variations have also been noticed in many of the RS CVn binaries; the short and long-term variations will be reviewed. The recent discovery of radio and soft X-ray emission from several of the RS CVn binaries has been very exciting. The report here will attempt to summarize these observations and the resulting implications. Finally, this section will conclude with a review of the proposed evolutionary status of these stars. However, before beginning, it will be useful to state the properties of RS CVn binaries which Hall (1976) proposed as the defining characteristics. They are as follows: 1. Orbital period between 1 day and 2 weeks 2. Strong H and K emission seen outside eclipse 3. The hotter star is F or G, IV or V The list of members in this group which has been developed over the last few years is given in Table 3. This list is derived from Hall's (1976) review paper and new discoveries. Spectroscopic characteristics The existence of strong H and K emission in the RS CVn binaries has been well documented by Struve (1946), Hiltner (1947), Eggen (1955), Popper (1967, 1970)* Oliver (1974) and Weiler Cl978a). The emission is strong in the sense that it is usually significantly above the continuum. In no case is this H and K emission to be confused with the normal emission core reversal in late-type single stars which gives rise to the Wilson-Bappu effect. Struve (1946) studied the variation in the strength of the H and K lines as a function of phase angle in several stars. It was his conclusion that the maximum strength was at the quadrature points (0-.25 and

PAGE 35

24 TABLE 3 LIST OF RS CVM BINARIES Name V Orbital Spectral Type Masses (a,c) m Period(b) hot + cool(b) hot + cool UX Ari 6.5 6.438 G5V + KOIV 0.63 + 0.71 CQ Aur 9.0 10.621 GO • • • • SS Boo 10.3 7.606 dG5 + dGB 1.00 + 1.00 SS Cam 10.0 4.824 dF5 + gGl • • • • • RU Cnc 10.1 10.173 dF9 + dG9 • • • • • RS CVn 8.4 4.798 F4V-IV + KOIV 1.35 + 1.40 AD Cap 9.8 6.118(d) G5 0.5: + 1.1: UX Com 10.0 3.642 G5-9 0.95 + 1.12 RT CrB 10.2 5.117 GO 1.27 + 1.34 WW Dra 8.8 4.630 sgG2 + sgKO 1.4 + 1.4 Z Her 7.3 3.993 F4V-IV + KOIV 1.22 + 1.10 AW Her 9.7 8.801 G2IV + saK2 1.38 + 1.36 MM Her 9.5 7.960 G8IV 1.20 + 1.24 PW Her 9.9 2.881 GO 1.4 + 1.6 GK Hya 9.4 3.587 G4 1.2: + 1.3: RT Lac 9.0 5.074 sgG9 + sgKl 0.6 + 1.5 AR Lac 6.9 1.983 G2IV + KOIV 1.30 + 1.30 RV Lib 9.0 10.722 G5 + K5 2.2 + 0.4 VV Mon 9.4 6.051 GO • • • • LX Per 8.1 8.038 GOV + KOIV 1.23 + 1.32 SZ Psc 7.3 3.966 F8V + KIV-IV 1.33 + 1.65 TY Pyx 6.9 3.199 G5 + G5 1.20 + 1.22 RW UMa 10.2 7.328 dF9 + KlIV 1.50 + 1.45 RS UMi 10.1 6.2(e) F8(e) • • • • HR 1099 5.9 2.8(e) G5(e) 0.18 + 0.23 HR 5110 5.0 2.613 F2IV + KIV 0.02 + 0.005 HD 5303 • ( 1.840(f) G2V + FO(f) • • • • • HD 224085 7.6(g) 6.724(g) K2-3IV-V(g) • • o W92 11.7(h) 0.745(h) KOIVp(h) • • Notes for Table 3. a Unless otherwise noted values from Popper and Ulrich (1977). b Unless otherwise noted values from Hall (1976). c M sin3 i d Popper and Ulrich (1977) list as 3.0 days. e Popper and Ulrich (1977). f Hearnshaw and Oliver (1977). g Rucinski (1977). h Walker (1978). = •^^^Ittmi -*** f1

PAGE 36

25 oPyS). Oliver (1974) summarized the existing data by saying that the emission was usually at a minimum during the secondary eclipse, but not in all cases, nor at all times. Hiltner (1947) had found a disappearance of the H and K emission lines at secondary eclipse in RS CVn. This led him to believe that the emission originated from localized sources at the extremities of a tidal bulge along the line joining the two stars. Struve (1946) had earlier offered a similar explanation for the origin of the emission in similar cases. Catalano and Rodono (1968) were unable to confirm the disappearance of the Ca II emission lines at secondary minimum, thus raising some doubt as to the validity of Hiltner's tidal bulge hypothesis. More recent studies by Weiler (1975a, 1978a) find that the emission is associated with the larger star, but the emission is not localized. Furthermore, Weiler does not find the strengthening at the quadriture points or the tendency for the emission to weaken at secondary minimum. The existence of Ca II emission is indicative of chromospheric activity (Young and Koniges 1977; Weiler 1975a; Naftilan and Drake 1977; and Weiler 1978a). This emission must originate from the larger (cooler) component because the emission lines have velocities which agree well with the absorption lines for this component (Popper 1961; Oliver 1974). In addition, the width of the emission lines is of the proper amount to be explained by the synchronous rotation of the larger star (Popper 1970). The emission lines of Ca II are not the only emission lines which have been reported. Weiler (1978a)studied 6 RS CVn systems and found H to be in emission in all 6. Naftilan (1975) found H to be in emisa a sion (weakly) in RS CVn itself. The H emission in AR Lac has been

PAGE 37

26 associated with the cooler star by Naftilan and Drake (1977). The H emission in the six systems studied by Weiler (1975a, 1978a) was variable to a significant degree in four of them. Similar emission in the H line has been reported by Bopp (1978) for the systems HR 1099 and UX Ari However, it was noted that these were the only two stars from a survey of about 30 stars which showed persistent H emission. Three other stars showed sporadic H emission at the resolution used. Weiler (1978b) points out that at higher resolution it is possible that all RS CVn binaries may show some filling in of the H line by emission. The H and H and K emission in several RS CVn binaries has shown a correlation with the phase position of the distortion wave and the phase of greatest emission (Bopp 1975; Herbst 1973; and Weiler 1975b, 1978a). In addition Weiler finds the distortion wave more pronounced the greater the correlation. This is strongly suggestive of a physical relationship between the causes of the two phenomena. Weiler (1978a) suggests that the emission is due to an active photosphere which in turn drives an active chromosphere in the region of the photospheric activity. Young and Koniges (1977) attribute this to tidal coupling which increases the density scale height and thereby changes the acoustic-wave power spectrum. These investigators feel that the results support Hall's (1972) model for a spotted surface on the cooler component in RS CVn, and possibly other stars with similar characteristics. Oliver (1974) found a variation in the absorption line strengths but the correlation with light curve variations was weak. The abundance of metals in binary systems was studied by Miner (1966). In the systems he studied, an underabundance of metals was found in eclipsing binaries. The underabundance does not appear to be

PAGE 38

27 as great in the 3 RS CVn systems which were included in the project as for the other eclipsing systems. The sub-giant components of 12 Algol like binaries were observed by Hall (1967) and found to have an underabundance of heavy elements. Naftilan (1975) found the cooler stars in RS CVn and RW UMa to be underabundant in iron and chromium, which he noted is in contradiction to a pre-main-sequence state of evolution. The cooler component of AR Lac was also found to be deficient in metals by Naftilan and Drake (1977). Anderson and Popper (1975) concluded that from the observed radius and temperature of the stars in TY Pyx there is an indication of an abundance (or opacity) anomaly in both stars. This would seem to indicate that RS CVn binaries are not very young. Naftilan and Drake (1977) have concluded from their research that the anomalously low metal abundance is not due to free-free emission filling-in the metal lines in AR Lac, nor is it due to a circumstellar shell. Recent soft ,X-ray emission from UX Ari has led Walter, Charles, and Bowyer (1978) to conclude that the heavy element depletion in this system is real, because they do not observe an Fe emission line at 0.85 KeV as was seen in the X-ray spectrum of Capella. Lithium (Li) has not been detected in several RS CVn binaries; this supports the view that these stars are not ^ery young (Naftilan and Drake 1977; Young and Koniges 1977; and Conti 1967). On the other hand, Rucinski (1977) has found a weak Li line in HD 224085. This system was recently added by Hall (1978) to the list of RS CVn type binaries. As has been mentioned previously, a correlation between chromospheric Ca II emission and tidal coupling has been found by Gratton (1950), Young and Koniges (1977), and Glebocki and Stawikowski (1977). The investigators do not agree, however, as to the cause of the emission.

PAGE 39

Young and Koniges believe that this is evidence that when a star's outer atmosphere is affected by gravitational attraction of a close companion the result is a change in the density scale height. This shifts the acoustic-wave power spectrum to lower frequencies, which results in a large increase in the dissipation of energy into the chromosphere. Gratton believed that the tidal distortion would produce localized regions of emission in accordance with Hiltner's model. However, the latter interpretation was excluded by Struve (1948) when he was unable to find the expected degree of linear polarization from such a localized region. Weiler (1978a) was also unable to find the variation in the H and K emission lines as a function of phase that would be expected from the tidally distorted bulge. He concluded that the emission may well be somewhat localized, but not at the extremities of a tidal bulge formed along the line joining the two stars. Glebocki and Stawikowski believe that their study of H and K emission supports the tidal bulge hypothesis, while Weiler feels that his research clearly points to an active chromosphere. Time may resolve the dispute. Photometric anomalies The light curves of many (if not all) of the RS CVn binaries show various anomalies. The most common and striking light curve anomaly is a quasi -sinusoidal wave that distorts the normal eclipse phenomenon as can be seen in Figure 1. This wave-like distortion has been referred to as the "distortion wave" by Oliver (1974); this term will be used throughout this dissertation. There are, however, other phenomena which are abnormal in the light curves of these binaries. Several of the systems show season-to-season changes in the system brightness, while a few have exhibited increases in brightness over very short time scales. The

PAGE 40

29 \ J 4 -* 1 m $ L I.... 1, .. NO o LTl a> E 3 Jo o tj -M c: m cu o > E 3 0-4 Its O o 4*^ O o LjJ > 00 so o < a -L -C a, r— ON o 3 CO > o vO O u-i o 0) Ol C3 LTl in C3 in in est A1ISN31N

PAGE 41

30 short time scale variations have been referred to as flare-like activity by some observers. These irregular changes in the light of the system cannot be explained by changing parameters of the distortion wave, and are therefore discussed as separate (but perhaps related) phenomena. Besides the variations in the light of the system, the light curves of these binaries have two additional anomalies which warrant mention. First, the depth of the primary eclipse in several systems has shown variations, which are not associated with changes in system brightness. Second, the secondary eclipse for many systems has shown variations in its position and depth. The distortion wave in RS CVn was first noted by Sitterly (1930) as a difference in the heights of the maxima. This observation was noted by several researchers before the true picture was developed by the Italian astronomers at Catania. Following the advice of Popper (1961) the Catania astronomers (Chisari, Lacona, Catalano, and Rodono) started a long-term program of photoelectric observations of RS CVn. This work produced the remarkable discovery that the difference in the heights of the maxima was changing, and the changes could be explained by a migrating quasi-sinusoidal wave superimposed on the light curve. Chisari and Lacona (1965) and Catalano and Rodono (1967, 1968) showed very convincing evidence for the existence of this wave, and for the slow migration to decreasing phase angle from season-to-season. They referred to the slow shift of the distortion wave to decreasing phase as a "retrograde migration." Oliver (1974) has shown that this property is very common in the RS CVn binaries which he studied. It is commonly held that the existence of the distortion wave and the retrograde migration are properties that all RS CVn binaries share. The evidence is not complete for all the (-'r— •?-;-" — -1

PAGE 42

31 systems considered to be of the RS CVn binary type, but many systems have shown this phenomenon (Bopp, Espenak, Hall, Landis, Lovell and Reucroft 1977; Oliver 1974; Hall 1972, 1977; Popper 1974; Chambliss 1976; Milone 1968; Nelson and Duckworth 1968; Hall, Henry, Burke, and Mullins 1977; Hall, Montle, and Atkins 1975, Blanco and Catalano 1970; Landis, Lovell, Hall, Henry, and Renner 1978; Hearnshaw and Oliver 1977; and Rucinski 1977), Many of the above investigators reported migration rate changes, and variations in the amplitude of the distortion wave from season-toseason. Perhaps significantly, Eaton (1977) has found the distortion wave to be moving to increasing phase in the system SZ Psc. The retrograde migration in SS Boo has apparently reversed itself according to Hall (1978). The color dependence of the distortion wave amplitude is very interesting. For most of the systems (reported in the aforementioned publications) the amplitude is greater in the V band than in the B band. However, there are notable exceptions to this: WW Dra (Oliver 1974), RT Lac (Milone 1968), UV Psc (Sadik 1978), and SZ Psc (Eaton 1977). In addition to variations in the amplitude of the distortion wave within a system, the size of the amplitude varies a great deal from system to system. The largest amplitude appears to be about o'l'z for RS CVn (in the V band), and the smallest appears to be about o'PoZ for several other systems. Recently, information as to the actual shape of the distortion wave has become available. Rucinski (1977) noted an interesting change in the shape of the light variations for HD 224085, and the present writer (Ludington 1978) has noted changes in the detailed shape of the distortion wave in RS CVn. Hall, Montle, and Atkins (1975) noticed a change in the shape and/or amplitude of UX Ari from their UBV and JHKL photometry in 1972. The significance of these variations is not clear, but they would seem to point to dynamic structures on the stellar surfaces.

PAGE 43

32 Popper (1967) and Oliver (1974) have noted that the RS CVn systems show small irregular variations in the system brightness. Wood (1946) was perhaps the first to observe these irregular variations in the system AR Lac. More recently, Bopp et al (1977) have found evidence for irregular variations of 01^02 in the output of HR 1099. Larger variations have been discovered in the brightness of UX Ari by Hall (1977) and Landis et al (1978). The latter group also detected a flare-like event of JD 2443054.75 which lasted for approximately one hour, and increased the system brightness by oI'lS. The irregular variations discussed in the last paragraph refer to the total system brightness. Light variations have been reported during the primary eclipse by Wood (1946) and Keller and Limber (1951) for AR Lac and RS CVn, respectively. Similar changes during primary eclipse have been noted by Popper (1961) for RS CVn; Milone (1977) for RT Lac; Nelson and Duckworth (1968) for RS CVn; and Oliver (1974) for SS Boo, WY Cnc, RS CVn, Z Her, AR Lac, RT Lac, and SZ Psc. It should be noted that several of these systems have total (occultation) primary eclipses. Therefore, if the variation is seen during this total phase, it is expected that the variation is due to intrinsic variability of the larger (cooler) star only. In the case of AR Lac, this is not the case. The total portion of primary eclipse was seen to have small or no variation (Kron 1947). Kron found that the variation occurred during the ingress and egress branches of the eclipse. Since the primary eclipse in RS CVn is total, then the secondary eclipse will be annular. Thus, since the larger star is still visible, it is not surprising that this eclipse also shows anomalous behavior. ^Tl'***-'*l! *— •r.r — --rnr ...

PAGE 44

33 Keller and Limber (.1951) found that from the depth of the eclipse the ratio of intensities was much less than would be expected for stars of the spectral types which make up RS CVn. Popper (.1961) found the same inconsistency with the system, but also found the discrepancy to be less severe. In addition, Keller and Limber reported a small eccentricity from the displacement of secondary eclipse. Neither the spectroscopic orbit of Joy 0930), nor the orbit of Popper 0961) showed anything but a circular orbit. The distortion wave discovered by the Catania observers supplies the explanation for both the changing depth of primary minimum and for the displacement of the secondary eclipse from the 0^5 position. The variation in brightness at the total phase of primary eclipse and the displacement of secondary eclipse are correlated with the migration of the distortion wave. Hall's 0972) model took the distortion wave explanation one step farther. If the spotted region that Hall predicts does indeed exist, then the anomalous depth of secondary eclipse is explained by the variation of the surface brightness of the larger star. Hall's spot model also explains the displacement of secondary eclipse in more concrete terms. Optical and radio polarization The polarization of the electromagnetic radiation from RS CVn binaries was first searched for by Struve (1948). In this study he attempted to locate the linear polarization which would result from the tidal bulge proposed by Hiltner (1947). as the origin of the Ca II emission. The H and K lines of AR Lac showed no evidence of linear polarization. Struve placed an upper limit of 10% on the polarization from this star. In a survey of unevolved and evolved main-sequence binary systems Pfeiffer and Koch (1977a) found that the unevolved

PAGE 45

34 systems showed no significant linear polarization. The evolved binaries showed intrinsic linear polarization if the log S was greater than or approximately equal to 1.0. Here the 'S' represents the separation of the stellar photospheres in units of solar radii. They further stated that the incidence of polarization in this group does not depend on massratio, total system mass, fractional component size, rotational velocity, the stage of evolution (Case A or Case B), or the detached or semidetached state of the system. It was their belief that this was evidence for the necessity of sufficient "free" volume to allow more material and/ or greater asymmetry to produce the linear polarization. Three RS CVn binaries have been reported to have some degree of polarization. RS CVn was reported to display variable linear polarization by Pfeiffer and Koch (1973). The variation was cyclic with orbital period and showed random short-term variation. This was suggestive to them of electron and/or Rayleigh scattering in an active circumstellar envelope. Only an upper limit could be set by Pfeiffer and Koch (1977b) for the linear polarization in the visual band for HR 1099 (less than 0.02%). At radio wavelengths no significant linear polarization has been detected for HR 1099 or UX Ari but a significant degree of circular polarization has been detected (Owen et al 1975; and Spangler 1977). The degree of circular polarization was found by them to be a function of wavelength, and was only detected during outburst activity. This was suggestive of microwave bursts like those observed from the sun. Pfeiffer (1978) recently reported on some very detailed polarization studies of RS CVn. He concludes that the polarization is due to scattering in a large cloud which engulfs the system. He also comments that RS CVn itself is the only RS CVn binary in which he has been able

PAGE 46

35 to detect linearly polarized light, as of the time of his presentation. Ultraviolet and infrared excess Oliver (1974) has done the most comprehensive study of ultraviolet (UV) excess in the RS CVn binaries. It was his conclusion that an ultraviolet excess was a common occurrence in the U-B color index of the cooler component. Since few of the stars have UBV data available, it is conceivable that virtually all the systems have a cooler component with a UV excess. Recently, Rhombs and Fix (1977) presented data which confirmed very clearly the UV excess in RS CVn, AR Lac, and UX Ari They also were able to show that the cooler component was responsible in each case. Hall (1972) suggested that the excess could possibly be analogous to the excess in T Tauri stars. Rhombs and Fix, on the other hand, concluded that free-free emission from a hot circumstellar gas was the best explanation. Infrared (IR) excess, like the ultraviolet excess, appears to be a common characteristic of nearly all RS CVn binaries. The problem of the infrared excess has been discussed by several authors (Atkins and Hall 1972; Hall, Montle, and Atkins 1975; Hall 1976; and Milone 1975a, 1976b). There is general agreement that at least the majority of RS CVn binaries display some degree of infrared excess, but the source of the excess is controversial. Milone Cl976b) found an IR excess in 10 of 14 systems showing light curve asymmetries, which were chosen at random for study. Of this group, 5 systems are classed by Hall (1976) as RS CVn binaries. Three of these were definitely found by Milone to have an infrared excess. He cautioned, however, that the other two stars (SS Boo and WW Dra) may well show the excess because the spectral type and light ratios were taken from the literature and could cause a mis-evaluation of

PAGE 47

36 the excess. Atkins and Hall (1972) found an infrared excess in 5 or 6 systems for which they had sufficient data to make an adequate evaluation. Milone Cl976a,b) considers the IR excess to be due to a circumstellar gas around the more massive component of the system. Atkins and Hall (1972) did not consider a circumstellar cloud a possible explanation for the JHKL photometry they had obtained. This question remains unsettled, but in light of the polarization data of Pfeiffer (1978) it would seem that a circumstellar cloud may be the correct explanation at least in the single case of RS CVn itself. Period variations The period variations in many of the systems listed by Hall (1976) are very pronounced. He noted that a linear ephemeris in some cases can lead to errors of about a quarter of an orbital cycle in only 10 years or so. Hall suspects that virtually all of the systems have these large period variations, because about a third are known to, and the rest have insufficient data. Since the RS CVn binaries are detached systems, the period changes are not due to the same mechanism as in the semi-detached Algol -type binaries. In the previous section on the history of RS CVn it became apparent that the period changes are also not due to apsidal motion or light-time effects of orbital motion. Therefore, it is very clear that the mechanism responsible is rather unusual. Flare-type mass ejection from one hemisphere has been proposed as an explanation for the short-term period changes (Hall 1972; Arnold and Hall 19.73; Hall ig75b; and Hall 1976). In this model the brighter hemisphere is ejecting matter by a high-velocity impulse-type mechanism. This results in a correlation between the observable short-term period

PAGE 48

37 changes and the observable phase of the distortion wave minimum. The mass loss rate required to account for the period variations is rather large: 10" M^/year. In the latest version of this model, Hall (1976) suggests that the effective moment arm is some Alfven radius so that the required mass loss rate is reduced. Several aspects of this model have been criticized. Catalano and Rodono (1974) objected to ejection of material from the brighter hemisphere on the grounds that one would expect flare-type mass ejection from the active spotted hemisphere. They also pointed out that the measurement of the time of minimum was affected by the deformation of primary eclipse by the distortion wave. This effect would have the same sense as the correlation of distortion wave minimum with period change. Hall (1975b) was able to show that, while it was true that the effect had the same sense, the magnitude of the 0-C variations by deformation of primary eclipse were 25 times too small. In the case of AR Lac it has been possible to use a modification, for this specific system, of the model to explain the long-term period changes (Hall, Richardson and Chambliss 1976). The long-term period variations in the other systems have not been adequately explained. Further research, both observational and theoretical, is greatly to be desired in this area. The possibility of an enhanced stellar wind in RS CVn binaries has been proposed by Oliver (1974), Ulrich and Popper (1974) and Popper and Ulrich (1977). This is a conceivable source of period changes and deserves further investigation as pointed out by Hall (1976). *r3Ce;Tt^-->>,,

PAGE 49

38 Emission at radio wavelengths The detection of an RS CVn binary at radio wavelengths by Gibson and Hjellming (.1974) was believed by them at first to indicate mechanisms similar to those for known Algol -like flares. The spectral index of the flare was definitely non-thermal as was the case for the Algol-like flares. Later work by Gibson, Hjellming, and Owen (1975) showed that the flares were non-thermal in UX Ari but that an evolving synchrotron source was a more likely mechanism than the infall of matter. Gibson et al (.1975) compared the flare from UX Ari with those of UV Ceti stars, and found that there was little similarity. The spectral index for a UX Ari flare was about +0.2, while typical values for UV Ceti stars range from -3 to -5. Even at the end of the flare observed on 11, 12 August 1974 the spectral index of UX Ari only reached -0.6. Therefore, the type of flare is different from those in UV Ceti stars. This was supported by the decay time-scales in the 2 types of flares. Gibson et al 0975) found that a UX Ari flare decayed on a time-scale of days. This was about 100 to 200 times the decay rate of a flare in a typical UV Ceti star. Circularly polarized emission has been detected at radio wavelengths by Spangler 0977), and Owen, Jones, and Gibson (_1976) from 2 RS CVn binaries CUX Ari and HR 1099). The level of oolarization was about 5% (for UX Ari) to 20% (for HR 1099) at 1400 MHz, about 8% (for HR 1099) at 8085 MHz, and less than 2% (for HR 1099) at 2595 MHz. The detection of circular polarization in these stars contrasts sharply with the lack of circularly polarized emission from Algol. No linear polarization has been detected at radio wavelengths from any RS CVn binary at the time of this writing. Owen et al (1975), : •^:>~~irv.._ ,..^.^v

PAGE 50

39 however have put an upper limit of 2-3% at 2695-8085 MHz for the linearly polarized emission from HP. 1099, No correlation has been found between optical and radio variability as reported by Chambliss (1975) and Spangler (1977). This is not a surprising result if the flare-like activity is similar to the typical solar microwave flare. In these solar flares the energy output in the radio region is much greater than in the optical region. Radio binaries tend to be of late spectral type (G and K) and they tend to be above the main-sequence according to Owen and Spangler (1977). This may be part of the explanation for the high frequency of radio emitters among RS CVn binaries. On the other hand, and perhaps more likely, the statistics may be biased by the selection of RS CVn binaries as candidates for radio emission surveys. More data are required to establish this point more clearly either way, Owen and Spangler (1977) were unable to detect any change in the observed flux from AR Lac at 4585 MHz during any eclipse. This is a good indication, as they pointed out, that the source is not a compact region between the two stars. They computed that the radius and brightness temperature of a source located in this region would be limited by r > 3 X 10 ^ cm, and T^ > 4 X 10^ K. Gyrosynchrotron radiation has been suggested as the source of the radiation (Gibson et al. 1975; Owen et al 1976; Spangler 1977; and Owen and Spangler 1977). These authors have found that this mechanism explains the radio flare observations better than other alternatives they have considered. It accounts for the observed non-thermal spectral index, the circularly polarized emission during flare events, and the absence of linear polarization (if reasonable assumptions are made about the physical properties of the emitting region).

PAGE 51

40 A magnetic field of about 30 Gauss and an electron density of 10 -3 about 2.4 X 10 cm would be indicated by Spangler's (1977) calculations. Spangler et al (1977) felt that this model compliments Mullan's (1974, 1976) theory, and therefore would also seem to support the starspot hypothesis of Hall (1972, 1976). Soft X-ray emission A most exciting discovery has been the recent detection of soft X-ray emission (0.2 to 2.8 KeV) from many RS CVn binaries. As of June 1978, Liller (1978) reported that 11 of the RS CVn binaries had been identified as X-ray sources. This compares with two or three identifications reported by Charles (1978) in April 1978. This discovery, along with the previously known radio emission, gave additional credence to the solar analogy of highly active regions in the atmosphere of the sub-giant component as proposed by Hall (1972, 1976). Cash, Bowyer, Charles, Lampton, Garraire, and Riegler (1978) were able to fit a solar abundance plasma at about lO'' K to the soft X-ray spectrum of Capella. This star was included as a related system to the RS CVn binaries in Hall's (1976) discussion. It is not a "classical" RS CVn binary, so the importance of the above paper is clear only when subsequent soft X-ray data are reviewed. The soft X-ray spectrum of the "classical" RS CVn binary UX Ari was fit with a plasma of 10^ K, but it could not be fit with a plasma of solar abundance (Walter, Charles, and Bowyer 1978a). This gives additional evidence for an underabundance of heavy metals in RS CVn systems. This result was confirmed in two other "classical" systems, RS CVn itself and MR 1099, by Walter, Charles, and Bowyer (1978b). The spectra of these two stars could not be fit as nicely

PAGE 52

41 as was the case for UX Ari but the authors found that the results were consistent with a 10 K thermal spectra in both cases. Walter et al (1978a) felt that the soft X-ray spectra of RS CVn binaries was consistent with an active spotted region. In this model they saw the active region as associated with flare-like activity, which in turn would continuously supply sufficient energy to power a 10 K corona. At this temperature they computed the velocity of the ions to be sufficient to rapidly deplete the matter. However, they noted that a magnetic field of only 50 Gauss would be enough to bottle up the hot plasma. In addition to the above, Walter et al (1978a) noted three interesting facts about the new information obtained from the X-ray detectors. First, they noted that if UX Ari is anything like a typical RS CVn binary, -5 -3 then from the space density of 'vlO pc the RS CVn binaries contribute a full 10% of the soft X-ray background at low galactic latitudes. Second, they computed the mass loss rate from their emission measure. The value they obtained (10~ M /year) is in reasonable agreement with that proposed by Ulrich and Popper (1974). Third, they reported that White, Sanford, and Weiler (1978) have detected a flare in the X-ray spectrum of HR 1099 which was coincident with a radio flare. The evolutionary status The evolutionary status of the RS CVn binaries has been an especially difficult problem. The mass of the components is generally of the order 0.5 to 1.5 M This is for both stars and therefore, with few exceptions, the mass ratio is very close to unity. The picture that has developed over the last 10 or 15 years regarding binary star evolution has, in general, shown that mass ratios near unity should be the ,T,i*^'iimm^.]i-

PAGE 53

42 exception. RS CVn binaries are much too numerous to be an exceptional case. Thus a problem appears; either the binary evolutionary scheme is wrong or the RS CVn systems do not exist. Obviously, this is much too "black-and-white" a statement. More to the point, it would be expected that the theory needs some adjustment in order for the large number of systems with unity mass ratio to be explained. It is important to realize that the binary evolutionary theory referred to above explains the evolution after the existence of the binary pair on the main sequence. The evolution prior to this point is not well understood, and could very easily be the key to the unity mass-ratio puzzle. The similarity of the characteristics of the cooler component of RS CVn to those of T Tauri stars led Hall (1972) to conclude that RS CVn was in pre-main-sequence evolution. This was in contradiction to the earlier investigation by Field (1969), who found that RS CVn as well as AR Lac were not in pre-main-sequence contraction. The age of the RS CVn binaries as determined by Monti e (1973) supported the pre-main-sequence evolutionary picture. Eventually, a clearer case arose for the post-main-sequence evolutionary status for the RS CVn binaries. This process started with Oliver's (1974) evaluation of the evolutionary status and his suggestion of a slow mass transfer by means of a strong stellar wind. Ulrich and Popper (1974) proposed that by allowing for such a stellar wind it would be possible for the evolutionary status of these stars to be explained on the basis of normal single star models. The pre-main-sequence status for binaries of the RS CVn type was almost conclusively eliminated as a possibility by Hall (1975b), and Biermann and Hall (1976). Hall (1975b) found that the visual companion of

PAGE 54

43 the eclipsing RS CVn binary WW Dra was a normal F8 V star. The most important thing about is was the estimate of its mass. It was less massive than either star in the WW Dra system. This clearly would indicate that the stars in WW Dra could not be in pre-main-sequence contraction. Hall also showed that there was sufficient evidence of binary motion for the possibility of an optical pair to be insignificant. Biermannand Hall (1976) gave very convincing arguments to exclude the pre-main-sequence evolutionary status. They concluded by a process of elimination that the RS CVn binaries were the result of the fission of a single star as it leaves the main-sequence. At the time of this writing, the consensus is that the evolutionary picture as presented by Popper and Ulrich (.1977) is the closest to reality. They presented the following circumstantial evidence of post-main-sequence evolution of RS CVn binaries: 1. They are not associated with regions of known star formation 2. For the mass and radius range the post-main-sequence life-time is 100 times longer than the pre-main-sequence life-time 3. The larger radius is associated with the more massive component 4. WW Dra and HR 1099 have dwarf companions of lower luminosity In addition, they recalculated the age of the RS CVn binaries using Montle's (.1973) value for the velocity dispersion and Wielen's (1974) calibration. The results indicated that the RS CVn binaries are about Q 3x10 years old Ci-e. about the same age as similar main-sequence stars). In fact, they felt that the age is very slightly greater than a mainsequence star, and that the RS CVn binary phenomenon develops when stars of this general nature reach the Hertzsprung gap. In some cases they proposed that it would be necessary to modify simple single star evolu-

PAGE 55

44 tionary processes by a slow stellar wind ('^.5 x 10""' ""Mo/year) in order to account for the system's current position on the H-R diagram. Scope of Dissertation The intent of this dissertation can be summarized by two goals: 1. To obtain two new light curves of RS CVn in (at the minimum) two colors, separated in time by approximately one year; however, the data for each must be obtained within a three month term in order to minimize the effect of a migrating distortion wave; 2. To determine the elements of the eclipsing system for RS CVn by a new technique which eliminates the problems introduced by the photometric distortion wave. In meeting these two goals, several others will, by necessity, result: 3. The constancy of the comparison star BD+35 2420 will be confirmed. 4. The distortion wave will be isolated so that it may be studied in a future research effort. 5. The radial pulsation model for the photometric distortion wave will be refuted.

PAGE 56

CHAPTER II INSTRUMENTATION The Basic Equipment The instrumentation used in collecting the data presented in this dissertation may appear to some in the avant-garde of instrumental development as antiquated. This sentiment is partially due to the enormous technological development during the past decade. In addition, this attitude reflects a prevailing view that innovation is superior. Snobbery and high technological advance aside, the important point is that the data presented here of RS CVn are of the highest quality. The 45 cm telescope used in this investigation is located at Rosemary Hill Observatory, 6.5 km from Bronson, Florida. The optics, telescope tube, equatorial fork mount, and pier were built by R. E. Brandt. The electrical drive, slow motion controls, secondary mirror mount, finder scope, counter weight, and setting circles were installed by the staff at the University of Florida (primarily, John P. Oliver, E. Whit Ludington, and Eli Graves). The optical system is an f/10.5 Ritchey-ChrStien design. The mirrors of the system are aluminized and Beral overcoated. The photometer has been described by Chen and Rekenthaler (1966). Four diaphragms are available; they are small circular openings of 0.500, 0.2500, 0.079 and 0.039-inch diameters on a rotatable disk. The smallest opening was used in all of the photometry presented here; this corresponds to a diameter of 42.5 arc seconds on the sky. 45

PAGE 57

46 There are three filters which the user may select. The light passes through only one filter at a time, and the observer must manually move the slide on which the filters are mounted to the desired filter before a reading is taken. The ultraviolet filter (u) is made from Corning 9863, the blue filter (b) is made from Corning 5030 and Schott GG13 in combination, and the yellow (or visual) filter (v) is made from Corning 3389. These filters, in union with the same instrumentation used in this photometry of RS CVn, have been found by Markworth (1977) to match closely the standard UBV system. The photomultiplier tube used in this work was an EMI 9781, operated at 900 volts. A DC electrometer amplifier designed by Oliver (1976) was used to amplify the current from the photomultiplier tube. This amplifier, called PA-IO, has many different gains which may be selected by rotary 5 switches. This allows an amplification from to 10 The amplifier was used with a time constant of h second. All of the data were recorded on a Heath chart recorder with a fiber-tip pen operated by a servo-type motor. The observer may select from a wide range of speeds on this chart recorder. In all the recordings of RS CVn, speeds of either 1 inch/min or 0.5 inch/min were used. The data from 5, 6 March 1976 onward were also recorded manually from a digital integrator. This instrument, referred to as DA10, was designed and built by John P. Oliver. It integrates the signal by counting the pulses from a voltage-to-frequency converter in the PA-10 amplifier. The observer has the option of many integration times from 1 second to 100 seconds. The integrations are started manually, but are stopped and displayed by the internal electronics.

PAGE 58

47 46 cm Ritcheyfelescope Chretien 42.5 arc second diaphragm EMI 9731 and ubv filters HIGH VOLTAGE SUPPLY 900 V PA-10 DC AMPLIFIER CHART RECORDER Fig. 2. -Schematic diagram of the instrumentation used to obtain the photometric data of RS CVn at Rosemary Hill Observatory during the years 1975 and 1976. W^*T1rW,j^*

PAGE 59

48 A schematic diagram of the instrumentation appears in Fig. 2. From MJD 42469 to MJD 42492, inclusive, the attachment of the photometer to the telescope required the use of a glass-prism diagonal. The glass in the prism is opaque to the ultraviolet region of the spectrum; for this reason only the v and b filters were used. Since no u data were obtained during this time, it was impossible to compute the u-b color. This explains the absence of values for these dates in the tabulation in the appendix. Amplifier Calibration It is desirable that the amplifier be linear and stable for high quality photometry. The linearity of the PA10 has been demonstrated by Oliver (1976). The stability can be demonstrated by the nightly calibrations obtained during the course of this research. Usually at the beginning and end of each night of observing, a calibration sequence was obtained. A calibration sequence consisted of a set of deflections with the input to the amplifier disconnected and the internal calibration source as the input current. The calibration consisted of four steps: 1. Establish the value of true zero. 2. Measure the relative gain of adjacent settings on the rotary switch that selects the smaller gain increments (called the fine-gain switch). 3. Measure the gain of each setting on the rotary switch that selects the larger gain increments (called the coarse-gain switch) relative to the "CAL" setting. 4. Check the zero value. The results of the above measurements were then used in the data reduction (see Chapter III)

PAGE 60

49 "08t7 -o c re Q9P O OPV •I— -a c OZV o c o 0017 4- (13 S_ •r— "re o 08 \0V -OS C\J rO C7) OD lO iD lO '^ -vt d d d d d CNOVIN) NIV9 Q .^ UJ 09 VCD O T3 c to J3 cn I u. I • o > > t -%f -. • ^ ^ + .. t '• + + o .> > + -• + + + 5 „ %f 9 • ^ 9 -0817 -0917 0l7t=' -OZP -0017 08 -09 T0t7 "OZ O lO o in o r-. (D (D iD lO c\i c\i c\i c\i c\j CNOV^N) N IV9 -o ra -Q +-> to c -''"N o 'r— o 4J lO ^ '" CM 113 CJ ^ 4-> jc: 1 en •^ Q c: n3 -) Z O N^_^ -o c OJ u 0) i: a h(T3 M SfO +-> (/I CD J= h>. -M •r— r— •r— J2 (0 +-> ;/) C pfO CD 0) c/1 i. ft3 O C_3 1

PAGE 61

50 In Figures 3 and 4, the relative gains for settings of the fine-gain and coarse-gain switches are presented, respectively. From inspection of these figures, it is clearly evident that the short-term stability and the long-term stability of the amplifier are very good. In Fig. 4 a difference in the level of the coarse-gain is evident from 1975 to 1975. This is of no significance in differential photometry such as that presented here on RS Canum Venaticorum.

PAGE 62

CHAPTER III PROCEDURE AND DATA REDUCTION Observational Procedure The accuracy that can be achieved with modern photoelectric photometers is limited by the earth's atmosphere more than by any other factor. The earth's atmosphere is not completely transparent; it does not even have the same transparency at all wavelengths of light. The problem of measuring the intensity of stars is further complicated by the random and unpredictable fluctuations in the transparency of the atmosphere as a function of time, and the somewhat predictable change as a function of airmass. There are means of reducing the effects of a real atmosphere on the measurement of a star's light. The most important is to measure the light differentially. By this it is meant that a star of constant brightness, called the comparison star, is chosen as a reference. The brightness of the program star, called the variable star, is measured under the same atmospheric conditions as the brightness of the comparison star. If the atmospheric conditions are exactly the same when the brightnesses of the two stars are measured, and the comparison star is indeed of exactly constant brightness, then any variation in the ratio of the variable star brightness to the comparison star brightness is due solely to the variable star. Of course, it is not possible in practice to guarantee that the atmospheric conditions are exactly the same during the measurement of 51

PAGE 63

52 both stars. The best way to insure that these conditions are as nearly identical as possible is to choose a comparison star which is very near in the sky to the variable star, and then to measure their brightnesses in as short a time span as possible. The nearness in the sky of the comparison star to the variable star and the nearness in time of measurement of their respective brightnesses are the two most important factors in high accuracy differential photoelectric photometry. Other criteria which will help improve the accuracy of the differential measurement are the following: 1. The comparison star should be nearly the same color as the variable star. 2. The comparison star should be of nearly the same brightness as the variable star. 3. The amount of atmosphere through which the measurements are taken should be kept to a minimum. 4. The amount of scattered light from the background sky (which cannot be avoided) should be measured and minimized. For the observations presented here, these conditions have been quantitatively met by the following procedures: 1. The comparison star is only 71 arc minutes from the variable star in the sky. 2. The typical sequence used to obtain the intensity measurement and the time required are given schematically on the following page:

PAGE 64

53 1975 time required (sec) 1976 time required (sec) 45 c 3 X 30 30 sc 3 X 30 30 c 3 X 30 45 V 3 X 30 30 vs 3 X 30 30 V 3 X 30 45 C 3 X 30 30 SC 3 X 30 45 V 3 X 30 30 vs 3 X 30 total time: 750 (=12% min) 510 (=8% min) Where C represents the measurement of the comparison star's brightness in three colors (v,b,u), CS is the three-color measurement of the sky near the comparison star, V is the three-color measurement of the variable star, and VS is the three-color measurement of the sky near the variable star. The integration time for each color measurement was always 30 seconds, the time to set the telescope on the comparison star or the variable star was usually about 45 seconds, and the time to move the telescope to a region of the sky near a star (or back again) devoid of visible stars was typically 30 seconds. 3. The colors of the comparison and variable stars are: Variable (RS VCn) B-V = 0.56 and U-B = 0.05 (Oliver 1974) BD+350 2420 B-V = 0.47 and U-B = 0.03 (Oliver 1974) 4. In no case was a differential measurement made through more than two air masses. 5. Typically the sky brightness was measured at least every half hour, or after the measurement of each star, if the sky brightness was changing rapidly. To minimize the sky contribution to the signal, the smallest diaphram available on the photometer was alv/ays used (42.5 arc seconds in diameter) 6. To determine if the comparison star was indeed of constant light, a check star was observed occasionally. The above discussion assumes that the instrumentation is linear and stable to within the requirements of differential accuracy. If this is the case and the above criteria are met, then all that remains is the calculation of the ratio of the variable star brightness to the fianWi^^Viin^K'f-T 'i

PAGE 65

54 comparison star brightness. In making these calculations it will be possible to correct, in part, for the atmospheric extinction which has been minimized, but not eliminated by the proper choice of a comparison star. It was pointed out in Chapter II that the majority of the data exists in two forms: chart records and tabulations manually recorded from the DA10 digital integrator. The chart records made prior to 5, 6 March 1976 were read and recorded in a tabulation form exactly like that used on and after 5, 6 March 1976. The keypunch shop of the Northeast Regional Data Center was engaged to punch these data on standard computer cards, in a format called the "Ludington-Oliver" format (see Table 4). A computer program called PHRED (PHotoelectric REDu ctions) was written to accept this format for the raw data and to do the reduction to the instrumental system (except for the inclusion of the effects of atmospheric extinction). The application of the effects of a real atmosphere to the partially reduced output of PHRED is handled by a computer program called DEXTOR. PHRED Introduction PHRED is a computer program that is written in the PLl programming language. It is a yery versatile program for reducing photoelectric observations to the instrumental system. It has far vaster capabilities and fewer limitations than any other available reduction program. It is limited by the size of the computer used rather than by the observations. It can, for example, handle the observations of over 600 different objects in 200 different filters taken during one night of observing. PHRED can be instructed to produce a plot for any object-

PAGE 66

55 filter combination the user may desire. This can be very helpful in evaluating the quality of the observations. In addition, the user can instruct PHRED to calculate the principal extinction coefficients, the outside-the-atmosphere magnitude and the standard errors of each. Furthermore, the program is not restricted to variable star data. It can also do the reduction of standard stars to the instrumental system. PHRED does all normal reduction, except atmospheric extinction and the reduction to the standard system. For example, it corrects for a zero offset in the data-gathering system. It converts to heliocentric Modified Julian Date. It applies gains, unless the user is using a pulse counting system, in which case the gains will be ignored. All in all, the user has a great deal of control over the operation of the program, and yery few assumptions have been made about the way the data must be taken, or the organization they must be in for reduction by this program. Of equal importance to the user of PHRED is the detailed log of the reduction and the warning messages to help the user gain the desired results. Program Control The user instructs the program to do certain things by use of Control Cards. These are records that start with an asterisk {*). The asterisk is followed by one letter of the alphabet. This letter determines the option that is to be used or the type of parameter cards that will follow it. Any characters after the first letter will not be recognized by the program. The first step in using PHRED is to have the data prepared on cards in the Ludington-Oliver format. The outline of this format is given in Table 4. Any item on which a deflection can be taken is defined by the user with an object code. This includes sky deflections.

PAGE 67

56 TABLE 4 LUDINGTON OLIVER FORMAT ITEM COLUMN FORMAT EXAMPLE-COMMENTS Object Code 01-02 A(2) CJ!S,SC,S1,S2, etc. Object Name 03-12 A(10) BD-15 1734, RS CVN, etc. Modified JD(a) 13-17 F(5) 42451, WW^, any 5 digits Filter Code 1 18 A(l) V, Y, R, etc. (c) UT 1 19-24 F(6) 043012, hhmmss Gain 1 25-27 A(l), A(2) D04, 'D' is coarse gain, '04' is fine gain Defl 1 28-32 F(5) 00120, i!5!!5120, 98765, etc. Filter Code 2 33 A(l) B, I, K, etc. UT 2 34-39 F(6) 105959 Gain 2 40-42 A(l), A(2) E04 Defl 2 43-47 F(5) 00001 Filter Code 3 48 A(l) U, S, B, etc. UT 3 49-54 F(.6) 001059 Gain 3 55-57 A(l), A(2) A02 Defl 3 58-52 F(5) 00000 Observer 63-65 A(3) EWL, JPO, REN, FBW, etc. Telescope 66-68 A(3) 046, 300, dia. in centimeters Photometer (b) 69-71 A(l), A(1),A(1) Codes for: amplifier, filter set, photomultiplier tube Observatory 72-74 A(3) RHO, FAS, MCD, etc. Notes for Table 4: (a) The Modified Julian Date of each deflection is calculated by the following equation: MJD(obs) = MJD(col 13-17) + DEC(UT)/24. (b) The photometer code is divided into three subcodes. The first is for the amplifier, the second is for the filter set used, and the third is for the photomultiplier tube used. (c) Each record has room for only three deflections. If there are more than three deflections for each object code, these are then put on the following cards with the proper filter code for each. All other columns should be copied from the first card.

PAGE 68

57 dark current, zero offset, variable star, standard star, etc. There are two characters on the card for the object code. There are no restrictions on which of the 256 characters of the EBCDIC character set may be used. The filter code is used in a like manner. There is room on a card for three filters to be coded. If more are required, the data are continued on the next card by copying the object code. The gain is an instrumental setting that causes the input from the photomultipier tube to be amplified by a specific amount. This must be accounted for in order to arrive at the true value before amplification. The code that is used on the Ludington-Oliver format is comprised of two parts. The first part is for a setting of a coarse-gain switch, while the second is for a setting of a fine-gain switch. PHRED does not make any distinction between the two. It reads the three characters as a single code; therefore, the user must supply (in the control card section) the value for this combination of coarse and fine-gain control settings. The deflection that is recorded will of course include the amplification indicated by the gain code. The deflection is restricted to five digits. This should be sufficient for the most majority of the photoelectric photometry. The deflection fields must not include embedded blanks. A deflection is possible even when the signal current from the photoelectric device is exactly zero. This is called the zero offset and must be removed from other deflections if the proper results are to be achieved. Therefore, PHRED will recognize an object code 'Z^' as the zero reading. It will ignore the gain setting used and take the average of all such readings for that night and substract that value from all deflections before the gains are applied. The user must be aware of the proper use of the time for each observation. The Modified

PAGE 69

58 Julian Date (which was defined by the lAU in 1973) is recorded on each card; this is actually the interger part of the Modified Julian Date. The Universal Time (UT) is also recorded for each deflection. Six columns are used for each UT. The first two digits are for the hours, the second two digits are for the minutes, and the last two digits are for the seconds. PHRED has been designed to perform several tasks for the user. PHRED can process one night or multiple nights of observations in a single submission. The first night of observations begins with a set of control cards; these might include the *LIBRARY, *FILTERS, *CODES, *SORT, *VARIABLE, *PLOTS, *BEGIN, and *TITLE control cards. The last two, however, have a special importance. The *BEGIN must be the first card in the control section and the *TITLE must be the last control card before the data. The other control cards may be in any order. There are three additional control cards which are of special importance. These are the *DATA, *ADD, and *END control cards. *DATA must follow the title cards and proceed the data. *END must follow the data. *ADD is used if the user wishes to add additional data, but does not wish them to be considered as the original data. For example, the observer may have neglected to take a comparison star deflection at the very beginning of the night. While this will not prevent the normal operation of PHRED, it will require extrapolation. To avoid this, the user can add an artificial deflection with the *ADD control card. After the original set of data has been ended with an *END card, the user inserts the *ADD card followed by as many cards of additional data (in the Ludington-Oliver format) as he desires. The additional data are also ended with an *END card. The next night of observations will then

PAGE 70

59 follow, beginning with the *BEGIN CARD. It is not necessary to repeat all control cards for the second night if they were already used in the first night's control card section. That is, the second night will be processed with the same instructions as for the first night, unless the user changes them. For example, it is unlikely that the gains will have exactly the same values from night to night. Therefore, the *GAIN control card will probably be necessary in the second night's control section. On the other hand, the stars that were observed and the filters that were used will probably be the same; therefore, the user does not need the *LIBRARY, *CODES and *FILTER control cards in the control card section for the second night. Four of the control cards work in a "flip/flop" fashion, i.e., they are "off" until they appear for the first time, then they are "on" until they appear again, and then they are "off", etc. These are *MAGNITUDES, *INTERPOLATE ALL SKY, *SORT, and *VARIABLE. In Figure 5 is a listing of the JCL cards for using PHRED. Notice that this assumes the existence of a load module for PHRED. //JOBLIB DD DSN=B0035001.S13.ATYLIB,DISP=SHR //STEPl EXEC PGM=PHRED //SYSPRINT DD SYS0UT=A,DCB=BLKSIZE=120 //RAWD DD SYS0UT=A,DCB=BLKSIZE=120 //GRAPH DD SYS0UT=A,DCB=BLKSIZE=120 //LOG DD SYS0UT=A,DCB=BLKSIZE=120 //NSKY DD SYS0UT=A,DCB=BLKSIZE=120 //DECK DD SYS0UT=A,DCB=BLKSIZE=100 //DISK DD UNIT=SYSDA,DSN=&&DISK,SPACE=(TRK,(3,3),,C0NTIG), // DCB=(RECFM=F,BLKSIZE=80,DS0RG=0A) ,DISP=(NEW, DELETE, DELETE) //CARDS DD *,DCB=(RECFM=F,BLKSIZE=80,LRECL=80) Fig. 5.JCL cards for PHRED Control Cards Listed here are the control cards and their meanings: *ADD -Adds additional Data Cards to those already read and writes them into the Raw Data file (RAWD). The additional data should be ended

PAGE 71

50 with *END. The Ludington-Oliver format is used for additional data. *BEGIN -The card should appear at the beginning of each new night of data. Each time this card is encountered, the previous night is known by PHRED to be complete and is then processed. *BOTTOM -This card should be the last card in the input deck. It will insure the processing of the last night of data. *CODES FOR OBJECTS -The following parameter cards define the object codes. A blank code terminates object code input. The codes are two characters long, left justified in a four-column field. For example, V SV C SC K SK is the default if no codes are defined. Any code used in the data but not defined will cause a warning message to be printed in the LOG file, and the data will be ignored. Any code that is defined, but for which there are no data will not, of itself, cause an error. Note that stellar codes should be odd (1st, 3rd, 5th, etc.), sky codes should be even (2nd, 4th, 6th, etc.). The order of the codes is important if the *VARIABLE option is used. *DATA -This card signals the beginning of the data card observations. The data should be ended with *END. The data will be written into the Raw Data file (RAWD). The *DATA card must follow the last title card (see *TITLE). *END -This card is used to end a group of data cards. Either the original data or any and all additions to it are ended with *END. *FILTER CODES -The following parameter cards define the filter codes. A blank code terminates the set. The codes are one character in length, left justified in two-column fields. For example, V B U is the default if no codes are defined. -t MiLitoM. I— J

PAGE 72

61 *GAINS -The following parameter cards define the gain codes and their values. A blank code and value terminates the set. The codes are three characters in length, while the value can be as much as 12 columns long. The code and its value are separated by one space (an equal sign or any other single character may be used). Therefore, together they comprise 16 columns. For example, 004=0.5049 £02=2.501234567 A06= -0.4989 is a valid gain code parameter card. The default for this control card is to apply a gain of zero magnitudes to all the data points. A message will be written into the LOG to indicate this. *HARDCOPY -This card is included if a punched deck (or other machine readable copy) is desired of the reduced data. The parameter card can be used to control the contents of this output file. The parameter card format is a six-character field in columns one through six. There are, at the present, only three possibilities for the user to choose from. ALL NONE V/C "ALL" will cause the total of the NSKY printed file to be put into the DECK output file. "NONE" will cause nothing to be put into the DECK output file, while "V/C" will cause only the variable minus comparison data to be put into the DECK output file. *INTERPOLATE ALL SKY — Usually an observer will take deflections on a star and on the nearby sky. This will allow him to subtract the sky from the star deflection and be left with just the deflection due to the star. If this card is inserted, the program will use any even •*ii^-*.r^^<-*i

PAGE 73

62 code interpolation of sky deflections. This means that if there are sky observations only with the comparison and none for the variable, the user must include this card. Without this card, the program subtracts the interpolated value of an even code from the value from the next smaller odd code. With this card, all even code values are combined and copied in place of the original even code values. *JD OVERRIDE -The following parameter card defines a fivedigit number that will override the integer Modified Julian Date on the data cards. It must not have a decimal point or sign. For example, 42451 is a valid parameter card. The default is to use the integer Modified Julian Date on the data cards. Note that the integer Modified Julian Date coded on each card is used to compute the time for each of the deflections on the card. Therefore, the use of this control card option will cause all the cards to have the same Julian Date, even if the original data cards for a single night contained more than one Julian Date. The default is reestablished at the beginning of a new night of data, -^ *K-EXTINCTION COEFF — If the user wishes to have extinction coefficients calculated, he may specify on the following parameter card(s) which star (or sky) and filter(s) he wishes used. There are no limits to this combination of object code and filter code. The format for the parameter card is a four-column field with the object code in the first two columns and the filter code in the third column (the last column is blank). For example, V]6V SVV C]6V SCV will produce extinction coefficients for the variable star, for the sky readings next to the variable, for the comparison, and for the

PAGE 74

53 comparison sky, all for the visual filter (assuming the object and filter codes defined in the examples for *CODES FOR OBJECTS and FILTERS). The default is to not calculate any coefficients. *LIBRARY STARS -The following parameter cards contain the "vital statistics" on the stars being reduced. The format for these cards appears below: ITEM VALUE EXAMPLE COLUMNS FORMAT Object code comp star Zh 01-02 A(2) name BD-151734 BD-15 1734 03-12 A(10) RA ^h^^m^^^ 7.2533333333 14-28 F(15,10) Dec -1532'28" -15.541111111 29-43 F(15,10) Note that when punched on the cards, the right ascensions and declinations must be converted to hours and decimal hours and degrees and decimal degrees. The last card must be a blank card to terminate the set. If no library parameter cards are used, then the *K-EXTINCTI0N COEFF control card option should not be used. *MAGNITUDE — If this card is used, the output will be in magnitudes instead of intensity units. The default is output in intensity units. *N FULL SCALE -The following parameter card will give the fullscale value expected for the data. This value will then be used to normalize all the deflections. This means that before anything else, the values punched on the data cards will be divided by this number. The number is read in from the first six columns of the parameter card using an F(6) format. For example, 100000 10000 1000 'k-IHKil^ESwJcV^-a

PAGE 75

64 are all valid full-scale values. The default value is 10000. *OBSERVATORY -The following parameter card is used to read in the longitude, latitude, and (optionally) the station code for the observatory at which the data were taken. For example, +82.5866666666 +29.377777777 RHO is the default and/or the parameter card for Rosemary Hill Observatory, It is read by (F(15,10) ,F(15,10) ,X(5) ,A(3)) PLl format. Longitude is a number between -180.0 and +180.0. *PLOTS -The following parameter cards are used exactly like the one for *K-EXTINCTION COEFF. They specify which object-filter combinations the user wants plotted. The codes and formats are the same as for the *K-EXTINCTION COEFF parameter cards. The plots are in magnitudes as a function of local time. No plot is the default. *SORT -This card, when used, will cause the sorting of every object-filter combination into time order. Sorted data are necessary for proper functioning of PHRED. *TITLE -This card signals the beginning of the title cards. The first of these cards will be used as a heading on all pages pertaining to this night of data. The rest (and there is no limit) will be printed on the heading of the RAWD print file. There must be a *TITLE card and at least one card following it. the *DATA card must then follow the last title card. *VARIABLE -If the data are arranged for it, the user can have the data treated as "variable star data." In this case the comparison star will be "removed" from the variable (to get relative brightness). This is done by dividing the variable star's reduced intensity by the interpolated comparison star's reduced intensity. If *MAGNITUDE has been used, the process will be the difference of the

PAGE 76

65 reduced magnitudes. The object codes must be listed after the *CODES FOR OBJECTS control card in this order: variable star, sky variable, comparison star, sky comparison, another star, another sky, etc. *X TIME OFFSET — The following parameter card can have up to a 15-digit number (read by F(15,14)). This number is added to the Julian data computed for each deflection. Its units must therefore be days. DEXTOR Program Outline DEXTOR is a program written in PLl which applies differential extinction coefficients to a dataset like that produced by PHRED. If the instrumental system is nearly the same as the standard UBV system, a simple linear set of equations can accurately describe the effects of a real atmosphere. The equations normally used are (la) v = v-k-X, (lb) (b-v) = ((b-v)-k^.X)/(l+k'rX), and (Ic) (u-b) = ((u-b)-k2rX)/(l+k^,X), where the superscript "o" indicates the outside-the-atmosphere color or magnitude of the star, X is the airmass, v,b, and u are the magnitudes of the star as viewed through the visual, blue, and ultraviolet filters, respectively, and k, k-^, k^, k^, and k^ are the extinction coefficients. For a detailed development of the above equations see Hardie (1962). The above equations apply to the measurement of one star, but the data can better be reduced differentially, rather than as individual magnitudes of the variable and comparison stars. In order to do this, it is necessary to develop a set of equations which describe the differential extinction computations. Start by defining a difference

PAGE 77

66 operator D(...) which is equal to the variable minus the comparison in magnitudes. The above equations can then be defined for the variable star and for the comparison star. It can be shown that equations (1) above become, (2a) D(v) = D(v)-k-D(X), (2b) D(b-v) = D(b-v)-ki-D(X)-4D(X.(b-v)) ^ ^^^ (l+kJ.X^) (1+k^.X^) (2c) D(u-b) = D(u-b)-k2-D(X)-k^.D(X.(u-b)) (1+k^.X^) (1+k^-X^) where the symbols have the same meanings as for equations (1), with the additions of X„ equals the airmass of the variable star, and X V c equals the airmass of the comparison star. The equations (2) above are the ones which are used by DEXTOR in computing the instrumental differential magnitudes of the variable star. The extinction coefficients must be computed separately and supplied to the DEXTOR program via control cards. In the computations performed by DEXTOR, a simplifying assumption has been made about the values of D(X*(b-v)) and D(X-(u-b)). It is assumed that the differences can be replaced by the approximations, (3a) D(X.(b-v))=!^A.B(b-v),and (3b) D(X.(u-b)) = V^.„(„.„^ The error introduced by this approximation is small if D(X) is small. For D(X) = 0.01 the error in D(b-v) is only ol'oOOA for typical extinction coefficients. No error was introduced in the reduction of the RS CVn data for D(u-b) because a value of zero was adopted for kA.

PAGE 78

67 Extinction Coefficients An average value for each of the extinction coefficients was determined by the method of weighted least squares. The data used were those from the comparison and check stars. The evaluation of the coefficients was based on equations similar to equation (la). The evaluation of these primary extinction coefficients was performed in the PHRED computer program for each night of data. The results of PHRED's computations were then weighted according to the precision of PHRED' s least squares determination, and the final extinction coefficients were obtained by an additional application of the method of least squares. The values adopted for application by DEXTOR to all the data (1975 and 1976) were: k = 0.308, k^ = 0.174, k| = -0.03, kp = 0.667, and k^ = 0.0. The values for ki and ki were adopted based on the closeness of the computed values to the expected values given by Hardie (1962). The details of the computations are not critical to the quality of the results. The effects of differential extinction are small. In fact, the average value of the correction on a typical night was 0.001 magnitudes in the D(v) value. Data Reduction PHRED Run After the data were punched onto computer cards, the cards were collected for processing by PHRED, It was necessary to first punch all ^,.*i ,,.

PAGE 79

68 of the control cards for PHRED and verify that all the supplemental data transferred to the program via the control section were correct and in proper sequence. When the above conditions were satisfied, the PHRED portion of the reduction was complete. The computer listings are not included here because they are bulky and do not easily conform to the required format. Copies are, however, available to interested investigators. Correction of Errors Since there were a large number of data, it was impossible to verify all numbers in the tabulations, reduction and printout. However, it was important to investigate all significant human errors so that they would not propagate through the remaining reduction. The first step to reduce human errors was taken during the keypunching. The tabulated data were punched and then verified by the keypunch staff. Second, a program was written to scan the punched cards and to flag changes in the deflection value that were obviously too large or were changes in time sequence. This would locate many transpositions of digits in the tabulation process, or keypunch errors. The program was only partially successful. Third, the reduced data were converted by use of the equation (4) MJD = 41825.042 + 4.797855E, to a common phase cycle and the light curve plotted. The linear ephemeris above is due to Catalano and Rodono (1974). Any datum which was obviously discrepant was carefully checked for errors in tabulation, keypunching, or data reduction. Fourth, to check the reduction process performed by PHRED, a sample set of calculations was performed manually with an HP-45 hand-held calculator. The sample f,-\ flfv^-s*..! #>^f-ii-^^Ktaa

PAGE 80

69 calculations, in every respect, agreed with the values from the PHRED program to within the expected accuracy. The majority of effort was devoted to the third method, described above, for detecting errors. More than 60 individual data were carefully checked in detail (requiring 10 full days of the writer's undivided attention). The majority of the errors detected occurred at the time the data were tabulated for keypunching. The corrections could easily be made and the data adjusted. In a few cases it was possible to identify the source of the error (miss-identification of star, clouds, telescope drift, etc.), but the information necessary to correct these errors was not available. In these few cases it was necessary to remove the offending data from the collection in order to avoid contamination of the results by these known errors. In only one case was a datum removed without an explanation that was completely satisfactory to this writer. The first star deflections (v,b,and u) were all significantly too high and the first variable star deflections (v,b and u) were significantly low on the night of 1, 2 April 1975. For the remainder of the night the data were ^ery good, therefore these first measurements were removed from consideration. Check Star Data The ratio of the check star (BD+352422) intensity to the comparison star intensity should not be time dependent if the stars are both of constant brightness. This allows the observer to have a 'check' on the assumption that the brightness of the comparison star is constant, and therefore that the variable-to-comparison ratio is a true measure of the variation in the variable star's brightness only Occasionally during the course of the observing program, measurements of the check star brightness were obtained. In Fig. 6 a "•V*:^'*'^-''*^-^)'— — • '-if^T^ — *t-tni^^iti*-l-i Tm-r

PAGE 81

70 CD o o o i i r" • • a • • •• 3* ••• •• 9 • • • • • • • 9 • • • •# • • • • • • as • • • • • .3—. L-J-., ) -L o o o 03 o t**< c? o u-i m \ o o un •^ CNJ -Jun 1 2 !o in o LTl o o o m o" o o o o > sMo O 1+s1/5 o •r— I — o OJ o C -r4T3 10 +J O C CL (a n3 > r— en +-> s<— OJ CM 4O) (t3 4-> 11 CM O) C O O) o O +J C SUD O ui S_ 3 rt o S<£> ^ o CU o I— 1 o S4o QJ c— 13 s • J= O) Ul 00 o o c ro QJ re OJ =5 +1 OJ Q. E r^ .E nj VO +-i 4-3 r— > o JC ra ri 4CD •rOJ E • O •-4-> ai o Jc ra 00 cu sII o :3 4-> 4 4-> 4> •r0) •I n3 oo c so rc 03 CU o 4-J O J= J= != C -^ 4-> o OJ +J •a Sra 0) O) +1 OJ > i. -p HSO -t-J "* qOJ E O ^ •r(/) ^— \ — I -O -Q 1/1 o. E • O CU o 0) 00 OJ JT Lfi ra s_ il -p r^ O (t! o^ o Hr-l 4J 00 > O 00 +-> OJ o c OJ 4-1 ^ S !s_ O +-> o re 5= a. CLM1 — 1 CM O r— CSJ s> in • CO-.00 cn OJ o -o + •r^ s_ c a U-P Q.-.C2

PAGE 82

71 TABLE 5 DIFFERENTIAL MAGNITUDES AND COLORS OF CHECK STAR HELIO. MJD D(v) D(b-v) D(u-b) 42469.33188 42469.40479 42478,31961 42480,34465 42480.42243 0.159 0. 141 0.150 0, 151 0.144 1 033 0.0869 0.0904 0.1019 42491.32879 42491.41073 42508.06754 42508,23996 42508.24524 0.129 0.148 0.158 0.145 0.143 0. 1084 0. 1046 0. 1111 0.0933 0.1536 0.0439 0.0857 0.0221 42508.41600 42508.42114 42515.38021 42515.38403 42515.41264 0, 144 0.148 0.145 0.137 0.117 0. 1086 0.1297 0. 1058 0.1050 0.0995 0.1082 0.0865 0.0518 0.0328 0. 1458 42518.12401 42518.31901 42519. 10308 42519.18606 42519.39703 0. 148 0,157 0.154 0. 141 0.130 0. 1143 0. 1046 0.1259 0. 1317 0. 1117 0.0848 0.0644 03 1 1 0.0521 0.0801 42843.30877 42843.38933 42855.22996 42355.43218 42886.22183 0.121 0.136 0.143 0.145 0.141 0. 1308 0.0912 0. 1042 0. 1254 0. 1059 0.0426 0.1122 0.0518 0.0814 0.0654 42886,29107 42895.25505 42896.10202 42896.15872 42896.28953 0.154 0.146 0.153 0.142 0.141 0.0966 0. 1038 0.0872 0.0890 0.0 954 0.0754 0.0499 0.0866 0.0982 0.0719 42896.36839 42917.17889 429 17.31388 429 23.12296 0.147 0. 142 0.157 0.149 0. 1124 0, 1022 0.0793 0.0929 0.0712 0.0715 0.0898 0.1160 • ":•, -Wi =i>^

PAGE 83

72 plot of the instrumental differential magnitudes is presented as a function of Modified Julian Date. Notice that the plot is not continuous 1n time; this is because the observing was carried out only during the spring months of 1975 and 1976. The data plotted in Fig. 5 appear in tabular form in Table 5. Variable Star Data The data for RS CVn obtained with the instrumentation described in Chapter II, during the 1975 and 1976 observing seasons from March to May, and reduced by PHRED and DEXTOR, appear in tabular form as instrumental differential magnitudes in the appendix. Transformation to Standard System The goals of this research do not require transformation to the standard system. Differential measurements with the same comparison star and subsequent use of WINK in the analysis (see Chapters IV and V) relaxes the requirements for standardization in the data. For these reasons, only a small effort was made to obtain transformation coefficients. The standard stars used were observed on two nights during the course of the observing program. The transformation equations that apply are given as follows: (5a) B-V = A^ + A2(b-v) (5b) U-B = A3 + A^(u-b) (5c) V-v = A^ + Ag(b-v) The values for the A's in equations (5) were computed by the method of least squares using the data obtained from the photometry of nine standard stars and the comparison star. The data for RS CVn has not been transformed with these coefficients because the accuracy is so

PAGE 84

73 very low. The transformation coefficients to the UBV system are as follows: A^ = 0.89 0.01 A2 = 1.06 0.01 (the estimated errors are standard errors) A. = 0.0 0.1 5 More accurate transformations can be found in Markworth's (1977) dissertation. His photometry used virtually identical instrumentation. A3 = -2.02 : t 0.32 \ = 1.06 0.15 5 = 7.97 0.03 ^fl1l=il rt/'ar-

PAGE 85

CHAPTER IV DATA ANALYSIS PROCEDURE Introduction The analysis of the data was carried out on an AMDAHL 470 computer at the Northeast Regional Data Center located on the Gainesville campus of the University of Florida. The processing was accomplished with several programs written in FORTRAN IV. One program (WINK), which was written by D. B. Wood (1971, 1972), models an eclipsing binary system. The remaining programs were written by the author except for the least square subroutine (used in the Fourier program) which was written by H. L. Cohen. The details of the operation will be discussed after an outline of the WAVE procedure is discussed. Outline of WAVE Procedure A simplified outline of the procedure appears in Fig. 7. The details of these computations are eliminated so that the process is clearer. The procedure that this figure represents was used as an in-stream procedure and was called WAVE. This term will be used in the remainder of this dissertation to refer to this sequence of computer programs which was used to analyze the data. The WAVE procedure starts basically with the WINK program which both improves the eclipsing binary elements and produces a theoretical light curve. The input data set to WINK (which it attempts to solve) is called OROBS. This term refers to the Old Revised OBServations from a previous WAVE run or to observations 74 '•I, 111 **rTT-!!'

PAGE 86

75 PREVIOUS PLOTS AND PRINTOUTS OROBS \A/ M ly PROGRAM CONTROL (USER) VV IN r\ CALCM 1 r ROMC CALC OBS .. ^ OMC FOURF T FOMC OMC TOMC R08S ^ f ROBS idlll t PLOTS AND PRINTOUT -CPLOT -rajj Fig, 7. -Outline of basic WAVE procedure -* l-^'t'-T— .-i''M'

PAGE 87

75 themselves when the procedure is initiated. In addition to the OROBS the user also supplies a set of control parameters to WINK. After five WINK iterations or after convergence (whichever comes first) the WINK program produces a dataset called CALCM. This is the theoretical light curve for the elements at the conclusion of the solution portion of WINK. The term (CALCM) refers to the fact that it is necessary to produce the calculated light curve in magnitudes in order to include the Quadriture Magnitude (QM) parameter in the values produced. This dataset and the observations (OBS) are used in the ROMC program which is next in the sequence. ROMC converts the magnitudes of the CALCM dataset to intensities and subtracts them from the OBS dataset. The result is the CMC dataset, which is a representation of the distortion wave. In addition, ROMC produces a CALC dataset which is the converted CALCM dataset. CALC is used later for plotting purposes. Next in the sequence is the program FOURFIT. It uses the CMC dataset to determine the coefficients of a truncated Fourier series, by the method of least squares, which represents the distortion wave. The Fourier representation is then subtracted from the OBS dataset. The result of the subtraction is a light curve of RS CVn as it would appear if it did not have the photometric complication. This dataset is called ROBS (Revised OBS). FOURFIT does additional computations which are used for plotting purposes. It computes a dataset from the truncated Fourier series at closely spaced phases. This dataset is called FOMC. Lastly, FOURFIT calculates the difference between the OMC dataset and the Fourier representation of it. This is called TOMC. The last significant program in the WAVE procedure is called LCPLOT. This program plots the datasets produced in the previous steps

PAGE 88

77 s.. I HUG 2:--. t^ *Ht* f : •^^fiM ifc* • '. Si o.' H 1 I 1rt: o.so — I ^o.ss o.ea —I ( 1— 7oVm 0-3 7.M 3.n }.i9 3.S0 a as 37io o.20 37 o. an aM I "i i 1 I I i 1 1 1 1 1V!i%.^ ^^-V" "'i'^ *\i*i*'' '"^ -^-•^fV%^ I I II >J4.40 .ao a.ia a to (7-dO a.tt a-co o.io o.zo o.30 0.^ 0.0 0*^0 Fig. 8. -A sample plot from LCPLOT program reduced 60% appears in (a) In (b) is an enlargement of primary eclipse. >wr,,^x,tji.— ,___.. _,._^,.,_. J,.

PAGE 89

78 of the procedure for evaluation by the user. A sample of the plots produced appears in Fig. 8. The WINK Program This program has been widely used to determine the elements of eclipsing binary systems. The program was written by D. B. Wood (1971, 1972) and has been updated by eight status reports (private communications), The model is that of triaxial ellipsoids. The parameters of the model which are pertinent to this investigation, their WINK codes and meanings are shown in Table 6. TABLE 6 WINK PARAMETERS WINK Code Symbol Meaning orbital inclination e is the orbital eccentricity and w is the longitude of periastron time (or phase) of conjunction linear limb darkening coefficient for star A linear limb darkening coefficient for star B reflection albedo of star A reflection albedo of star B quadrature magnitude effective temperature of star A effective temperature of star B radius of a sphere with a volume equal to that of the triaxial ellipsoid of star A (equivalent radius of star A) ratio of equivalent radii (an/a ,) gravity exponent for star A gravity exponent for star B mass ratio (star B to star A) polytropic index of star A 1 i 2 e sin to 3 e cos 0) 4 ^c 5 ^A 6 ^B 9 ^ 10 ^B 11 QM 13 ^A 14 'b 15 ^oA 16 k V 17 ^A 18 ^b 19 q 41 n.

PAGE 90

TABLE 6 Continued 79 WINK Code Symbol Meaning 42 nn polytropic index of star B 43 X effective wavelength of observations 45 log g. logarithm of surface gravity of star A 45 log gn logarithm of surface gravity of star B For systems like RS CVn in which the stars are sensibly spherical the equivalent radii are useful parameters. On the other hand, they have '^ery little physical meaning and the ellipsoidal axes are to be preferred. The reader is cautioned to remember that any set of parameters (whether it's a spherical radius, a set of radii for a triaxial ellipsoid, or 3 radii of a Roche lobe) is merely a way of conveying quantitatively information about a natural phenomena, which most likely does not actually conform (in detail) to any of the model parameters. The WINK program as it was used here both improved the elements by the method of differential least sqaures and produced a synthetic light curve (the CALCM dataset referred to earlier). The integration was performed using the 4x4 Gaussian quadrature option, which has an accuracy of 0.5%. The model atmosphere used is that which was supplied by Wood in Status Report #7. The first 19 parameters (only 16 of which are used here) may, by user selection, be improved by the differential least squares subroutine. These parameters, for the purpose of this research were divided into 4 groups by the author: the first-order parameters are i, '^v' ^oA' ^^^ '^Q' "^^^ second-order parameters are w., Wg, u,, and Ug. The third-order parameters are T and QM. The fourth-order parameters are e sin co, e cos lo, T^, q, 6^, and gg. The other parameters

PAGE 91

80 of the WINK model must be assigned by the user and cannot be improved by the differential least squares routine. In this dissertation the terms "free-parameter" and "adjustableparameter" will refer to a parameter from the above set which has been designated by the user as a parameter to be improved by the differential least squares routine. Likewise, the term "fixed -parameter" refers to a parameter which has been assigned by the user a particular value and not allowed to be changed by the WINK routines. No third light was allowed, and only the linear limb darkening law was used. Certain parameters were by necessity assumed at the outset and never altered. These parameters and their assumed values are given in Table 7. TABLE 7 ASSUMED PARAMETER VALUES Parameter Assumed Value e sin CO 0.0 e cos w Q Q i.e., a circular orbit ^A 6700K from Popper (1961) q 1.045 from Popper (1961) "a 3.5 "b 3.5 log g^ 4,0 from Gray (1976) log gg 3.5 from Gray (1976) The program was modified to allow for up to 200 data to be read or v/ritten, and to produce an additional page of output, which is merely a summary of the least square iterations. In all other respects the program is complete through Status Report #8. The version of the WINK model used here was updated through Status Report #8. -j-^mm*^

PAGE 92

81 The ROMC Program This program is \/ery simple. It reads the CALCM dataset produced by WINK and converts the magnitudes (m) to intensities (I) by the relation I = 10-Q-^^ This conversion is performed for each successive record in the CALCM dataset. At the same time a record from the OBS dataset is read. The phase of the two records are checked to assure that they are the same. If they are not the same, an error message is written and the program continues. After the subtraction of the CALC record intensity from the OBS record intensity the result is written to the OMC dataset along with the phase from the OBS record. These calculations are repeated until all the records have been processed. It should be noted that the CALC dataset is written for plotting by the LCPLOT program later in the procedure. The FOURFIT Program This program reads all the records from OMC dataset and by the method of least squares determines the coefficients of the following truncated Fourier series which best represents the data in OMC. 1(e) = Aq + A^ cos e + Ar, sin 9 + A^ cos 26 + A^ sin 29. Since the data in and around secondary eclipse are confused by the transit of the smaller star across the assumed non-uniform surface of the larger star these points (from phase 0.43 to phase 0.57) are excluded from the least squares process. After the coefficients of the truncated series have been determined they are used to evaluate the expression at each value of phase in .—-.. -*_YW^.|. .— .. '"t-**^Vtr-*!.-

PAGE 93

82 the OBS dataset. The result of each evaluation is then subtracted from the OBS intensity at that phase. The results are what one would expect if RS CVn was not complicated by the non-uniform surface brightness of the larger star. This is not true, however, for the secondary eclipse because the photometric effects of the transit geometry cannot be so simply removed. These effects do_ contain important information about the surface brightness distribution on the larger star. The other functions of FOURFIT are to produce two datasets for plotting by LCPLOT. The first dataset, called FOMC, is the evaluation of the truncated Fourier series at 240 phase points so that the plot of this dataset will appear to be a continuous line. The second dataset, called TOMC, is the difference between the intensity of a record in the OMC dataset and the evaluation of the Fourier series at the phase for that record. In other words, it is the difference between the "real" distortion wave and the Fourier fit to it. These points, when plotted, should be randomly displaced (by only a small amount) about a straight line of slope zero if the elements of the eclipsing system are nearly correct. Here again, the region of secondary eclipse is an exception. The LCPLOT Program This program is \/ery complex and for the present purpose need not be discussed in detail. It plots the datasets the user wishes as a function of phase. It is a general purpose program and is not restricted to use in the WAVE procedure. Detailed WAVE Procedure The detailed JCL WAVE in:-stream procedure appears in Fig. 9. It differs from the above only in the details of the procedure, but not in the results. \tMjatimr*''-*'' -'-'((/'rTww-^miii ,**-;-•,,—,; *vr

PAGE 94

83 //WAVE PROC ROMC='ROMC' ,WINKOUT='&&CALCM' ,CALCM=,WINKIN='&&OROBS' //GENO EXEC PGM=IEBGENER,C0ND=(4,LT) //SYSPRINT DD DUMMY //SYSIN DD DUMMY //SYSUn DD DDNAME=REVO //SYSUT2 DD DSN=&&0R0BS,DISP=(MEW,PASS),SPACE=(TRK,(2,1),RLSE), // UNIT=SYSDA,DCB=lBECF?i=FB,LRECL=80,BLKSIZE^6400,DS0RC=PS) //GENl EXEC PGM=IEBGENER,C0ND=(4,LT) //SYSPRINT DD DUMMY //SYSIN DD DUMMY //SYSUTl DD DDNAME=PARA //SYSUT2 DD DSN=&&PARMS,SPACE=(TRK,(2J),RLSE),DISP=CNEW,PASS), // DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DS0RG=PS),UNIT=SYSDA //GEN2 EXEC PGM=IEBGENER,C0ND=(4,LT) //SYSPRINT DD DUMMY //SYSIN DD DUMMY //SYSUTl DD DDNAME=DATA //SYSUT2 DD DSN=&&0BS,SPACE=(TRK,(2,1)RLSE),DISP=(NEW,PASS), // DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DS0RG=PS) ,UNIT=SYSDA //GEN3 EXEC PGM=IEBGENER,C0ND=(4,LT) //SYSPRINT DD DUMMY //SYSIN DD DUMMY //SYSUTl DD DDNAME=PRED //SYSUT2 DD DSN=&&PRED,SPACE=(TRK,(2,1),RLSE),DISP=(NEW,PASS), // DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DS0RG=PS) ,UNIT=SYSDA //GEN4 EXEC PGM=IEBGENER,C0ND=(4,LT) //SYSPRINT DD DUMMY //SYSIN DD DUMMY //SYSUTl DD DDNAME=STOP //SYSUT2 DD DSN=&&ST0P,SPACE=(TRK,(2,1),RLSE),DISP=(NEW,PASS), // DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DS0RG=PS) ,UNIT=SYSDA //GEN5 EXEC PGM=IEBGENER,C0ND=(4,LT) //SYSPRINT DD DUMMY //SYSIN DD DUMMY //SYSUTl DD DSN=&&OBS,DISP=(OLD,PASS) DD DSN=&&STOP,DISP=(OLD,PASS) //SYSUT2 DD DSN=&&NGRM,SPACE=(TRK,(2,1),RLSE),DISP=(NEW,PASS), // UNIT=SYSDA,DCB=BLKSIZE=6400,LRECL=80,RECFM=FB,DS0RG=PS) //WINC EXEC PGM=WINK,C0ND=(4,LT) DSN=&&PARMS,DISP=(OLD,PASS) DSN=&WINKIN,DISP=(OLD,PASS) DSN=&&PRED DISP= (OLD PASS ) DSN=&&NORM,DISP=(OLD,PASS) SYSOUT=A DSN=&WINK0UT,SPACE=(TRK,(2,1),RLSE,DISP=(NEW,PASS), // DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DS0RG=PS),UNIT=SYSDA //FT08F001 DD SYSGUT^A //OMCA EXEC P6M=&R0MC,C0ND=(4,LT) //FTOlFOOl DD DSN=S&OBS,DISP=(OLD,PASS) Fig. 9. -The WAVE procedure. //FT05F001 DD II DD II DD II DD //FT06F001 DD //FT07F001 DD

PAGE 95

84 //FT03F001 DD DSN=&&0MC,SPACE=TRK,(2,1) ,RLSE) ,DISP=(NEW,PASS) // DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DS0RG=PS),UNIT=SYSDA //FT06F001 DD SYSOUT=A //FT08F001 DD DSN=&WINKOUT,DISP=(OLD,PASS) //FT09F001 DD &CALCM.DSN=&&CALC,DISP=(NEW,PASS) ,UNIT=SYSDA,SPACE=(TRK, // (2,1),RLSE),DCB=(RECFM=FB,LRECL=80,BLKSIZE=6400,DS0RG=PS) //FOUR EXEC PGM=F0URFIT,C0ND=(4,LT) //FTOlFOOl DD DSN=&&OBS,DISP=(OLD,PASS) //FT03F001 DD DSN=&&OMC,DISP=(OLD,PASS) //FT04F001 DD DSN=&&ROBS, DISP=(NEW, PASS) ,SPACE=(TRK, (2,1) ,RLSE) // DCB=( RECFM=FB LRECL=80 ,BLKSI ZE=64G0 DSORG=PS ) UN IT=SYSDA //FT06F001 DD SYSOUT=A //FT18F001 DD DSN=&&TOMC,DISP=(NEW,PASS) ,UNIT=SYSDA, // SPACE=(TRK,(2,1),RLSE),DCB=(RECFM=FB,LRECL=80,BLKSIZE=5400, // DSORG=PS) //PUN EXEC PGM=IEBGENER,C0ND=(4,LT) //SYSPRINT DD DUMMY //SYS IN DD DUMMY //SYSUTl DD DSN=&&OMC,DISP=(OLD,PASS) //SYSUT2 DD SYS0UT=6,DCB=BLKSIZE=80 //LCPT EXEC PGM=LCPL0T,C0ND=(4,LT) //SYSPOUT DD SYGUT=A //SYSVECTR DD DSN=&&VECT,UNIT=SYSDA,DISP=(MGD,PASS) // DCB=BLKSIZE=2400,SPACE=(TRK,(75,10),RLSE) //FT05F001 DD DUMMY //FT07F001 DD SYSOUT=B //FT05F001 DD DDNAME=PLGTS //FT08F001 DD DSN=&&OBS,DISP=(OLD, DELETE) //FT09F001 DD DSN=&&CALC,DISP=(OLD, DELETE) //FTlOFOOl DD DSN=&&OMC,DISP (OLD, DELETE) //FTUFOOl DD DSN=&&ROBS,DISP (OLD, PASS) //FT12F001 DD DSN=&&NORM,DISP (OLD, DELETE) //FT13F001 DD DSN=&&STOP,DISP (OLD, DELETE) //FT14F001 DD DSN=&&PARMS ,DISP (OLD, DELETE) //FT15F001 DD DSN=&&PRED,DISP (OLD, DELETE) //FT15F001 DD &CALCM.DSN &&CALCM,DISP (OLD, DELETE) //FT17F001 DD DSN=&&OROBS,DISP (OLD, DELETE) //FT18F001 DD DSN=&&TOMC,DISP (OLD, DELETE) //FT19F001 DD DSN=&&FOMC,DISP (OLD, DELETE) //PUNCH EXEC PGM=IEBGENER,C0ND=(4,LT) //SYSPRINT DD DUMMY //SYS IN DD DUMMY //SYSUTl DD DSN=&&ROBS,DISP=(OLD, DELETE) //SYSUT2 DD SYS0UT=B,DCB=8LKSIZE=8O // PEND Fig. 9. -Continued. -.'t'-l-.'Via 1^

PAGE 96

85 //CALL EXEC WAVE //GENO.REVO DD the OROBS dataset phase and intensity read by (2F10.5) /* //GENl.PARA DD the WINK parameters and model atmosphere /* //GEN2.DATA DD the OBS dataset phase and intensity read by (2F10.5) /* //GEN3.PRED DD -1.0 the "true-false" card (defines the free-parameters) WINK 47 0.0 48 0.0 49 1.0 86 1.0 -100.0 /* //GEN4.ST0P DD -1.0 STOP /* //LCPT. PLOTS DD the LCPLOT control cards for the generation of plots (see Fig. 8) /* //PLIT EXEC PLOT Fig. 10. -The input stream which uses the WAVE procedure. Note that a partitioned load module library must be supplied with the necessary programs in it.

PAGE 97

86 The input stream which uses the WAVE procedure is given in Fig, 10 The missing datasets depend on the application of the procedure.

PAGE 98

CHAPTER V ANALYSIS AND SOLUTION Introduction The WAVE procedure was described in the preceding chapter. It was developed to assist in the solution of the light curves of RS CVn because previous techniques were inadequate. The WAVE procedure is not capable of arriving at a satisfactory solution without the critically important supervision of a knowledgeable human being. The human must be capable of analyzing intermediate results and determining the subsequent steps by which a better solution might be obtained. At this point, WAVE has been used in the analysis of the light curves of RS CVn, and it has not yet been determined whether the procedure can be applied to other eclipsing or non-eclipsing systems. It is the opinion of the author that WAVE will prove to be helpful in obtaining solutions, in either case, where unexplained photometric complications exist. Therefore, in order to assist with the implementation of WAVE in further research, a detailed account of the process by which the present solution of RS CVn was obtained will be presented. The Data Analyzed The light curves of RS CVn that have been analyzed with the use of the WAVE procedure are listed in Table 8. These do not represent all of the published data which are available, but they are a selection which meets the requirements of the research effort undertaken as the topic of this dissertation. 87

PAGE 99

88 TABLE 8 SOURCE OF DATA Publication MJD of observations ^e Name Sitterly (1930) 22759.2 22898.2 5150A 1921 Chi sari and Lacona (1965) 38109.9 38227.0 5150A 1963 Chisari and Lacona (1965) 38468.9 38572.0 5150A 1964 Catalano and Rodono (1967) 38871.8 38944.0 5150A 1965 Catalano and Rodono (1967) 39213.9 39316.0 5150A 1966 This Dissertation 42469.0 42534.3 5500A 1975V This Dissertation 42469.0 42534.3 4490A 1975b This Dissertation 42506.0 42534.3 3770A 1975U This Dissertation 42843.3 42929.2 5500A 1976V This Dissertation 42843.3 42929.2 4490A 1976b This Dissertation 42843.3 42929.2 3770A 1976U In Table 8 the last column is a "name" which has been given to the data for easy reference in this present work. This "name" is also the year (and color in some cases) in which the data were obtained. In a few cases it will be convenient to group the 1963, 1964, 1965, and 1966 data into a set, and to refer to this set as the "Catania data." The astronomers who published these data were all observers at the Catania observatory. All of the Catania data and the author's data of RS CVn were obtained using BD+35'^ 2420 as a comparison star. This greatly facilitates the comparison of the light curves from the different years, because the differential magnitudes are in the same light units. The difference in the effective wavelength used by the Catania observers and that used by the author has the effect of changing (only slightly) the effective light unit. Since the bandwidth of the filter used by the Catania observers was not available, it was impossible to make allowances

PAGE 100

89 for any differences in the two instrumental systems. Fortunately, to some extent this difference does not cause a problem with the analysis because the WINK model uses the effective wavelength as an input parameter. Thus, the majority of the WINK parameters that are subsequently determined are independent of the wavelength. In Table 8 the specific dates for the observations are given because only portions of the published data were used for the 1921 and Catania light curves. The migration of the distortion wave would "wash-out" some of the detail in the light curve if the duration of the observing seaso;n was too long. For this reason the data which produced the light curves used in the WAVE procedure were limited to those points taken over a period of less than 140 days. The data taken by the author was deliberately limited to a short time span (65 days in 1975 and 86 days in 1976). The modifications to WINK (see Chapter IV) extended the capacity of the model from 100 points to 200 points. This would have allowed light curves to be made with up to 200 normal points. However, such light curves would have been prohibitively expensive to run on the computing system available. Therefore, a compromise was made between the cost of computing (which increases approximately as the square of the number of normal points) and the desirability of a large number of normals which would give a good resolution of the details in the light curves. The compromised value was 150 normal points per light curve, or as close to this value as was realistic. The calculation of the normal points was carried out on the digital computer. In computing the normal points the first step was to compute the phase for each individual differential magnitude from the -^j i iX f ^rfiy^^H.jtLj' p J t~~^-,->.Tii>iLL^^J t—

PAGE 101

90 linear ephemeris MJD (minimum light) = 41825.042 + 4f797855E. The period of this ephemeris was computed by Catalano and Rodono (1974). The initial epoch is from an observed minimum, published in the same paper, closest to the start of the author's observations in 1975. Only the decimal fraction was retained from the computation of the phase. The second step involved sorting, into phase order, all magnitude-vsphase points. This process was done separately for each dataset as they are listed in Table 8. The final step in the normal point calculations was the most important. The average value of the phase, and the magnitude of the average value of the intensity for all points within many small phase intervals were computed. These calculations were defined by three parameters. The first two parameters together defined a section of the light curve. This was called the phase range. The third parameter defined a 'bin size' within the phase range. For example, suppose that a phase range of 0?0 to 1?0 is defined (i.e., the entire light curve), and a bin size of oPl is also defined. The first normal point will be computed from the individual points between phase 0.0 and 0.1. The second normal point will be computed from the individual points between oPl and 0?2. This process is continued until the last normal point is computed from the individual points between 0?9 and 1?0. In this example it is possible to have, at the most, 10 normal points. The actual number would depend on the distribution of individual points throughout the light curve. In practice it is better to have more than one phase range and bin size for a light curve. There are two reasons for this. First, the distribution of individual points will, in all probability, be unequal.

PAGE 102

91 Therefore, it would be advisable to choose the phase range and bin size to accommodate the real distribution of data in the light curve. Second, and more importantly, the slope of the light curve is much greater during eclipses than in the rest of the light curve. For this reason it is necessary to have a small bin size during an eclipse in order to accurately represent the individual points with the normal points. When the phase ranges and bin sizes are chosen, all of the above factors must be considered. The final set of normal points will inevitably be a compromise. The data which are ultimately used should be the ones which best represent the individual points. The normal points which were used in the WAVE procedure are here presented in Tables 12 through 22. Notice that each table gives the phase, differential magnitude (variable minus comparison), and number of individual points used for each normal point. In addition, the phase range and bin size used in the computations are given. The Analysis There were many computer runs using the WAVE procedure before a final solution was selected; 103 in fact. It would not be profitable to discuss each of these runs individually. The better approach is to group them according to steps in which the runs are related in some procedural way. This reduces the number to approximately a dozen steps, which serve to simplify the discussion which follows. In the future applications of the WAVE procedure it will be possible to reduce the number of runs and the number of steps considerably based on the experience which was gained in this effort for RS CVn. In this section, an

PAGE 103

92 o 00 o LlI >a: 4-i* CM o o LO o OO CXD "=:]OO r-H LD LO LO en oo oo r^ o oo o o cr> ^ t — ( CM r—l CM CM Cvj o o CM B • • r-^ r^ 1— 1 ^ o • • • o o ^,—4 CO o r1 o o UD ^Jo CM O O o o d o ^ CTI C\J o o LD o O CO "^ CM LO LO LO LO LO ,-H en ro ^ r>. o oo o o O CM ,-H O ,-H O CM CM CM r-H O > .— ) • • • • • r-CO --H O r-H O • • • o o ? — I un o CO o r-H o o i-D -1o o CM O O o o 6 6 -a 0) o cr KO ot CM O o un o 5^ UD CM >-H r-s CM LO LO LO LO "=r oo r~ O oo o o UD CM O r--. ,-1 CM CM CM O CD O n • • 6 r^ en ^ o CO o > O 1 sz CO o CO o V— i o o ^o ^ O O) ,-H O o o o O o CM o o tn o CM >— 1 r^ CM 1 LO LO LO LO OO en 0) =^ r-o oo o LO LO r-H r-H O O CM Csj C\J CM ,-H o 3 O-i • • • • o (^ r-H O o o • o o OJ lO o r-l o o Sys O o r-H o o y3 53• O o o 03 OJ CO o o CM O o o > S(0 ^ vjD CM O o LD o l£3 LO LO r-H CM oo LO LO ir> OCM •TD ro ro r~. O ro o LD I — I CM O r-^ T-H CM CM CM ,-H O OJ E r*N, • • • • o CO o o r-I O O O (/I O i^ z. OT CO t— 1 1— 1 I— t * r-H I— 1 LO en r-H r~~ CM CM CM o o O 2 U3 • ( • t • • • o LO (-H en • o o ro o o o o o o o o U3 =3• o o o -P OJ CO o t-H o o puta f th UD CO o oo en isO iTi r^ r^JD o CM "^ CO LO 1 — LO oo CO CM LO LO O^ LO oo E O r-H CO CO in en <=f CM O O oo un tn LO --H O =dO "vf CM ,-H LD LO OO r-l ,-H o LT) • > o >* ,-H O O -H • • o o CJ OJ ^ o o o o o O --H o o ^£3 =s • > • O LO o o ,-H O 3 CO o o CM O o o 0) .— CO m o o rH r- CO -vf o ^H <::aen CM ,-H (n LO in •=JO CM E CU m -rt OJ o oo '^ CM t-H LO CO t-H r-H O LO CM CM CM o r-H O O CD 'S. • • • • o LO <-H O en o • • o o SfC r-v. o o r-H o o o o U3 =3o o — i • • Iti. CO o o ,-H O o o OJ LO > •rrtS un o O o o o o ^en LO LO ^ CM CM 1O) oo OJ O o o UO LO t-H 00 CM CM o LO rH o ^ ro • • o LO 1-H o o o S-(-> i~o t— 1 CD o UD =d• O O — 1 s_ co o CM 6 6 CU 00 X! SSr-. .— 1 o o o o o o ^ LO en r-H O oo LO LO ^ CD CM n3 O I— ( oo OJ CM o o o LO LO -H O :d-f-H CM CM o Cvj ,-H t: sCVJ > • o LO ^ o o o • o o c i. IX) o o o r-H o o lO "=3O O r-H res cu CO o o CM O 6 6 -1-3 (/I T3 sCO o CM CM o o o O CM o r-. CM r-H . ^ o o <-! O o o '-O ^ • • • • o o ^H =! -M CO o o ,-H O d 6 cr cn CD CD E < +sz sz fO <: CQ < CQ < ca o P
PAGE 104

93 outline of the process by which the light curves of RS CVn were solved will be presented. A summary of the solution process is given in Table 9. The step names are listed as they are used in the discussion which follows The values for the parameters in Table 9 are averages of the computer runs for each step. The standard error, below each value, is actually the average of the standard errors from the WINK program. The reader is cautioned that these are computed by assuming that all fixed-parameters are exactly known. Thus they represent an optimistic estimate of the precision with which the parameter was determined. If no standard error is listed, the number in the table was used as a fixed-parameter value for all of the WAVE runs of that step. The values of Table 9 are only a guide as to the evolution of the solution process. In any given step it is possible that not all of the 11 light curves listed in Table 8 were run. Furthermore, in many steps the 1975v or 1965 light curves, or even others, may have been run several times. The 1921 light curve is of less precision than the others, but the averages were computed by giving it the same weight as the other light curves. The wavelength of the observations is different for some of the light curves, and this would also influence the validity of the averages for those parameters which are wavelength dependent. Therefore, the values of Table 9 are to be considered as only illustrative of the process by which a final solution was eventually determined. At the outset of the solution process it was assumed that the solution was that of two bodies in circular orbits. Therefore, the eccentricity of the orbit and the value of third light were assumed to be zero.

PAGE 105

94 Step One The solution process was started by using the published elements (see Table 2) of Popper (1961) as the initial parameters. The 1975v light curve was used, and after only three runs a greatly improved distortion wave resulted. The procedure was then used only once with the 1976v light curves. These four runs showed that the WAVE procedure would give improved results compared with previous techniques. This step was in actuality a preliminary test of the WAVE procedure. The in-stream procedure which was used in this step was not as sophisticated as that which was developed later. The in-stream procedure described in Chapter IV was used in steps three and following. These preliminary results showed that the KO star corresponds, in the WINK model, to star B. The hotter star is the smaller and less massive star. It is designated by the 'A' subscript. It is especially important in the case of RS CVn to avoid the use of the terms "primary" and "secondary", because the terms are yery ambiguous. For example, in the case of RS CVn the spectroscopic primary (i.e., the more massive KO star) is the photometric secondary component (i.e., the fainter star). Step Two The same preliminary in-stream procedure was used in step two as in step one. The Catania data were used in an effort to obtain plots which would show the evolution of the distortion wave during the four years covered by these data. The plots were presented at an informal meeting of the RS CVn working group of lAU Commission 42 at Socorro, New Mexico in early April 1978. Step Three The WAVE procedure as described in Chapter IV was developed

PAGE 106

95 and first used in step three to improve the value of only the thirdorder parameters (T and QM). The results from steps one and two were preliminary, but of sufficient quality to begin a more rigorous process using them as the initial parameters. The third-order parameters are not actually elements of the model, but they must be determined in order to arrive at a satisfactory solution. The eleven runs of step three were the first to use the full in-stream WAVE procedure. Therefore, this step provided the needed values for the third-order parameters and the ROBS dstasets necessary for subsequent improvement of the other parameters. Since T and QM are unique to each light curve no meaningful average can be computed for them. For this reason no third-order parameters are indicated in Table 9 for step three. However, it is of interest to compare the average RMS error for the 11 light curves of step three with the subsequent steps. Steps Four and Five These are ^^ery similar steps. They both represent runs which helped the author gain the necessary "feel" for the effects of various parameters and combinations of parameters on the solution and cost of running the procedure. Starting with step five the value of log gn was changed from 4.00 to 3.50 to agree with the published values in Gray (1976). The fourth-order parameters 6a and gg were made free-parameters for two runs. The results indicated that these parameters could not be improved, and the theoretical von Zeiple values were adopted for both stars (0.25). Experimentation with the value of q (mass ratio) and the second-order parameters was also performed. The results indicated that the spectroscopic mass ratio was better determined than the photometric r ili-jTi' I bT.! if^'-i-nmi -iim iiu \fc-L--y tUlgg-^Mtg?-?

PAGE 107

value of q, and the reflection albedoes were very poorly determined by the data. The limb darkening coefficients were better known. Step Six The first-, third-, and fourth-order parameters seemed to be reasonably well determined based on prior results. Therefore, it was decided that the second-order parameters should be improved before returning to the first-order parameters for their final adjustment. This was the expected sequence of events. However, it was quickly found that the solution could not be improved by having only the second-order parameters as free-parameters. It was necessary to add QM, i, and Tn to the list of adjustable-parameters. Various combinations of these parameters with the second-order parameters were attempted in order to improve the solution. At the conclusion of step six it was felt that the second-order parameters were as well determined as was possible with the available data, and they were never changed again. The values which were adopted were based on a selection of the better runs of all previous steps. Step Sevan This step consisted of only three computer runs using the 1976v data. The purpose of these runs was to establish if it was necessary to improve all of the first-order parameters, or if a smaller subset would be sufficient. It was hoped that the inclination and temperature of star B were sufficiently well determined so that only k and a ^ would need to be improved. Unfortunately, it was found that all four parameters had to be changed from the average values which had been adopted in order for the WINK model to adequately represent the ROBS dataset. -tii-:-jf'," —

PAGE 108

97 Step Eight From the results of step seven it was obvious that the average values for the first-order parameters were not adequate to represent all of the light curves. So, the light curves for all the datasets in Table 8 were run with all four first-order parameters as adjustable-parameters. The intent was to find a trend in one or more of the parameters as a function of time and/or the position of the distortion wave. No clear trends appeared except for an unexpected variation from light curve to light curve in the value of the inclination. It seemed totally impossible that the inclination of the system could have changed from about 82 in 1921 to about 89 in 1975. This inexplicable result led to the sequence of runs described in step nine. Step Nine The 1975v data were about the best of any used in this analysis, so this light curve was chosen to investigate the nature of the inclination of the system. It was hoped that by fixing the value of the inclination to an intermediate value (86?4) between the extremes found in step eight, and than solving for various combinations of the other first-order parameters an adequate solution could be found. After six computer runs it was deemed impossible to find a solution with an inclination of 86?4 which was as acceptable as the one previously found with i = 89. Step Ten There seemed to be no reasonable explanation to the inclination problem. Therefore a complete review of previous results was made to see if some error had been made. Indeed an error had been committed between steps one and two. Originally in step one Tg had been taken as T^^iWiri—'r-ruii-rvn-mM't — ---> j._,~',~^-v-tf*^-^^iZimi'^-^ti^-,\r—j^^i^r^^Jid^t^-^i&. .'n^^r^^^'-^-x-r^:.,^. i n ti i rim im'T^ti
PAGE 109

98 a well known value because the color of this star could be observed independent of the other star during primary eclipse. The few runs of step one had resulted in a temperature of 5050 K for star A. This value was then used as a fixed-parameter value for all subsequent runs and T^ was adjusted. While this would not cause a large error in the determination of the relative brightnesses of the two stars it was noticeable in the determination of the solution. So, step 10 was a single run to test if taking 6700 K (Popper 1961) as the value of T„ could resolve the inclination problem. As one might have expected, the temperatures of the stars had little affect on the value of the inclination. However, it did improve the Rf-IS error of the WINK determination for the 1975v light curve. At the conclusion of the run it was realized that the inclination problem was not really a problem at all. It was merely a manifestation of the non-uniform surface brightness of the KO star. Since the structure of this surface brightness distribution is a changing function of time, the transit of the smaller star will mimic different inclinations. Step Eleven The normal points in secondary eclipse were removed from all the light curves. Using the resulting datasets as input OBS decks a new set of runs were made with i, T QM, !„, a ,, and k as free-parameters. The new values for these first-order parameters were remarkably similar for each light curve. For example, the range in the value of the inclination was from 84?3 for 1964 to 861 for 1975u. Step Twelve The results from step 11 almost completed the solution. There was, however, one other use for the WAVE procedure which could add insight into the nature of RS CVn.

PAGE 110

99 If the KO star was pulsating it would follow that the temperature and radius of this star would be different for each light curve. On the other hand, if the surface of the KO star is non-uniform, the radius would not change, only the temperature would vary. With the above conditions in mind and the points of secondary eclipse still removed, another set of 11 runs was made with only Tg and k as free-parameters. The radius of star A (a ,) was a fixed-parameter, so the changes in k would be solely due to the radius of star B (agg)The value of a „ was almost identical for all light curves, while qB tha value of Tg was somewhat diffident. This would support a starspot D model over a radial pulsating model. Step Thirteen The last step was to return the secondary eclipse points to the datasets, and run the WAVE procedure to produce a new set of ROBS datasets. The solution portion of WINK was not used because the solution from steps 11 and 12 was felt to be the best that could be achieved. This step was intended only to provide the final ROBS and OMC datasets. Table 9 does not have a listing for this step because there were no changes from step 12. The Final Solution It was noted in step 12 above that Tj, was the only element which was significantly different in the 11 light curves which have been solved with the WAVE procedure. The value of T„ which has been determined for each light curve is an average over the non-uniform surface of the KO star. In addition to different values of Tg, the various light it "s iFn-n— ^•^^ r, >— TT-,-*

PAGE 111

100 TABLE 10 FINAL VALUES OF WINK PARAMETERS Parameter Value Max. s.e. Orbital inclination (i) e sin w e cos w limb darkening coef. star A (u.) limb darkening coef. star B (up) reflection albedo of star A (Wa) reflection albedo of star B (Wp) temperature of star A (T^,) temperature of star B (Tp) equivalent radius of star A (a ,) ratio of radii (k = a^^/a n) ^ V oB oA' gravity exponent of star A (3„) gravity exponent of star B (3d) mass ratio (q = ^d/^jx) polytropic index of star A {n.) polytropic index of star B (np) log surface gravity of star A (log g.) log surface gravity of star B (log gn) 85?34 U?32 assumed 0.0 assumed 0.0 0.72 0.17 1.00 0.08 0.3 1.5 0.05 0.35 assumed 6700K '\.4800K 150K 0.1141 0.0032 2.12 0.08 assumed 0.25 5.3 assumed 0.25 0.7 assumed 1.04 1.5 assumed 3.5 assumed 3.5 assumed 4.0 assumed 3.5 Notes for Table 10. The maximum standard error (Max. s.e.) is defined in the text. This method has also yielded 0.0009 for T and 0.00152 for QM.

PAGE 112

101 LjJ DC < Q. Q I— < Q. (— 1 LU Q LU 1 _l n: CQ o < o i— Q. LlJ 00 LlJ 1 — I Ll_ 3 en > en :3 m en LD en > LD en ^£3 ID cn en CM to a. in r~^ r^ 1— 1 o o 1— 1 CD CD "* CM CO ^ cn CM CO CM o CO .— 1 r^ ^dr— 1 o CO 'cf Ln I— 1 1— 1 CO CM CM CM ^ cn CM ^ t-H r— 1 ^H CM r^ IX! CO r— i r-^ CM r~^ CM CO CM en r-H ^ ^ CD ( — 1 o 53o o ^ O CvJ 1 — ) 1 — i 1— < — ( o CM o O O O o O • 1 • • o O o 1 CD 1 o o 1 O 1 o 1 o o 1 o cn (Si CM CO o o cn o cn CO CM r^ CD CO CO CD in =drr~~ r-l ^ CO en o CD OO O CO ^ 1-H CM r-H cn in CO r-H CM P-. r-CO T—l CD r— 1 o 1 — 1 CD r-H ^ i-H a~i ^ CD 1 — 1 O ^ CO o Ln x—i CsJ CM o t— ( ^ =r o CM CO oo CM CO CO 00 1-H CM O IX) r-^ r-^ .—1 m t— ( CM o OO o oo OO 1 — 1 CM CO r--. l-H .— t CM r^ r— ( o CO i-H m 1— i CM I-H o t-H CO ^ CD un O <=r o o r-. r-H CO CO o t-H =dro O >* o O O o o o o O o d o d o 1 d 1 o d 1 d LO Ol in CM CO o o Ln =3cn o CO cn CM cn P-~ =dLn CD U3 CO cn CM CO m ^ o O en r^ en Ln =^ CM o CO CO oo CO <-< 1—4 r~ oo !— 1 CM ^ CM cn CO cn CO r^ CO cn ^ =3CO o •5J* CM ^Joo o o o t-H Ln <— H o CM O o o o o o d o o 1 o 1 d d 1 d 1 d 1 o o 1 o CO ro CO r^ m cn CO CO cn T—t oo 1—1 Ln CO 1-H 1-H CO o cvj r-^ o t— 1 m o CD cn CO 1—1 tn m cn CO CO <^ CD CO CO I— 1 CO CO =d1 — f O CD o cn CO cn LD o "* o I— 1 '^ =!• r-H o o I-H Ln o "^ CM 1 — 1 Ln Ln CM o o I-H Ln oo o =*• o o o o o o d d O 1 d 1 O d 1 o 1 d d d 1 d IJD LO 1^ m r^ (T< cn CO Ln CD CD CO LO CO in Ln CD r-H CO CO CO CO i-H cn O CM en "^ O •=3CO Ln CD m Ln I-H en i^ ^O "—I OJ CO CO CD I — I o 00 CM CM O CM o OvJ cn CO CO o r— 1 '^ r— I CM Ln Ln r-H o r-H t-H LO ro O "^ O o o o o o d d o 1 o d d 1 o 1 d 1 d d d CM cn (^ CO m OO oo r-CO X — 1 -* CM o rCO CO LO crs =t O CM CM 1 — U3 CM t— 1 o CO CM CD I— 1 CD CM •* r^ r-^ CO LD r— 1 LO i~CM 1 — I x—t in >-H OO .— f CO 1 — 1 Ln t-H cn O cn -— 1 t — 1 <* 1X3 O i-H r-o o o CO r-ro o OO o o o o o o • • • • • • • • • • o o o 1 o o o o o 1 o 1 o o CO LO o r^ CO CO '^lr— 1 ; — in CO cn =1CO CM CO r-~. en CO cr> CO r— i r—l T 1 o CO CD CM o T— 1 "ir Osl 00 o ^ r-. CO IvO r--. 00 CM Ln 1—1 I-H T-i 1— < Ln t-H CO r-H CO CO CO ^ 1 — 1 ^ CO 1 — t CD rr-H I-H o CO cn ro o oo o O o O o o d o CD 1 o d o 1 O d 1 d d d rCO CM o d 1 d 1 d d d d cy o OJ c X CM CO =:!• •1— 03 <
PAGE 113

102 curves also have different Fourier coefficients to represent the distortion waves. Table 10 gives the elements of the system which are common to all light curves. Table 11 gives the values which are unique for each light curve as determined from steps 11,12 and 13. The errors quoted in Table 10 are standard errors determined with the use of the WAVE procedure. The correlation among the system parameters makes it difficult to assess the precision of the determination of each value. The ideal method to obtain an estimate of this precision would be to use all the WINK model parameters as free-parameters and thus allow the least squares routine to determine the standard error. The only method currently available with the WAVE procedure technique is to use the maximum number of free-parameters allowed (9) to estimate the standard errors. By repeating this two additional times, it is possible to include all of the parameters which can be adjusted. This was done using the 1975v light curve. The standard error given in Table 10 is the maximum value of the standard error from the three runs. The Distortion Wave The last step of the solution process produced a set of Fourier coefficients which represent the distortion wave. These coefficients are given in Table 11. The standard error of each coefficient is given below the parameter value. As a reminder, and for the convenience of the reader, the truncated Fourier series from which these coefficients have been determined is (5) 1(9) = Ag + A^ cos e + A2 sin 6 + A^ cos 26 + A^ sin 29. The A^ term is a constant which resolves the normalization differences between the OBS light curve and the CALC light curve. Presumably, had it been possible to accurately normalize the observed light curve to

PAGE 114

103 unity outside eclipse, QM and A would both be zero. Unfortunately, this was impossible to do, a priori, in the case of RS CVn because of the large asymmetric and dynamic distortion wave, as well as the large period changes in the system. The other terms of the truncated Fourier series represent the shape of the distortion wave. It is possible to use this shape, the A term, and the apparent normalized luminosity of star B (In, a quantity printed by WINK) to produce a light curve of the KO star as it would appear if the brighter star were removed from the system. If the OMC dataset is used in place of the truncated Fourier series, the result will include the original observational error which has been partially smoothed from the data by use of the truncated Fourier series. The computations which are outlined above were performed on each light curve. The equation that represents this process is (7) Lg(8) = OMC(e) + lg-10"-^^^^^ where Lg(e) is the intensity at phase 6 of the isolated KO star, OMC (8) is the intensity of the distortion wave at phase 9 is the normalized apparent luminosity of star B, and QM is the quadriture magnitude. The latter two quantities have been listed for each light curve in Table 11. The above equation produced light curves of the KO star which are in units of the comparison star's brightness. These light curves are displayed in Figs. 11 through 21. The region of secondary eclipse, in these figures, is complicated by the transit phenomenon, and therefore this region does not represent the light changes due solely to the KO star. The values of distortion wave minimum and maximum (6 • and 6 ) ^ min max are listed in Table 11. They have been computed by differentiating the

PAGE 115

104 Fourier series of equation (5) with coefficients from Table 11, setting the result equal to zero, and evaluating the solution by Newton's method. Period Changes If the period of a binary system changes with time it is an indication that the angular momentum of the system has changed or that the distance to the system has changed. There are many ways in which the siystemi'sangular momentum can be altered. The one which comes to mind most frequently is the transfer of mass from one star to the other through the inner Lagrangian point. This method of mass transfer has been of great interest during the last two decades as a means of explaining the evolution of binary stars. It is mentioned here, not as a possible explanation for period changes in RS CVn, but as a reminder that it is only one of several ways to change the angular momentum of a binary system, and only currently enjoys a large degree of attention. This is not intended to minimize the importance to astronomical knowledge of any particular period change mechanism, but rather to help explain the current state of affairs. Batten (1973) has a good review of period change mechanisms, briefly they are as follows: apsidal motion, the presence of a third body, and real changes in orbital period which maybe due to mass transfer, mass loss, or mass gain. The later three mechanisms are in actuality changes in the angular momentum of the system. The mass exchange due to evolution is simply a special case. Of course, there is always the possibility of another unknown mechanism, RS CVn and RS CVn binaries may prove to be extremely important laboratories for research into changes in angular momentum of binary systems, because it is reasonably certain that the period changes are

PAGE 116

105 not due to a light-time effect (orbital motion about a third body) or to mass transfer. Neither is it likely that mass loss nor apsidal motion are the causes of the quasi-periodic period changes. The research in the coming decades may return to one of these causes of period change, but at the present all seem impossible. Therefore it is important that the period be measured as accurately as possible. In the case of star systems like RS CVn which have yery asymmetric primary eclipses it is difficult to accurately determine the time of minimum. This is compounded by the long periods (and earth-bound photometry). The WINK parameter T can be determined to an accuracy equivalent to less than 40 seconds in the case of RS CVn. Unfortunately, this is somewhat misleading because the absolute time is not known. The parameter T is that which best represents a light curve. The mean epoch for the data which comprise the light curve is difficult to determine because the computation is complicated by the random nature of the data acquisition and the unequal effect on T of each datum. Nevertheless, the T parameter can be a useful tool in determining the nature of period changes since it affords a higher degree of confidence than other methods. This will allow the investigation of angular momentum changes due to processes that are more insidious.

PAGE 117

106 o o d A1ISN31N CD o diffcurves d e that a er light ^ O -P o OJ -C r— 1 +J CS4 00 o a for ers fr C\J fO Cfo 930) d ale di T— to o CO >, LlI -P o < terl tens o CL 0) CD O -M d based re fore 00 C 0) o n RS C and t [^ •rE o star d by h (D CO O f the was u lO o i. o > +-> S_ CO o ^ +-> CO -C -1o Fig. ll.-Lig erent compar

PAGE 118

107 CD d if) o d en O CM d d o d o d GO d O < X CL en so 14+-> a in o o -o c: S"3 CO •r— JZ o c: o -a (/) > 00 o +-> t/1 CD o O 0) +-! MID O d > A1ISN31N! o en _J I OJ — I CD u. "i^—a'^i^-jii^^rf^ipt^^i ^#H -^^,-'ij^,_^ "YWi^tf 4rB^rt

PAGE 119

108 UJ < X a. o (T3 o CO O U (O a c_? 00 srO +J (/) O (U 4J 4O i. a CD I A11SN31N1

PAGE 120

109 o o lO d 2 O" A11SN31N o d o o d XT d Ll! < a. to o re +-> -a CTi O o -a o Di -a c: (T3 +J o T3 I/) to 00 o 1CO CC o O 0) iD ^o d OJ 2 U •r— r* iLM(|ltur-— (r.L rn^j4ti.^u-i 'sbiMHivta^

PAGE 121

no o T3 o c o a o a: re u Q_ o c o T3 CD (/) > o s+-> t/l O i^ O) M MO 0) > sO A1!SN31N tn TO #;ii*C(-.^v. -.(-. ^B—

PAGE 122

Ill CD d T3 C 0) Q. lO <: O CD -u c ^ o (T3 cu a. o. n n3 d •r.E 3 Cvi (13 4-> O tT3 -a o d d GO d d CD d d d UJ 10 < a. AliSN31N > in o en -a 3 -a to ns C :> o (/I o i^ cu -i-j 4O CU > O -P xz en 1X3 o>

PAGE 123

112 A11SN31N -o c o > o 4-> CD -o 3 o (/r x: o +-> o >3 o 4-) 05 I ra

PAGE 124

113 O lO C3 d CO d CM d o o d d 00 d u CO < a. 0) a. <: s_ Cl n3 n3 +J re c o CD c c o OJ re -Q > o u re (D s O 0) -i-j lO o d > iO Al!SN3iN I 00 T-l a '!**r*r fir fUtMt Im-^h

PAGE 125

114 CD d a c 0) ID Q. < O OJ -C p s= ^ •" O 1/5 ir3 0) Q. n Q. O •T— j: 3 CM re +j o 03 -a LlI 00 < I A11SN31N J2 o o -a CO > (/) n3 +J CO o 0) .c 4J i^O 0) > o +J x: Ol •r_1 1 an en

PAGE 126

115 LjJ < A1ISN31NI Q. CL <. 0) (/I Scu Q. CL re JZ a +J a 3 un o en -a 3 C O o cu 1/1 > o GO a;' iui O :^ 0) 14O > 3 O +-> en O 05 vJ*Y-t'rrt*

PAGE 127

116 LT) < Q_ AllSNdlN I Q. SCL Q. =5 en c o +-1 C7> C •r-a 3 c o T3 0) ra c: > o Of M O ^o > so en •1 — _J t r-J CM cn ||"— -r" -f" —I" ^>_-^ia-il,-(;

PAGE 128

117 TABLE 12 NORMAL POINTS FOR 1921 DATA Bin Size : 0.0020 Phase Range: 0.0000 to 0.0800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0013 -0.530 2 0.0212 -0.600 1 0.0477 -1.560 1 0.0031 -0.560 1 0.0227 -0.600 2 0.0489 -1.505 2 0.0051 -0.600 1 0.0240 -0.710 1 0.0508 -1.557 3 0.0069 -0.610 2 0.0314 -0.890 1 0.0537 -1.830 1 0.0093 -0.530 2 0.0328 -1.022 2 0.0549 -1.770 2 0.0109 -0.630 2 0.0348 -1.108 5 0.0568 -1.800 3 0.0127 -0.570 2 0.0368 -1.213 5 0.0666 -1.870 2 0.0144 -0.520 1 0.0389 -1.330 2 0.0689 -1.876 2 0.0191 -0.563 2 0.0410 -1.337 3 0.0705 -1.850 2 Bin Size : 0.0100 Phase Range: 0.0800 to 0.4200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.1283 -1.877 5 0.1988 -1.870 1 0.3544 -1.892 5 0.1337 -1.899 7 0.2031 -1.900 5 0.3764 -1.841 8 0.1449 -1.976 2 0.2160 -1.861 15 0.3845 -1.810 9 0.1529 -1.907 5 0.2218 -1.902 5 0.3929 -2.100 1 0.1678 -1.965 4 0.3350 -1.907 5 0.4046 -1.960 1 0.1762 -1.960 1 0,3431 -1.883 6 0.4137 -1.790 5 0.1878 -1.970 2 0.3587 -1.935 2 Bin Size : 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.4210 -1.900 1 0.4628 -1.864 3 0.4909 -1.858 3 0.4232 -1.844 4 0.4650 -1.817 6 0.4990 -1.817 3 0.4249 -1.876 2 0.4669 -1.889 4 0.5011 -1.805 2 0.4270 -1.851 2 0.4689 -1.837 3 0.5033 -1.746 2 0.4289 -1.860 1 0.4713 -1.827 3 0.5310 -1.820 1 0.4435 -1.760 1 0.4728 -1.871 2 0.5331 -1.888 2 0.4451 -1.950 1 0.4746 -1.865 2 0.5349 -1.890 1 0.4454 -1.910 1 0.4775 -1.830 1 0.5357 -1.780 2 0.4488 -1.870 1 0.4793 -1.790 1 0.5394 -1.850 1 0.4513 -1.920 1 0.4812 -1.851 2 0.5410 -1.866 2 0.4527 -1.899 3 0.4829 -1.833 3 0.5430 -1.870 1 0.4545 -1,842 3 0.4848 -1.755 2 0.5445 -1.837 2 0.4561 -1.850 1 0.4868 -1.856 2 0.4610 -1.870 1 0.4889 -1.850 2 t->-^*-At1l!fV

PAGE 129

118 TABLE 12 Continued Bin Size : O.OIOC 1 Phase Range: 0.5800 to 0.9200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5894 -1.850 2 0.5662 -1.821 9 0.7618 -1.730 1 0.5952 -1.852 11 0.6742 -1.831 13 0.7859 -1.834 7 0.6036 -1.845 7 0.6849 -1.834 7 0.7980 -1.817 5 0.6253 -1.823 7 0.7397 -1.800 1 0.8247 -1.782 6 0.5354 -1.847 7 0.7440 -1.795 5 0.8342 -1.790 8 0.6567 -1.856 7 0.7563 -1.782 6 0.8407 -1.754 3 Bin Size : 0.002C ) Phase Range: 0.9200 to 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.9231 -1.761 2 0.9488 -1.803 4 0.9747 -1.113 4 0.9249 -1.800 1 0.9519 -1.730 1 0.9773 -0.970 2 0.9270 -1.814 3 0.9531 -1.800 1 0.9791 -0.916 2 0.9298 -1.750 1 0.9549 -1.760 2 0.9806 -0.840 1 0.9312 -1.770 2 0.9572 -1.660 2 0.9829 -0.691 2 0.9333 -1.800 1 0.9590 -1.673 4 0.9850 -0.620 2 0.9347 -1.840 2 0.9606 -1.578 3 0.9871 -0.565 2 0.9371 -1.815 2 0.9629 -1.610 2 0.9891 -0.547 3 0.9391 -1.860 3 0.9652 -1.445 2 0.9914 -0.536 2 0.9407 -1.823 3 0.9671 -1.370 2 0.9940 -0.450 1 0.9429 -1.770 5 0.9690 -1.361 4 0.9970 -0.550 1 0.9448 -1.789 5 0.9710 -1.294 3 0.9987 -0.510 1 0.9467 -1.724 5 0.9729 -1.221 5

PAGE 130

119 TABLE 13 NORMAL POINTS FOR 1963 DATA Bin Size : 0.0020 Phase Range: 0.0000 to 0.0800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0010 0.622 11 0.0227 0.648 3 0.0530 0.057 4 0.0030 0.637 11 0.0251 0.632 3 0.0549 -0.013 7 0.0051 0.631 11 0.0267 0.635 2 0.0572 -0.088 6 0.0070 0.638 7 0.0373 0.613 4 0.0613 -0.173 2 0.0090 0.652 4 0.0391 0.575 2 0.0628 -0.201 3 0.0112 0.635 3 0.0410 0.502 7 0.0650 -0.241 4 0.0129 0.635 3 0.0430 0.449 5 0.0670 -0.295 3 0.0150 0.645 4 0.0450 0.362 5 0.0688 -0.317 3 0.0171 0.639 5 0.0468 0.292 6 0.0706 -0.324 2 0.0190 0.654 3 0.0490 0.216 7 0.0208 0.643 6 0.0510 0.133 7 Bin Size : 0.0100 Phase Range: 0.0800 to 0.4200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0894 -0.343 3 0.1956 -0.306 11 0.3344 -0.235 23 0.0950 -0.341 23 0.2070 -0.293 10 0.3448 -0.224 22 0.1053 -0.345 22 0.2151 -0.285 14 0.3552 -0.225 11 0.1103 -0.350 1 0.2246 -0.289 15 0.3682 -0.224 7 0.1373 -0.343 8 0.2348 -0.285 16 0.3753 -0.216 9 0.1449 -0.332 17 0.2400 -0.292 1 0.3847 -0.213 17 0.1550 -0.331 16 0.2542 -0.263 13 0.3954 -0.218 15 0.1650 -0.316 15 0.2654 -0.266 15 0.4024 -0.213 7 0.1748 -0.316 28 0.2730 -0.264 10 0.4155 -0.203 11 0.1831 -0.311 17 0.3280 -0.240 12 Bin Size : 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.4232 -0.210 2 0.4451 -0.207 4 0.5409 -0.156 4 0.4250 -0.212 3 0.4472 -0.217 2 0.5431 -0.165 5 0.4270 -0.205 4 0.4493 -0.226 3 0.5449 -0.171 5 0.4291 -0.212 2 0.4508 -0.212 2 0.5470 -0.189 3 0.4331 -0.205 3 0.4529 -0.203 4 0.5488 -0.193 3 0.4350 -0.215 3 0.4554 -0.204 2 0.5509 -0.201 4 0.4371 -0.213 4 0.4568 -0.210 2 0.5532 -0.198 3 0.4391 -0.203 3 0.5353 -0.153 3 0.5551 -0.210 7 0.4413 -0.201 3 0.5370 -0.150 5 0.5572 -0.215 5 0.4430 -0.212 3 0.5388 -0.162 4 0.5589 -0.221 6 fmi^iinG^Ttr^irN>'bF-' ii

PAGE 131

120 TABLE 13 Continued Bin Size 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5611 -0.224 7 0.5670 -0.235 7 0.5731 -0.250 7 0.5629 -0.238 3 0.5690 -0.250 7 0.5795 -0.247 4 0.5650 -0.236 6 0.5711 -0.248 7 Bin Size : 0.0100 Phase Range: 0.5800 to 0.9200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5844 -0.254 43 0.7144 -0.321 12 0.8250 -0.372 16 0.5944 -0.248 18 0.7355 -0.338 11 0.8345 -0.379 18 0.6271 -0.285 10 0.7454 -0.348 28 0.8452 -0.392 17 0.6344 -0.293 14 0.7548 -0.351 49 0.8689 -0.383 3 0.6451 -0.304 16 0.7652 -0.353 45 0.8748 -0.378 16 0.6543 -0.309 12 0.7750 -0.359 30 0.8845 -0.379 13 0.6645 -0.319 16 0.7851 -0.356 34 0.8943 -0.382 12 0.6871 -0.318 5 0.7941 -0.365 26 0,9046 -0.378 14 0.6948 -0.323 14 0.8053 -0.373 14 0.9142 -0.379 15 0.7056 -0.323 13 0.8147 -0.374 13 Bin Size : 0.0020 Phase Range: 0.9200 to 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.9493 -0.385 1 0.9669 -0.343 3 0.9872 0.141 4 0.9511 -0.348 1 0.9709 -0.285 2 0.9889 0.218 3 0.9531 -0.388 3 0.9729 -0.255 4 0.9909 0.303 5 0.9551 -0.384 4 0.9749 -0.223 3 0.9930 0.357 5 0.9572 -0.359 2 0.9768 -0.164 4 0.9950 0.439 4 0.9591 -0.359 3 0.9791 -0.093 4 0.9970 0.516 8 0.9609 -0.369 3 0.9811 -0.056 3 0.9989 0.589 7 0.9630 -0.364 4 0.9830 0.006 4 0.9651 -0.356 3 0.9850 0.076 5

PAGE 132

121 TABLE 14 NORMAL POINTS FOR 1964 DATA Bin Size: 0.0020 Phase Range: 0.0000 to 0.0800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0593 -0.144 4 0.0611 -0.180 4 0.0631 -0.234 5 0.0651 -0.263 7 0.0669 -0.297 5 0.0690 -0.328 4 0.0710 -0.335 3 0.0731 -0.344 4 0.0753 -0.347 3 0.0770 -0.357 2 0.0790 -0.337 4 0.0008 0.621 3 0.0328 0.631 4 0.0029 0.628 3 0.0350 0.632 4 0.0049 0.636 4 0.0371 0.578 4 0.0070 0.633 3 0.0391 0.513 5 0.0093 0.654 3 0.0410 0.448 3 0.0113 0.640 2 0.0430 0.381 4 0.0130 0.642 3 0.0450 0.307 4 0.0152 0.639 3 0.0469 0.229 3 0.0170 0.640 3 0.0489 0.153 4 0.0187 0.642 2 0.0509 0.096 3 0.0273 0.649 3 0.0529 0.027 4 0.0291 0.640 4 0.0550 -0.037 3 0.0308 0.645 4 0.0570 -0.090 4 Bin Size: 0.0100 Phase Range: 0.0800 to 0.4200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.3248 -0.202 17 0.3344 -0.200 10 0.3453 -0.200 8 0.3552 -0.196 9 0.3634 -0.201 5 0.4157 -0.200 5 0.0857 -0.339 13 0.2248 -0.240 11 0.0949 -0.333 18 0.2340 -0.238 7 0.1028 -0.335 9 0.2880 -0.218 6 0.1770 -0.293 5 0.2947 -0.215 10 0.2060 -0.255 7 0.3030 -0.214 10 0.2142 -0.248 7 0.3150 -0.208 13 Bin Size: 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5152 -0.161 6 0.5171 -0.158 5 0.5189 -0.157 5 0.5209 -0.163 6 0.5229 -0.170 6 0.5249 -0.181 7 0.5270 -0.173 6 0.5292 -0.186 5 0.5310 -0.188 5 0.5329 -0.190 3 0.5348 -0.204 3 0.5369 -0.198 4 0.4588 -0.213 3 0.4909 -0.154 3 0.4608 -0.209 3 0.4930 -0.144 4 0,4717 -0.200 2 0.4950 -0.147 3 0.4731 -0.209 3 0.4969 -0.129 3 0.4749 -0.210 2 0.4989 -0.130 3 0.4770 -0.192 4 0.5009 -0.146 3 0.4791 -0.182 3 0.5029 -0.143 4 0.4809 -0.175 3 0.5050 -0.132 3 0.4829 -0.172 3 0.5069 -0.157 3 0.4848 -0.175 3 0.5088 -0.153 4 0.4869 -0.152 4 0.5107 -0.147 3 0.4891 -0.143 3 0.5130 -0.158 6

PAGE 133

122 TABLE 14 Continued Bin Size : 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5393 -0.212 5 0.5513 -0.228 3 0,5689 -0.288 3 0.5409 -0.208 5 0.5534 -0.242 3 0.5710 -0.298 3 0.5431 -0.229 6 0.5551 -0.262 2 0.5732 -0.302 4 0.5458 -0.208 1 0.5572 -0.265 2 0.5751 -0.287 3 0.5475 -0.223 2 0.5656 -0.275 1 0.5771 -0.290 1 0.5493 -0.227 3 0.5669 -0.285 2 0.5791 -0.296 2 Bin Size : 0.0100 Phase Range: 0.5800 to 0.9200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5860 -0.303 7 0.6750 -0.358 8 0.8053 -0.391 7 0.5963 -0.308 7 0.6838 -0.376 6 0.8134 -0.386 7 0.6051 -0.317 7 0.7452 -0.384 7 0.8677 -0.403 4 0.6149 -0.322 9 0.7513 -0.397 2 0.8747 -0.402 7 0.5232 -0.331 5 0.7887 -0.410 1 0.8851 -0.399 8 0.5670 -0.360 5 0.7939 -0.390 7 0.8910 -0.399 2 Bin Size : 0.0020 Phase Range: 0.9200 to 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.9253 -0.391 3 0.9468 -0.386 3 0.9711 -0.262 3 0.9270 -0.389 3 0.9491 -0.381 2 0.9731 -0.227 2 0.9288 -0.389 3 0.9512 -0.383 2 0.9746 -0.210 2 0.9309 -0.393 3 0.9528 -0.402 3 0.9869 0.187 4 0.9330 -0.395 4 0.9572 -0.397 3 0.9889 0.251 4 0.9350 -0.395 3 0.9597 -0.410 1 0.9908 0.320 4 0.9369 -0.390 3 0.9611 -0.374 4 0.9932 0.408 3 0.9395 -0.385 1 0.9631 -0.367 3 0.9950 0.472 4 0.9409 -0.392 3 0.9649 -0.371 3 0.9970 0.539 4 0.9425 -0.400 2 0.9665 -0.354 2 0.9989 0.592 3 0.9451 -0.383 3 0.9699 -0.282 1

PAGE 134

123 TABLE 15 NORMAL POINTS FOR 1965 DATA Bin Size : 0.0020 Phase Range: 0.0000 to 0.0800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0011 0.865 1 0.0312 0.839 4 0.0571 -0.051 4 0.0029 0.842 2 0.0331 0.844 3 0.0590 -0.098 3 0.0052 0.828 2 0.0348 0.823 6 0.0607 -0.112 2 0.0071 0.895 1 0.0369 0.714 5 0.0632 -0.169 7 0.0088 0.847 2 0.0389 0.655 5 0.0651 -0.191 6 0.0110 0.840 1 0.0409 0.568 7 0.0669 -0.206 6 0.0128 0.863 2 0.0427 0.489 2 0.0690 -0.251 4 0.0193 0.858 3 0.0450 0.357 6 0.0708 -0.267 4 0.0210 0.851 8 0.0472 0.301 5 0.0723 -0.247 1 0.0231 0.845 5 0.0492 0.228 4 0.0747 -0.271 2 0.0249 0.845 4 0.0508 0.161 4 0.0766 -0.250 1 0.0269 0,855 6 0.0530 0.075 5 0.0789 -0.266 2 0.0291 0.847 5 0.0550 0.033 4 Bin Size : 0.0148 Phase Range: 0.0800 to 0.4500 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0876 -0.263 10 0.2224 -0.252 19 0.3545 -0.228 10 0.1075 -0.270 3 0.2341 -0.249 24 0.3697 -0.218 20 0.1171 -0.259 12 0.2501 -0.248 11 0.3831 -0.225 13 0.1314 -0.262 9 0.2651 -0.244 12 0.3986 -0.222 11 0.1469 -0.266 22 0.2794 -0.224 12 0.4124 -0.231 11 0.1605 -0.258 14 0.2901 -0.236 6 0.4278 -0.242 4 0.1758 -0.244 11 0.3120 -0.237 14 0.4430 -0.239 19 0.1902 -0.247 9 0.3241 -0.218 12 0.2073 -0.255 10 0.3361 -0.201 2 Bin Size : 0.0032 Phase Range: 0.4500 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.4517 -0.241 2 0.4810 -0.188 6 0.5166 -0.109 2 0.4548 -0.225 3 0.4840 -0.162 8 0.5196 -0.144 3 0.4592 -0.230 1 0.4879 -0.172 2 0.5231 -0.149 3 0.4615 -0.229 3 0.4905 -0.163 2 0.5267 -0.157 3 0.4649 -0.219 2 0.4935 -0.137 3 0.5302 -0.189 2 0.4678 -0.205 3 0.4971 -0.122 3 0.5331 -0.155 3 0.4714 -0.204 2 0.5008 -0.116 3 0.5361 -0.212 2 0.4748 -0.216 5 0.5042 -0.107 2 0.5380 -0.178 1 0.4778 -0.181 7 0.5071 -0.103 3 0.5429 -0.215 2

PAGE 135

124 TABLE 15 Continued Bin Size : 0.0032 Phase Range: 0,4500 to 0.5800 Phase Magn. No, Phase Magn. No. Phase Magn. No. 0.5458 -0.220 3 0.5619 -0.282 5 0.5718 -0.295 5 0.5482 -0.231 1 0.5649 -0.295 4 0.5747 -0.320 2 0.5592 -0.296 3 0.5691 -0.298 4 0.5785 -0,324 2 Bin Size : 0.0148 Phase Range: 0.5800 to 0.9500 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5870 -0.318 12 0.7210 -0.391 14 0.8567 -0.382 15 0.6034 -0.334 18 0.7358 -0.389 29 0.8679 -0.372 21 0.6157 -0.351 15 0.7510 -0.361 22 0.8834 -0.361 12 0.6320 -0.356 11 0.7648 -0.370 19 0.8966 -0.369 14 0.6462 -0.351 16 0.7798 -0.393 26 0.9128 -0.354 12 0.6634 -0.366 6 0.7948 -0.403 20 0.9296 -0.339 12 0.6789 -0.382 6 0.8105 -0.389 25 0.9428 -0.332 23 0.6911 -0.391 11 0.8228 -0.392 25 0.7060 -0.385 9 0.8362 -0.374 9 Bin Size : 0.0020 Phase Range: 0.9500 to 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.9504 -0.323 2 0.9689 -0.183 3 0.9869 0.411 2 0,9530 -0.337 4 0.9710 -0.130 4 0.9887 0.469 1 0.9553 -0.331 4 0.9732 -0.041 4 0.9915 0.577 2 0.9570 -0.311 4 0.9747 -0.048 2 0.9930 0,654 1 0.9588 -0.315 5 0.9758 0.002 2 0.9948 0,711 2 0.9607 -0.315 4 0.9793 0.093 2 0.9971 0,780 2 0.9628 -0.277 3 0.9813 0.176 1 0.9994 0.806 2 0.9650 -0.255 4 0.9832 0.241 2 0.9672 -0.225 3 0.9850 0.304 1 I jui'^ #iirf-v*-f:r-^

PAGE 136

125 TABLE 16 NORMAL POINTS FOR 1966 DATA Bin Size: ; 0.0020 Phase Range: 0,0000 to 0.0800 Phase Magn. No. Phase Magn. No, Phase Magn, No. 0.0012 0.889 1 0.0289 0.973 5 0.0574 -0,011 2 0.0030 0.883 2 0.0308 0.964 5 0.0589 -0.041 3 0.0050 0.891 1 0.0329 0.891 5 0.0611 -0,082 4 0.0068 0.884 2 0.0349 0.815 5 0.0630 -0.117 2 0.0091 0.879 2 0.0359 0.729 4 0.0646 -0.142 3 0.0110 0.872 1 0.0391 0.624 4 0.0673 -0.163 2 0.0132 0.929 3 0.0412 0.538 2 0.0691 -0.165 1 0.0150 0.949 3 0.0429 0.451 3 0.0710 -0,170 2 0.0173 0.956 5 0.0451 0.359 3 0,0729 -0.164 1 0.0195 0.959 3 0.0471 0.289 3 0.0747 -0.167 2 0.0211 0.954 3 0.0489 0.227 3 0.0771 -0.170 2 0.0230 0.980 6 0.0510 0.170 3 0.0790 -0.170 1 0.0251 0.965 4 0.0530 0.097 1 0.0269 0.980 5 0.0549 0.042 2 Bin Size : 0.0148 Phase Range: 0.0800 to 0.4500 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0833 -0.169 6 0.2057 -0.180 29 0.3178 -0.246 2 0.1047 -0.161 6 0.2209 -0.185 27 0.3690 -0.243 7 0.1168 -0.173 21 0.2342 -0.192 19 0.3887 -0.250 3 0.1329 -0.172 18 0.2451 -0.207 3 0.3978 -0.256 22 0.1464 -0.175 27 0.2685 -0.211 11 0.4107 -0.277 11 0.1505 -0.171 16 0.2792 -0.222 21 0.4322 -0.267 11 0,1779 -0.173 19 0.2961 -0.248 9 0.4426 -0.268 22 0.1908 -0.180 37 0.3095 -0.262 12 Bin Size : 0.0032 Phase Range: 0.4500 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.4516 -0.259 6 0.4808 -0.240 4 0.5101 -0.181 3 0.4551 -0.281 5 0.4843 -0,223 6 0.5136 -0.172 4 0.4591 -0.276 2 0,4873 -0.213 3 0.5164 -0.185 5 0.4616 -0.287 2 0.4908 -0.227 3 0.5203 -0.181 5 0.4645 -0.287 4 0.4938 -0.193 4 0.5234 -0,181 4 0.4677 -0.267 2 0.4970 -0.192 5 0.5259 -0,183 4 0.4712 -0.257 4 0.5001 -0.175 3 0.5295 -0,188 2 0.4746 -0.258 6 0.5038 -0.173 3 0.5329 -0,193 3 0.4780 -0.249 6 0.5069 -0.189 2 0.5360 -0,221 2 T-..^.lll-^lW-^l -"Jh*-.--,-.rr-T-*J It*

PAGE 137

126 TABLE 15 Continued Bin Size : 0.0032 Phase Range: 0.4500 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5390 -0.216 3 0.5527 -0.279 2 0.5644 -0.325 1 0.5425 -0.237 3 0.5555 -0.289 6 0.5716 -0.320 3 0.5460 -0.252 3 0.5589 -0.301 5 0.5755 -0.333 2 0.5495 -0.265 3 0.5618 -0.308 4 0.5785 -0.322 3 Bin Size : 0.0148 Phase Range: 0.5800 to 0.9500 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5855 -0.339 8 0.7039 -0.341 11 0.8231 -0.282 16 0.6043 -0.324 4 0.7210 -0.328 16 0.8390 -0.257 10 0.5143 -0.349 8 0.7360 -0.334 20 0.8539 -0.272 19 0.6382 -0.330 1 0.7492 -0.327 19 0.8694 -0.250 10 0.6462 -0.324 12 0.7666 -0.320 18 0.8832 -0.241 10 0.6600 -0.338 12 0.7776 -0.325 15 0.8984 -0.240 9 0.6772 -0,334 10 0.7972 -0.311 5 0.9072 -0.234 2 0.6911 -0,345 14 0.8096 -0.304 13 Bin Size : 0.0010 Phase Range: 0.9500 to 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn, No. 0.9710 -0.091 1 0.9804 0.227 1 0.9907 0.814 0.9723 0.036 1 0.9817 0.351 2 0.9918 0.876 0.9734 0.080 2 0.9829 0.447 2 0.9931 0.958 0.9746 0.113 2 0.9843 0.518 0.9943 1.037 0.9758 0.164 2 0.9855 0.597 0.9986 0.888 0.9770 0.173 2 0.9868 0.649 0.9999 0.889 0.9782 0.230 2 0.9881 0.725 0.9793 0,256 2 0.9893 0.832

PAGE 138

127 TABLE 17 NORMAL POINTS FOR 1975V DATA Bin Size : 0.002C ) Phase Range: 0.0000 to 0.0800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0004 0.778 0.0369 0.051 2 0.0570 -0.296 3 0.0035 0.781 0.0388 -0.013 2 0.0593 -0.286 2 0.0118 0.783 0.0410 -0.088 3 0.0615 -0.292 1 0.0149 0.780 0.0434 -0.140 2 0.0631 -0.277 1 0.0173 0.748 0.0451 -0.172 2 0.0644 -0.282 1 0.0187 0.707 2 0.0463 -0.188 1 0.0351 0.081 2 0.0550 -0.299 1 Bin Size : O.OIOC 1 Phase Range: 0.0800 to 0.4200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0834 -0.279 2 0.2569 -0.300 2 0.3560 -0.354 4 0.0975 -0.267 4 0.2630 -0.311 2 0.3655 -0.367 2 0.1282 -0.281 2 0.2773 -0.308 2 0.3750 -0.373 8 0.1343 -0.293 3 0.2861 -0.305 2 0.3832 -0.376 4 0.1415 -0.289 2 0.2968 -0.317 1 0.3947 -0.384 6 0.1587 -0.279 1 0.3025 -0.321 5 0.4057 -0.396 5 0.1639 -0.282 3 0.3383 -0.333 2 0.4150 -0.391 7 0.1759 -0.286 4 0.3423 -0.360 4 Bin Size : 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn, No. Phase Magn. No. Phase Magn. No. 0.4201 -0.391 1 0.4667 -0.344 1 0.5032 -0.255 1 0.4226 -0.389 2 0.4686 -0.338 2 0.5049 -0.259 2 0.4252 -0.394 2 0.4711 -0.330 2 0.5067 -0.273 1 0.4275 -0.417 1 0.4730 -0.325 1 0.5093 -0.260 1 0.4286 -0.402 1 0.4741 -0.324 1 0.5110 -0.266 2 0.4308 -0.392 2 0.4811 -0.285 2 0.5133 -0.270 2 0.4473 -0.409 1 0.4831 -0.287 1 0.5150 -0.265 1 0.4489 -0.403 2 0.4850 -0.269 2 0.5270 -0.327 1 0.4506 -0.400 1 0.4869 -0.270 1 0.5285 -0.350 1 0.4525 -0.390 2 0.4892 -0.252 2 0.5392 -0.391 2 0.4547 -0.382 2 0.4912 -0.257 1 0.5417 -0.407 1 0.4571 -0.389 1 0.4929 -0.259 2 0.5427 -0.402 1 0.4581 -0.374 1 0.4946 -0.250 1 0.5448 -0.429 2 0.4635 -0.366 1 0.4966 -0.245 2 0.5496 -0.428 1 0.4652 -0.349 2 0.5013 -0.259 2 0.5510 -0.423 1 .Mr->*YST,in,_J£,,„— ™**.,rMrt*.l'>-'''--f -' — r-~*tT*

PAGE 139

128 TABLE 17 Continued Bin Size: 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5530 -0.438 1 0.5595 -0.436 1 0.5721 -0.424 1 0.5552 -0.438 1 0.5677 -0.441 1 0.5741 -0.435 1 0.5574 -0.429 1 0.5699 -0.436 1 0.5763 -0.438 1 Bin Size: 0.0100 Phase Range: 0.5800 to 0.9200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5864 -0.439 3 0.7070 -0.434 5 0.8470 -0.380 8 0.5952 -0.439 5 0.7148 -0.427 7 0.8551 -0.372 5 0.6018 -0.438 1 0.7211 -0.439 2 0.8647 -0.371 5 0.6585 -0.448 2 0.7425 -0.413 1 0.8766 -0.365 8 0.6648 -0.437 6 0.7925 -0.398 3 0.8849 -0.357 10 0.6747 -0.439 8 0.8084 -0.387 2 0.8907 -0.363 2 0.6893 -0.433 2 0.8125 -0.395 5 0.6952 -0.435 6 0.8357 -0.381 3 Bin Size: 0.0020 Phase Range: 0.9200 to 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.9341 -0.336 1 0.9594 -0.051 2 0.9787 0.665 0.9363 -0.336 1 0.9619 0.019 2 0.9801 0.711 0.9387 -0.339 1 0.9650 0.132 2 0.9848 0.749 0.9445 -0.319 1 0.9667 0.195 2 0.9862 0.752 0.9464 -0.309 2 0.9688 0.277 3 0.9884 0.757 0.9492 -0.267 2 0.9710 0.377 1 0.9916 0.763 0.9510 -0.244 1 0.9724 0.436 1 0.9943 0.763 0.9532 -0.208 1 0.9749 0.530 2 0.9968 0.763 0.9563 -0.138 1 0.9772 0.608 1 -ft-'rf — 4'.-i.<. r-.tT-f-.'— rr— .-

PAGE 140

129 TABLE 18 NORMAL POINTS FOR 1976V DATA Bin Size: : 0.0020 Phase Range: 0.0000 to 0.0800 Phase Magn. No. Phase Magn. No. Phase Magn No. 0.0251 0.480 1 0.0448 -0.149 2 0.0654 -0.234 3 0.0275 0.381 3 0.0464 -0.174 1 0.0672 -0.232 3 0.0289 0.326 3 0.0488 -0.211 2 0.0687 -0.235 1 0.0311 0.244 2 0.0507 -0.229 2 0.0708 -0.235 4 0.0325 0.186 1 0.0526 -0.248 2 0.0733 -0.241 1 0.0350 0.104 3 0.0546 -0.245 2 0.0749 -0.236 3 0.0380 0.002 1 0.0572 -0.257 1 0.0772 -0.236 3 0.0399 -0.036 1 0.0586 -0.247 2 0.0791 -0.231 3 0.0411 -0.071 2 0.0610 -0.240 4 0.0424 -0.107 1 0.0631 -0.240 4 Bin Size : O.OIOC 1 Phase Range: 0.0800 to 0,4200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0823 -0.239 3 0.1912 -0.258 2 0.2918 -0.340 2 0.1157 -0.225 8 0.2053 -0.261 3 0.3024 -0.363 4 0.1253 -0.223 10 0.2371 -0.294 7 0.3654 -0.400 5 0.1307 -0.228 2 0.2451 -0.302 11 0.3752 -0.404 10 0.1564 -0.237 4 0.2555 -0.315 10 0.3813 -0.413 1 0.1548 -0.238 8 0.2671 -0.324 7 0.3966 -0.413 6 0.1747 -0.245 9 0.2750 -0.329 7 0.4059 -0.415 5 0.1854 -0.255 9 0.2848 -0.336 9 0.4161 -0.416 12 Bin Size : 0.002C ) Phase R ange: 0.4200 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.4207 -0.420 4 0.4471 -0.425 2 0.4889 -0.281 1 0.4229 -0.423 4 0.4491 -0.408 2 0.4910 -0.288 2 0.4242 -0.421 1 0.4510 -0.405 3 0.4936 -0.286 2 0.4255 -0.409 1 0.4528 -0.420 0.4948 -0.284 1 0.4292 -0.425 2 0.4543 -0.419 0.4960 -0.290 1 0.4336 -0.413 1 0.4568 -0.392 0.5013 -0.279 1 0.4349 -0.413 1 0.4583 -0.398 0.5708 -0.402 1 0.4369 -0.417 2 0.4606 -0.396 0.5730 -0.412 2 0.4391 -0.417 1 0.4623 -0.373 0.5751 -0.396 1 0.4431 -0.426 3 0.4852 -0,301 0.5756 -0.395 2 0.4450 -0.429 2 0.4874 -0.297 2 rt^r--— ,r—-fll-.V— '*-^.l--^' 'f"v'''^t,mt 1' -ii*r-S'*-V*f,
PAGE 141

130 TABLE 18 Continued Bin Size : 0.0100 Phase Range: 0.5800 to 0.9200 Phase Magn No. Phase Magn. No. Phase Magn. No. 0.5847 -0.396 8 0.5989 -0.346 1 0.8356 -0.329 9 0.5918 -0.391 4 0.7049 -0.343 7 0.8444 -0.328 4 0.6078 -0.382 2 0.7153 -0.340 8 0.8547 -0.326 5 0.6159 -0.371 8 0.7217 -0.340 2 0.8648 -0.325 4 0.5295 -0.358 1 0.7334 -0.331 6 0.8730 -0.316 2 0.6357 -0.357 2 0.7494 -0.317 2 0.9195 -0.334 1 0.6475 -0.345 3 0.7563 -0.339 4 0.6549 -0.338 4 0.7611 -0.328 1 Bin Size : 0.0020 Phase Range: 0.9200 to 1,0000 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.9203 -0.329 1 0.9471 -0.243 1 0.9710 0.478 3 0.9225 -0.309 2 0.9487 -0.227 3 0.9731 0.566 3 0.9253 -0.302 2 0.9510 -0.196 3 0.9753 0.560 3 0.9275 -0.285 1 0.9530 -0.138 2 0.9771 0.724 2 0.9283 -0.283 1 0.9552 -0.089 3 0.9788 0.777 2 0.9318 -0.298 1 0.9572 -0.017 2 0.9827 0.816 2 0.9326 -0.301 1 0.9587 0.014 3 0.9851 0.829 2 0.9349 -0.321 2 0.9606 0.073 3 0.9865 0.835 1 0.9373 -0.331 2 0.9628 0.204 4 0.9957 0.845 1 0.9413 -0.286 1 0.9646 0.217 1 0.9972 0.841 2 0.9431 -0.266 1 0.9670 0.316 2 0.9985 0.850 1 0.9447 -0.288 1 0.9694 0.409 2 ill— !*•'-: -I

PAGE 142

131 TABLE 19 NORMAL POINTS FOR 1975B DATA Bin Size 0.0020 Phase Range: 0.0000 to 0.0800 Phase Magn No. Phase Magn. No. Phase Magn. No. 0.0004 1.304 0.0369 0.247 2 0.0570 -0.159 3 0.0035 1.310 0.0388 0.145 2 0.0593 -0.169 2 0.0118 1.327 0.0410 0.101 3 0.0615 -0.170 1 0.0149 1.325 0.0434 0.032 2 0.0631 -0.167 1 0.0173 1.272 0.0451 -0.012 2 0.0644 -0.175 1 0.0187 1.149 2 0.0463 -0.050 1 0.0351 0.327 2 0.0550 -0.181 1 Bin Size : 0.0100 Phase Range: 0.0800 to 0.4200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0834 -0.169 2 0.2569 -0.182 2 0.3560 -0.223 4 0.0975 -0.155 4 0.2630 -0.187 2 0.3655 -0.211 2 0.1282 -0.158 2 0.2773 -0.186 2 0.3750 -0.226 8 0.1343 -0.163 3 0.2861 -0.189 2 0.3832 -0.230 4 0.1415 -0.160 2 0.2968 -0.193 1 0.3947 -0.234 6 0.1587 -0.161 1 0.3025 -0.185 5 0.4057 -0.245 5 0.1639 -0.159 3 0.3383 -0.202 2 0.4150 -0.239 7 0.1759 -0.165 4 0.3423 -0.208 4 Bin Size : 0.002C Phase Range: 0.4200 to 0.5800 Phase Magn No. Phase Magn. No. Phase Magn. No. 0.4201 -0.236 1 0.4667 -0.198 1 0.5032 -0,129 1 0.4226 -0.237 2 0.4686 -0.203 2 0.5049 -0.135 2 0.4252 -0.240 2 0.4711 -0.194 2 0.5067 -0.151 1 0.4275 -0.243 1 0.4730 -0.193 1 0.5093 -0.121 1 0.4285 -0.247 1 0.4741 -0.188 1 0.5110 -0.151 2 0.4308 -0.248 2 0.4811 -0.152 2 0.5133 -0.160 2 0.4473 -0.252 1 0.4831 -0.165 1 0.5150 -0.147 1 0.4489 -0.245 2 0.4850 -0.152 2 0.5270 -0.178 1 0.4506 -0.238 1 0.4869 -0.147 1 0.5285 -0.203 1 0.4525 -0.242 2 0.4892 -0.132 2 0.5392 -0.249 2 0.4547 -0.235 2 0.4912 -0.131 1 0.5417 -0.253 1 0.4571 -0,229 1 0.4929 -0.131 2 0.5427 -0.256 1 0.4581 -0.217 1 0.4946 -0.139 1 0.5448 -0.267 2 0.4635 -0.213 1 0.4966 -0.128 2 0.5496 -0.246 1 0.4652 -0.208 2 0.5013 -0.145 2 0.5510 -0.273 1 „-^^.i—^^s-*_— >.-•*-' '%*• ^* '-v'^tTrT-^^^

PAGE 143

132 TABLE 19 Continued Bin Size: 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. 0.5530 -0.269 1 0.5595 -0.282 1 0.5721 -0.284 1 0.5552 -0.279 1 0.5677 -0.293 1 0.5741 -0.285 1 0.5574 -0.272 1 0.5699 -0.288 1 0.5763 -0.287 1 Bin Size: 0.0100 Phase Range: 0.5800 to 0.9200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5864 -0.282 3 0.7070 -0.265 5 0.8470 -0.232 8 0.5952 -0.279 5 0.7148 -0.268 7 0.8551 -0.233 5 0.6018 -0.285 1 0.7211 -0.271 2 0.8647 -0.229 5 0.6585 -0.274 2 0.7425 -0.272 1 0.8766 -0.217 8 0.6648 -0.277 6 0.7925 -0.254 3 0.8849 -0.215 10 0.6747 -0.275 8 0.8084 -0.245 2 0.8907 -0.235 ? 0.6893 -0.276 2 0.8125 -0.239 5 0.5952 -0.267 6 0.8357 -0.248 3 Bin Size: 0.0020 Phase Range: 0.9200 to 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn. No, 0.9341 -0.205 1 0.9594 0.149 2 0.9787 1.150 0.9363 -0.204 1 0.9619 0.235 2 0.9801 1.211 0.9387 -0.203 1 0.9650 0.379 2 0.9848 1.262 0.9445 -0.180 1 0.9667 0.458 2 0.9862 1.276 0.9464 -0.163 2 0.9688 0.572 3 0.9884 1.283 0.9492 -0.127 2 0.9710 0.713 1 0.9916 1.280 0.9510 -0.097 1 0.9724 0.789 1 0.9943 1.287 0.9532 -0.037 1 0.9749 0.943 2 0.9968 1.287 0.9563 0.050 1 0.9772 1.066 1 -—I^'

PAGE 144

133 TABLE 20 NORMAL POINTS FOR 1976B DATA Bin Size: 0.0020 Phase Range: 0.0000 to 0.0800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0251 0.865 1 0.0448 -0.015 2 0.0654 -0.115 3 0.0275 0.674 3 0.0464 -0.037 1 0.0672 -0.117 J 0.0289 0.594 3 0.0488 -0.085 2 0.0687 -0.116 i 0.0311 0.474 2 0.0507 -0.107 2 0.0708 -0.119 4 0.0325 0.409 1 0.0526 -0.121 2 0.0733 -0.121 1 0.0350 0.301 3 0.0546 -0.122 2 0.0749 -0.128 0.0380 0.187 1 0.0572 -0.131 1 0.0772 -0.117 3 0.0399 0.122 1 0.0586 -0.122 2 0.0791 -0.118 3 0.0411 0.080 2 0.0610 -0.126 4 0.0424 0.051 1 0.0631 -0.122 4 Bin Size : O.OIOC Phase Range: 0.0800 to 0.4200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0823 -0.124 3 0.1912 -0.137 2 0.2918 -0.195 2 0.1157 -0.113 8 0.2053 -0.128 3 0.3024 -0.217 4 0.1253 -0.109 10 0.2371 -0.157 7 0.3654 -0.243 b 0.1307 -0.109 2 0.2451 -0.168 11 0.3752 -0.252 lU 0.1564 -0.120 4 0.2555 -0.181 10 0.3813 -0.255 i 0.1548 -0.121 8 0.2671 -0.191 7 0.3966 -0.263 b 0.1747 -0.128 q 0.2750 -0.193 7 0.4059 -0.256 b 0.1854 -0.133 9 0.2848 -0.198 9 0.4161 -0.258 12 Bin Size : 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.4207 -0.262 4 0.4471 -0.272 2 0.4889 -0.152 1 0.4229 -0.265 4 0.4491 -0.259 2 0.4910 -0.173 2 0.4242 -0.296 1 0.4510 -0.248 3 0.4936 -0.164 2 0.4266 -0.261 1 0.4528 -0.261 0.4948 -0.146 1 0,4292 -0.261 2 0.4543 -0.266 0.4960 -0.170 i 0.4336 -0.281 1 0.4558 -0.247 0.5013 -0.174 1 0.4349 -0.268 1 0.4583 -0.247 0.5708 -0.251 i 0.4369 -0.261 2 0.4606 -0.244 0.5730 -0.249 2 0.4391 -0.257 1 0.4623 -0.236 0.5751 -0.230 i 0.4431 -0.258 3 0.4852 -0.184 0.5766 -0.251 2 0.4450 -0.271 2 0.4874 -0.172 2 -!.*-/"•^-nZ-T"'

PAGE 145

134 TABLE 20 Continued Bin Size; : 0.0100 Phase Range: 0.5800 to 0.9200 Phase Magn. No. Phase Magn No. Phase Magn No. 0.5847 -0.243 8 0.6989 -0.199 1 0.8356 -0.187 9 0.5918 -0.236 4 0.7049 -0.192 7 0.8444 -0.186 4 0.6078 -0.230 2 0.7153 -0.201 8 0.8547 -0.189 5 0.6159 -0.224 8 0.7217 -0.188 2 0.8648 -0.189 4 0.6295 -0.221 1 0,7334 -0.193 5 0.8730 -0.187 2 0.6357 -0.213 2 0.7494 -0.183 2 0.9195 -0.198 1 0.6475 -0.199 3 0.7563 -0.191 4 0.6549 -0.198 4 0.7611 -0.189 1 Bin Size : 0.002C 1 Phase Range: 0.9200 to 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.9203 -0.193 1 0.9471 -0.095 1 0.9710 0.838 3 0.9225 -0.173 2 0.9487 -0.084 3 0.9731 0.958 3 0.9253 -0.183 2 0.9510 -0.045 3 0.9753 1.098 3 0.9275 -0.150 1 0.9530 0.033 2 0.9771 1.210 2 0.9283 -0.144 1 0.9552 0.089 3 0.9788 1.277 2 0.9318 -0.173 1 0.9572 0.161 2 0.9827 1.330 2 0.9325 -0.181 i 0.9587 0.199 3 0.9851 1.349 2 0.9349 -0.182 2 0.9606 0.284 3 0.9865 1.366 1 0.9373 -0.201 2 0.9628 0.449 4 0.9957 1.385 1 0.9413 -0.183 1 0.9646 0.486 1 0.9972 1.367 2 0.9431 -0.108 1 0.9670 0.609 2 0.9985 1.358 1 0.9447 -0.131 1 0.9694 0.735 2

PAGE 146

135 TABLE 21 NORMAL POINTS FOR 1975U DATA Bin Size: : 0.0020 Phase Range: 0.0000 tc ) 0.0800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0004 1.797 1 0.0118 1.857 1 0.0173 1.710 1 0.0035 1.824 1 0.0149 1.865 1 0.0187 1.542 2 Bin Size: : 0.0100 Phase Range: 0.0800 tc ) 0.4200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.3030 -0.071 4 0.3655 -0.096 2 0.4057 -0.134 5 0.3383 -0.116 2 0.3750 -0.117 8 0.4150 -0.134 7 0.3423 -0.120 4 0.3832 -0.123 4 0.3550 -0.102 4 0.3947 -0.118 5 Bin Size : 0.0020 Phase Range: 0.4200 to 0.5800 Phase Magn No. Phase Magn. No. Phase Magn. No. 0.4201 -0.129 1 0.4635 -0.130 1 0.4912 -0.026 1 0.4226 -0.130 2 0.4652 -0.110 2 0.4929 -0.027 2 0.4252 -0.119 2 0.4667 -0.114 1 0.4946 -0.036 1 0.4275 -0.108 1 0.4686 -0.103 2 0.4966 -0.029 2 0.4286 -0.128 1 0.4711 -0.101 2 0.5013 -0.055 2 0.4308 -0.135 2 0.4730 -0.102 1 0.5032 -0.015 1 0.4473 -0.118 1 0.4741 -0.116 1 0.5049 -0.028 2 0.4489 -0.122 2 0.4811 -0.078 2 0.5057 -0.068 1 0.4506 -0.148 1 0.4831 -0.050 1 0.5093 -0.044 1 0.4525 -0.128 2 0.4850 -0.056 2 0.5110 -0.054 2 0.4547 -0.118 2 0.4869 -0.067 1 0.5133 -0.052 2 0.4571 -0.116 1 0.4892 -0.055 2 0.5150 -0.042 1 0.4531 -0.101 1 0.4912 -0.026 1 Bin Size : O.OIOC 1 Phase Range: 0.5800 to 0.9200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.6585 -0.172 2 0.7070 -0.144 5 0.8771 -0.095 6 0.6648 -0.143 5 0.7148 -0.141 7 0.8849 -0.113 5 0.6747 -0.154 8 0.7211 -0.152 2 0.8907 -0.124 2 0.6893 -0.150 2 0.8084 -0.122 2 0.6952 -0.154 6 0.8125 -0.115 5 i.-r*.l,>-1IH*'>i'T

PAGE 147

136 TABLE 21 Continued Bin Size : 0.0020 Phase Range: 0.9200 tc 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.9462 -0.045 0.9670 0.722 1 0.9801 1.707 0.9497 0.027 0.9690 0.851 2 0.9848 1.753 0.9532 0.076 0.9710 0.983 1 0.9862 1.748 0.9563 0.191 0.9724 1.101 1 0.9884 1.788 0.9591 0.290 0.9749 1.298 2 0.9916 1.812 0.9619 0.422 0.9772 1.473 1 0.9943 1.793 0.9658 0.646 0.9787 1.584 1 0.9968 1.775 t *! — i K" .r-t-

PAGE 148

137 TABLE 22 NORMAL POINTS FOR 1976U DATA Bin Size : 0.0020 Phase Range: 0.0000 to 0.0800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.0251 1.133 1 0.0448 0.091 2 0.0654 -0.019 3 0.0275 0.932 3 0,0464 0.057 1 0.0672 -0.044 3 0.0289 0.821 3 0.0488 0.019 2 0.0687 -0.026 1 0.0311 0.661 2 0.0507 0,004 2 0.0708 -0.037 4 0.0325 0.581 1 0.0526 -0.008 2 0,0733 -0.035 1 0.0350 0.466 3 0.0546 -0.020 2 0.0749 -0.046 3 0.0380 0.324 1 0.0572 -0.026 1 0.0772 -0.044 3 0.0399 0.249 1 0.0586 -0.030 2 0.0791 -0.042 3 0.0411 0.207 2 0.0610 -0.037 0.0424 0.161 1 0.0631 -0.027 Bin Size : O.OIOC ) Phase Range: 0.0800 to 0.4200 Phase Magn, No. Phase Magn, No. Phase Magn. No. 0.0823 -0,042 3 0,1912 -0.047 2 0.2918 -0.119 2 0.1157 -0,035 8 0.2053 -0.058 3 0.3024 -0.102 4 0.1253 -0,042 10 0,2371 -0.062 7 0,3654 -0,144 5 0.1307 -0.047 2 0.2451 -0.077 11 0,3752 -0,138 10 0.1564 -0.034 4 0.2555 -0.074 10 0.3813 -0,137 1 0,1648 -0.037 8 0.2671 -0.084 7 0.3966 -0,153 6 0.1747 -0.031 9 0.2750 -0.087 7 0.4059 -0.147 5 0.1854 -0.041 9 0,2848 -0.094 9 0,4161 -0.128 12 Bin Size : 0.002C ) Phase Range: 0.4200 t 0.5800 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.4207 -0.139 4 0.4471 -0.154 2 0.4889 -0.080 1 0,4229 -0,150 4 0.4491 -0.145 2 0.4910 -0.089 2 0.4242 -0.215 1 0,4510 -0,156 3 0.4936 -0.063 2 0.4266 -0.113 1 0.4528 -0.145 0.4948 -0.060 1 0.4292 -0.164 2 0.4543 -0.175 0.4960 -0.094 1 0.4336 -0.147 1 0.4568 -0.155 0.5013 -0.084 1 0.4349 -0.133 1 0.4583 -0.124 0.5708 -0.103 1 0.4369 -0.120 2 0.4606 -0.105 0.5730 -0.131 2 0.4391 -0.164 1 0.4623 -0.103 0.5751 -0.121 1 0.4431 -0.122 3 0.4852 -0.075 0.5766 -0.139 2 0.4450 -0.157 2 0.4874 -0.091 2 riUI*;-^|s?>^*-Vs.j-F > r--

PAGE 149

138 TABLE 22 Continued Bin Size : 0.0100 Phase Range: 0.5800 to 0.9200 Phase Magn. No. Phase Magn. No. Phase Magn. No. 0.5847 -0.133 8 0.6989 -0.049 1 0.8356 -0.065 9 0.5918 -0.127 4 0.7049 -0.082 7 0.8444 -0.076 4 0.6078 -0.119 2 0.7153 -0.081 8 0.8547 -0.076 5 0.6159 -0.109 8 0.7217 -0.089 2 0.8648 -0.071 4 0.6295 -0.125 1 0.7334 -0.092 6 0.8730 -0.081 2 0.6357 -0.110 2 0.7494 -0.057 2 0.9195 -0.089 1 0.6475 -0.080 3 0.7563 -0.089 4 0.6549 -0.096 4 0.7611 -0.061 1 Bin Size : 0.0020 Phase Range: 0.9200 to 1.0000 Phase Magn. No. Phase Magn. No. Phase Magn, No. 0.9203 -0.090 1 0.9471 -0.002 1 0.9710 1.139 3 0.9225 -0.082 2 0.9487 0.016 3 0.9731 1.316 3 0.9253 -0.065 2 0.9510 0.073 3 0.9753 1.480 3 0.9275 -0.084 1 0.9530 0.172 2 0.9771 1.571 2 0.9283 -0.060 1 0.9552 0.218 3 0.9788 1.762 2 0.9318 -0.054 1 0.9572 0.308 2 0.9827 1.850 2 0.9326 -0.041 1 0.9587 0.365 3 0.9851 1.873 2 0.9349 -0.051 2 0.9606 0.462 3 0.9865 1.888 1 0.9373 -0.094 2 0.9628 0.616 4 0.9957 1.902 1 0.9413 -0.093 1 0.9646 0.675 1 0.9972 1.884 2 0.9431 0.007 1 0.9670 0.832 2 0.9985 1.870 1 0.9447 -0.087 1 0.9694 1.030 2 R-^^lt^i— .MA.-fW .^T''*-^

PAGE 150

CHAPTER VI DISCUSSION Introduction The topic of this, the last chapter, will be the implications of the data presented in the foregoing five chapters. First, the properties of the distortion wave will be considered. The dates of maximum and minimum light will be computed. The resulting quantities will be referred to as MOD and iMJD respectively. From these values it will be possible to compare the peak-to-peak amplitude for each of the 11 light curves under investigation. The values for the phase at minimum and the amplitude of the distortion wave can then be compared with those in Hall (1972, 1975a). By taking advantage of the complication in the distortion wave around secondary eclipse due to the non-uniform intensity of the surface on the KO (star B) component an estimate of the temperature of the starspot will be made. The discussion of the distortion wave will conclude with some comments about the nature of the phenomenon. The problems associated with the non-uniform period changes will be considered. The existence of short-term period variations, first pointed out by Hall (1972, 1975a), are not confirmed by the more accurate and realistic WAVE procedure model. The much longer period variations remain unexplained, at least in classical terms. The Distortion Wave The value of the phase at maximum and minimum light of the distortion wave are listed in Table 11. It would be more convenient if 139

PAGE 151

140 these values were not dependent on the ephemeris which was used to compute the phases for the construction of the light curves. As a first step in this direction, new estimates for the times of minimum (MJD ) were computed for each light curve. These values for MJD are listed in Table 23. They were computed by using the value of T (from Table 11) to correct the time predicted by the linear ephemeris (equation 4). The published values of the times of minimum (Catalano and Rodono 1974) for the Catania data were used as a guide in establishing the number of orbital cycles. For the light curves of 1975 and 1975 a value, MJD, was computed by averaging the observed dates of primary minimum, weighted by the square root of the number of points on each date. This value was then used to compute a cycle number, and thus a value of MJD for each of these six light curves, by incorporating the appropriate values of T from Table 11. The next step in computing estimates for the dates of maximum and minimum light of the distortion wave (MJD and MJD ) involved ^ max min^ the calculation of the number of days after MJD that these events occurred. From Table 11 the values of 9 • and 9 can be obtained. min max By multiplying these values by the period (4.797855) used in the linear ephemeris, the appropriate delay (in days) was obtained. This would have been somewhat inaccurate because 9 and 9 from Table 11 are min max dependent on the linear ephemeris. To reduce this effect, the appropriate value of T was added to the phase before it was multiplied by the period. The resulting phase values are listed in Table 23 as 9". and ^max" '^^^ values of MJD^.^ and MJD^^^ are also listed in Table 23. The values that were computed by this method are more reliable than previously publ ished values. H irri*--r --.^ I*

PAGE 152

141 TABLE 23 TIMES OF MINIMA AND CHARACTERISTICS OF THE DISTORTION WAVE l:^"9h^ ^ ._ ^jO ^jO Wave Amp. Curve rrnn mm max max Av 1921 0.832 0.211 -0.15 1963 38145.176 0.408 38147.134 0.991 38149.931 -0.18 1964 38557.785 0.355 38559.488 0.953 38562.357 -0.22 1965 38888.828 0.323 38890.378 0.774 38892.542 -0.16 1966 39215.071 0.182 39215.944 0.600 39217.950 -0.17 tl975v 42491.939 0.181 42492.807 0.556 42494.607 -0.20 1975b 42491.939 0.186 42492.831 0.557 42494.611 -0.14 1975U 42491.935 0.147 42492.640 0.542 42494.535 -0.14 tl976v 42870.962 0.141 42871.639 0.464 42873.188 -0.22 0.767 42874.642 1976b 42870.962 0.143 42871.648 0.463 42873.183 -0.17 0.762 42874.518 1976U 42870.963 0.142 42871.644 0.459 42873.165 -0.14 0.753 42874.624 Notes for Table 23. These values were not computed because the accuracy of the original data did not warrant the calculation. t The period from the times of minima of these two light curves is 4.797758 0.000010 days. The amplitude of the distortion wave has also been calculated using the results from the WAVE procedure. Using the Fourier coefficients in Table 11 and the values of distortion wave minimum and maximum from Table 11, the amplitude in magnitudes was computed. The results are listed in Table 23 as Av (this is the peak-to-peak amplitude). The values are in excellent agreement with those in Table 1 of Hall's (1972) paper. Unfortunately, the agreement with Hall's paper ends there. '•*•*uifi k ^' <-'[ -"-^-Tirt* St— *j i)pitln-

PAGE 153

142 -0.00 2000 3000 /fOOO Fig 22. -The visual band amplitude of the distortion wave plotted as a function of the orbital cycle (E) from Hall (1972). Hall predicted that the variation in amplitude of the distortion wave was the result of a 23J5-year "sunspot cycle" operating in the subgiant of the system. Fig. 22 shows a plot of distortion wave amplitude in the visual band. The filled circles are from Hall's (1972) paper, while the crosses are from Table 23. The abscissa is plotted using Hall's emphemeris. The solid line is the functional dependence predicted fay the 1800 orbital cycle (23Vyear) "sunspot cycle." Note that the new observations are in direct conflict with the predictions, but the new estimates of the amplitude from the Catania data agree very well with Hall's graphical estimates. This is circumstantial evidence that the phenomenon in RS CVn is not the same, in all respects, as that known as sunspots. Both effects are probably surface phenomena resulting in a non-uniform surface brightness, but they are quite different in other ways. Another consequence of Hall's "sunspot" model was a periodic variation in the migration rate of the distortion wave. The data for 1975 and 1976 are again in conflict with the extrapolation of this relationship. Hall plotted the phase of distortion wave minimum as a function of orbital cycles. The difference between the observed

PAGE 154

143 Fig, 23. -The phase of distortion wave minimum versus orbital cycle. Filled circles are from Hall (1972), while crosses are from the 1975 and 1976 data presented here. In the lower part are plotted the residuals from Hall's uniform migration rate equation for the distortion wave. value of 6„. and a uniform rate was also plotted. In Fig. 23, Hall's min 3 3 plots have been extended. The period of the variation in the distortion wave amplitude (1800 orbital periods) and the discontinuities in migration rate at E = and E = 1800 led Hall to believe that the photometric phenomenon was similar to the sunspot cycle in our sun. The amplitude variation was considered akin to the variation in sunspot number, while the nonuniform migration rate of the distortion wave was considered to be the result of "sunspot" migration form high latitudes towards the equatorial region. In the sun the latter characteristic is represented by the familiar butterfly diagram: Hall discusses this in somewhat

PAGE 155

144 more detail. Since the analogy with the sunspot has not withstood observational testing, a more detailed discussion will not be given. The distortion wave in RS CVn is not the result of a phenomenon similar in all respects to sunspots; at least the similarity is not as great as it was originally portrayed. The distortion wave is almost certainly caused by temperature variations on the surface of the cooler star of the system. If the size of the cooler region is larger than the disk of the smaller star as the transit is viewed from earth, then an estimate for the temperature in the cooler region can be made. In addition, the amplitude of the distortion wave also gives an estimate of the temperature variations. The latter approach will be considered first. The average temperature of star B (Tp) and the normalized apparent luminosity (In) can be used to estimate the value of a in the following relation: (8) 'b'-'-^ ~ '^'^B B" The value for Tg, r^, Ig and QM are taken from Tables 10 and 11, and -14 give an average value of 1.8 x 10 for a (in units of the comparison star's energy output per unit orbital radii squared per degree Kelvin to the fourth power). The maximum temperature on the KG star can be estimated by assuming that the hemisphere facing the earth at the maximum of the distortion wave is not spotted. This value is approximately 5000K, with a range from 4900K (1963) to 5100K (1975v). Similarly, the temperature of the cooler region can be estimated to be about 4400 K. Another way to estimate the maximum temperature of star B is to assume that the hemisphere facing the earth during secondary eclipse in ^tr^i-. 'fi^-Jf; >i-i..

PAGE 156

145 1975 and 1976 was the brighter unspotted hemisphere. The smaller star will then block more light than the WINK model predicted for star B with an average temperature of !„. This method gives a temperature of approximately 5100K. This is the same as the previous method and would therefore give the same temperature for the cooler region as before. The temperature of the spotted region can be estimated by making similar assumptions as were made above. In actuality the estimates are only upper limits on the temperature of the cooler region. The upper limit on the temperature for a spot covering one hemisphere is (from the brightness of star B at distortion wave minimum, as was computed above) 4400K, The probing effects of the smaller star during transit can be put to advantage only for the 1963 light curve. In this case the upper limit for a spot larger than the apparent disk of star A is 4400K. The similarity in value from the two estimates would indicate that the size of the active region is almost the size of one hemisphere of star B. In addition, it indicates that the spotted area is probably symmetrical with the equator of star B, unless it is so asymmetric as to be entirely on one side of the equator of star B. Before leaving the subject of spots it is important that the reader differentiate between the spots of RS CVn and those of the sun. The phenomenon observed on the sun may be quite different from that in RS CVn,. The term "spot" has been used because it is convenient and it conveys the idea of a region of lower temperature surrounded by a hotter photosphere. The shape of this region is not circular, necessarily. This is demonstrated by the shape of the distortion wave in the 1963 light curve. The shape of the spot on the KO star would

PAGE 157

146 LONGITUDE Fig. 24. -The shape of the spot is indicated by the shaded area. be something like that shown in Fig. 24. This shape is indicated because the light curve for 1963 is more of a "saw tooth" than a sine wave. Since the distortion wave is never flat at maximum in any of the light curves studied so far it is necessary -that the spotted region extend at least 180 degrees in longitude on the star. It is also apparent from the double minimum in 1976 (see Fig. 17 in Chapter V) that the concentration of spots is not limited to the region which migrates (approximately) uniformly. The significance of this is not clear, but certainly any model devised to explain the photometric distortion wave must be capable of reproducing the rapid changes in the detailed shape of the distortion wave. This is best visualized by comparing the changes in shape from 1975 to 1976 (see Figs. 16 and 17), or the changes from 1963 and 1964 (Figs. 12 and 13). The radial pulsation of star B cannot be resposible for the photometric distortion wave. If the pulsation of starBis assumed, then it would cause a change in system brightness and a subsequent change in the radius of star B. In order for a change in only the radius to

PAGE 158

147 cause the observed amplitude of the distortion wave, the radius would have to change by approximately 20%. The data studied here represents only about a quarter of a migration cycle, thus a change of about 5% should present itself if radial pulsation is the cause of the distortion wave. The variation in an in the computer runs of step 11 in Chapter V show a 2% variation, at the most. Additional, and higher quality data could improve the confidence with which radial pulsation is rejected as a cause for the distortion wave. However, the results here are reasonably convincing that radial pulsation, from observational data, is not responsible for this anomalous photometric behavior. Obscuration of the light from the KO star by intervening material as an explanation for the distortion wave has been rejected by Oliver (1974, 1975). Other possible explanations include non-radial pulsation, unusual convection patterns, magnetic effects (as in sunspots), and "something else." Time will perhaps eventually show what is the correct explanation. Orbital Period Variations The short-term period variations in RS CVn have been attributed to mass ejection by Hall (1972, 1975a). Hall claimed that mass was being ejected from the brighter hemisphere of star B. When this hemisphere was facing in the direction of orbital motion it would tend to reduce the period. In Fig. 25 are plotted the times of minima as corrected by Hall (1975a) for the effects of the distortion wave, and the times of minima as they appear in Table 23. Hall's estimates are the filled circles, while those from Table 23 appear as crosses. The data in Fig. 25 are from Catalano and Rodono (1974), and were published as times of minima. Hall corrected these values by

PAGE 159

148 !— -1 r — r— \ 1 r— +0.02 ; 1 f + + • a 0.00 • • • m 2-0.02 — • • • • u ^ •a o -0.04 -i. 1 E 1 i 1 _600 -400-200 200 400 600 800 Fig. 25, -The 0-C curve of RS CVn based on photoelectric times of minima. Filled circles are points corrected for the distortion wave effects by Hall (1975a). Crosses are points as computed in this dissertation. Arrows indicate when the period is predicted to decrease and increase according to Hall (1972, 1975a). estimating the effect of the distortion wave on the actual times of conjunction. The WAVE procedure has accomplished the same thing (albeit with more effort) with greater accuracy. Unfortunately, it was only possible to do this with the published data for 1953, 1964, 1965, and 1966, and of course, the 1975 and 1976 data obtained by the present writer. The arrows indicate when Hall predicts an increase (or decrease) in orbital period due to the mass ejection from the brighter hemisphere. Note that with the change of the single point for 1966 the variation becomes less obvious. In addition, the predicted decrease apparently did not occur in 1975 or 1975. It would appear that Hall's model for the short-term period variations is on "thin ice." >i-aaiVrm-^-K,-^^^A'^'^-.-^.A^^.

PAGE 160

149 It is difficult to imagine that the short-term variations which appear to remain are observational error. This is, however, a possibility. If they are indeed real, then an adequate explanation would probably follow along similar lines to those of Hall, but with less reliance on the sunspot analogy. On the other hand, it would be expected that both stars are losing mass via a stellar wind, since they are very similar in age and mass. If this is the case, then variations in the difference in the loss rates might cause the short-term period changes. The data presented here do not show that any short-term variations exist. If they do not, the mechanism for the much longer term variations also vanishes. Here again, a stellar wind may be operating in one or both stars to cause the Calmost) periodic 0-C variations. If this cannot account for the variations, then it may be necessary to return to the consideration of a yery under-luminous third body, such as a white dwarf, neutron star, or black, hole. The latter two possibilities are highly unlikely. Conclusion Additional light curves of RS CVn have been obtained as a result of this research. They are the first complete light curves in more than one color to be published. The light curve for 1976 has shown a previously unknown characteristic of the system, namely, that the distortion wave can consist of more than one minimum. The 1976 distortion wave also shows an amplitude as large or larger than any previously published. The computer program WINK and associated programs which comprised the WAVE procedure have provided a set of elements which are better than any previously obtained. The technique has also provided a mathematical characterization of the distortion wave which can be treated by less complicated models than are currently being used (Eaton 1977). This T^'-J^*i—irY-t'-

PAGE 161

150 simplification is due to the less complicated case of studying the phenomenon of the distortion wave with the "complication" of the eclipses removed, or nearly removed. The additional light curves and improved solution method have added more weight for the rejection of radial pulsation as the source of the distortion wave. Popper (1961) had far too little information with which to investigate the question. Catalano and Rodono (1968) perhaps had sufficient data, but they lacked a better and more efficient method of solution. Hall (1972) was in a similar predicament. Now, however, a measurement of the radius of star B to sufficient accuracy is possible. The analysis of the data has shown that the needed variation in Vn is D not seen. Confirmation of this with additional data is desirable in order to confirm that radial pulsation is not responsible for the distortion wave. The constancy of the comparison star BD+35 2420 has been confirmed (see Fig. 5) The analogy between the nonuniform surface brightness on the KO star of RS CVn and classical sunspots has been shown to be over-rated. The amplitude of the distortion wave does not appear to follow a quasiperiodic variation as closely as does the number of sunspots on the sun. Furthermore, the nearly-periodic variation in the migration rate of the distortion wave did not continue into 1975 and 1976 as was predicted. The migration rate was nearly constant from 1963 through 1976, showing a slight decrease in rate rather than the predicted increase. Finally, the short-term period variations which were considered an integral part of the sunspot analogy were not seen in the data used in this investigation. In fact, a new ephemeris can be computed for the Catania and 197576 data studied here. The resulting ephemeris.

PAGE 162

151 (9) MJDo = 42870.952 + 4'?797752E, indicates that tfie orbital period from 1953 to 1976 was nearly constant. The maximum deviation from the observed times of minima in Table 23 is 6 minutes (0.004 days) for the 1966 light curve. The shape, temperature, and life-time of the spots have been estimated. The shape of the distortion wave is frequently a "saw tooth" which implies a triangular or tapered shape (see Fig. 24). The upper limit for the temperature of the spotted region has been set at 4400K. The development time for a large-scale spot must be approximately one year. The smaller minimum in the distortion wave was clearly visible in 1976, but there was only a hint of its existence in 1975. In addition, an estimate of the surface temperature on the unspotted photosphere was made; it was 5100K. Additional research is needed before a complete model for RS CVn can be developed. High time-resolution photometry and spectroscopy in the optical region is desirable and would be especially useful during eclipses. Secondary eclipse could yield more information about the nature of the spots, i.e. uniform versus blotchy spots and a more detailed map of the distribution of the spot. Primary eclipse could provide information on the atmosphere of the KG star from observations during the four contact points. Of course, observations in other spectral regions would provide needed information. In addition, more information from the X-ray and radio regions would be helpful in determining if the distortion wave phenomenon is associated witK the amission at these wavelengths. You have not heard the last from RS CVn binaries.

PAGE 163

APPENDIX

PAGE 164

APPENDIX DIFFERENTIAL MAGNITUDES AND COLORS OF RS CVN HELIQ. MJD D(v) D(b-v) D(u-b) 42459.18048 42469. 19367 42469.20756 42469.22527 42469.27666 42469.29298 42469.31659 42469.33812 42469.37840 42469.39576 42477.23415 42477.24457 42477. 25603 42477.23380 42477. 29422 42477.30464 42477.31540 42477.35707 42477.36714 42477.37825 42477.33867 42477.39874 42478. 15986 42478,17132 42478.18278 42478. 19111 42478,20952 42478.22236 42478.23591 42478.31160 42478, 32375 42478.33660 42478.34945 42478.37619 42478.38799 42478.40014 42478.41264 42480.07865 42480.08594 4248C. 13351 42480,14115 42480,14913 42480.15399 42480.16198 42480. 16615 42480. 1S733 42480, 19393 42480.20365 42480. 21406 42480,22448 42480.23455 42480,27379 42480,28455 42480,29497 42480.30469 153 0.298 0.301 0.316 0.306 0,313 0.0829 0. 1532 0. 1243 0. 1235 0, 1229 0.304 0.303 0,308 0,317 0.309 0. 1212 0,1230 0, 1088 0. 1244 0. 1270 0,335 0.336 0.3 39 0.319 0,303 0.1310 0. 1320 0. 1360 0. 1390 0. 1442 0.272 0,244 O.0 42 0.025 0.099 0. 1345 0. 1470 0. 1941 0.2014 0.2270 0,177 0.255 0,279 0,282 0.300 0,2530 0. 2796 0.1186 0. 1265 0. 1316 0,291 0.287 0.291 0,288 0.279 0, 1290 0,1293 0. 1381 0.1207 0. 1183 0.280 0,277 0.289 0.288 0.2 85 0.1232 0. 1235 0.1216 0. 1162 0.1226 0.284 0.,287 0,327 0,350 0.382 0, 1213 0. 1238 0. 1493 0. 1473 0, 1347 0.400 0,407 0.402 0.425 0.433 0. 1499 0. 1536 0.1461 0. 1683 0.1548 0.428 0.423 0.438 0.438 0,429 0. 1822 0.1492 0. 1599 0.1591 0. 1570 0,436 0,441 0.436 0.424 0,435 0. 1540 0,1481 0. 1486 0. 1401 0. 1496

PAGE 165

154 APPENDIX Continued HELIO. MJD D(v) D(b-v) D(u-b) 42480,31545 42480.35434 42480. 36407 42480.37344 424 80.38143 -0.438 -0.438 -0,436 -0.442 -0.435 0. 1508 0.1590 0.1544 0. 1564 0.1538 42480.39671 42480.40678 42480,41719 42480.42761 42480.43758 -0.440 -0.440 -0.442 -0.436 -0.438 0. 1607 0.1683 0. 1537 0.1560 0. 1538 42486. 14052 42486,14990 42486.16136 42486.34747 42486.35719 -0.402 -0.385 -0.408 -0.387 -0.378 0. 1466 0. 1305 0.1560 0. 1308 0. 1243 42486.36830 42486,39678 42486,40962 42491.20340 42491.20583 -0.377 -0.371 -0.369 -0.394 -0.387 0. 1421 0. 1492 0, 1383 0,1490 0. 1628 42491,21034 42491.21451 42491,21833 42491.22215 42491.22631 -0.396 -0.364 -0.380 -0.380 -0.371 0.1627 0. 1488 0. 1425 0.1349 0.1301 42491.23499 42491. 24472 42491.26485 42491,27145 42491,27492 -0.370 -0.376 -0.372 -0.372 -0.375 0. 1364 0.1375 0. 1424 0. 1478 0. 1394 42491.28569 42491.29437 42491,30409 42491.31347 42491.32319 -0.367 -0.372 -0,376 -0.367 -0.365 0. 1417 0. 1477 0. 1423 0, 1423 0. 1476 42491.36728 42491.37701 42491.39124 42491.39437 42491.40305 -0.364 -0.359 -0.348 -0.345 -0.360 0. 1465 0. 1462 0. 1277 0.1303 0. 1453 42492.10930 42492.11520 42492. 11902 42492.12284 42492. 12770 0,100 0.062 0.056 0.046 -0.009 0.2334 0.2593 0.2172 0, 1758 0. 1740 42492. 13222 42492, 13638 42492.14090 42492. 14472 42492. 14992 -0.016 -0,055 -0.091 -0.117 -0.135 0. 1431 0.1763 0. 1849 0.2046 0, 1777 42492. 15409 42492.15791 42492. 16242 42492. 16624 42492.20756 -0.145 -0-169 -0.175 -0.188 -0.299 0.1665 0. 1716 0. 1483 0. 1380 1 1 83

PAGE 166

155 APPENDIX Continued HELIO. MOD D(v) D(b-v) D(u-b) 42492.21277 42492.21798 42492.22180 42492,22597 42492.23048 42492.23881 42492.24645 42492.25305 42492.34229 42492.34541 42492.40548 42492.40895 42492.41381 42492.41798 42505, 10190 42506.07931 42506,09593 42506.11299 42506, 12757 42506.14112 42506.15466 42506,17341 42506. 17931 42506.18528 42506.19181 42506. 19813 42506.20507 42506.21389 42506,21986 42506,22778 42506.23542 42506,24181 42506.26473 42506.27097 42506, 28174 42506.29702 42506.30986 42506.32202 42506.33938 42506.35431 42506.39389 42506.40882 42506,42062 42506.42444 42506.42965 42508.08344 42508.09872 42508.1 1315 42508, 11802 42508.12837 42508, 13344 425C8. 14080 42508, 14573 42508. 15413 42508. 15934 0.291 0.294 0,304 0.283 0,289 0, 1307 0. 1251 0. 1253 0. 1106 0. 1241 0.292 0,277 0.282 0,280 0.279 0. 1213 0.1101 0. 1070 0, 1172 0. 1043 0.273 0,263 0,267 0.263 0,413 0.1058 0. 1051 0.1023 0. 1317 0.1407 0.315 0,262 0.208 0.138 0,061 0,1487 0. 1448 0. 1710 0.1879 0.2058 0.1215 0.1442 0. 1132 0.1410 0.1445 0.013 0.165 0,214 0,266 0.312 0.2307 0.2684 0,2723 0.2858 0.3203 0.1787 0.2131 0,2358 0,2569 0,2622 0.377 0.436 0,507 0,554 0.6 08 0.3355 0.3 532 0.4036 0.4235 0,4584 0,2708 0.3120 0.3385 0,3714 0.4066 0,665 0.711 0.749 0.752 0.7 57 0,4846 0.4992 0.5138 0.5 233 0.5262 0.4343 0,4965 0,4909 0,4725 0.5047 0.753 0.763 0.763 0.778 0.781 0.5164 0. 5242 0.5235 0.5260 0.5288 0.5327 0.5060 0.4879 0.4929 0.5138 0.783 0.7 80 0,748 0.705 0,709 0. 5435 0.5457 0,5236 0.4860 0.3996 0,5309 0.5396 0.4377 0,3801 0.4042 0.369 0.366 0.367 0,361 •0.368 0. 1683 0.1451 0. 1540 0. 1396 0. 1479 0. 1121 0.1179 0,1257 0.0911 0,1110 G.368 0.373 0,370 0.392 0.386 0. 1459 0. 1495 0. 1416 0. 1497 0. 1479 0.0977 0.1113 0.0977 0,1167 0.1195

PAGE 167

156 APPENDIX Continued HELIO. MJD D(v) D(b-v) D(u-b) 42508.16760 42508. 17247 42508. 17983 42508,18469 42508.21295 -0.377 -0.376 -0.372 -0.379 -0.385 0. 1466 0. 1391 0,1488 0. 1502 0. 1508 0,1137 0,0969 0.1226 0.0950 0.1153 42508.21837 42508.22608 42508.23163 42508.24670 42508.25198 -0.379 -0.386 -0.387 -0.385 -0-383 0. 1480 0. 1571 0. 1545 0. 1481 0. 1424 0.1001 0.1214 0.1055 0.1257 0. 127 1 42508.25899 425C8. 27739 42508.23434 42508.29719 42508.30184 -0.3 98 -0.400 -0.383 -0.403 -0.396 0,1600 0, 1501 0. 1402 0. 1583 0.1477 0.1443 0.1020 0.0859 0.1188 0.1055 42508.31066 42508.31538 42508.32274 42508.32760 42508.33586 -0.388 -0.397 -0.387 -0.384 -0.396 0. I486 0. 1586 0. 1492 0.1469 0. 1613 0.1026 0,1159 0.1106 0.0922 0.1037 42508.34052 42508.34830 42508.35288 42508.36246 42508.36760 -0.392 -0,393 -0.391 -0.387 -0.391 0. 1491 0, 1507 0.1544 0, 1569 0. 1472 0.0992 0.1125 0.106 9 0.1093 0.1037 42508.37496 42508.38003 42508.38850 42508.39364 425C8. 40149 -0.395 -0.393 -0.417 -0.402 -0.398 0. 1556 0.1531 0.1735 0. 1554 0. 1519 0.1231 0.1185 0.1351 0.1191 0.1096 42508.40684 42515.32958 42515.33340 42515.34090 42515.34610 -0.386 -0.362 -0.363 -0.375 -0.365 0, 1352 0, 1475 0. 1488 0. 1536 0. 1434 0.1149 0.1197 0.1250 0.1302 0.1193 42515.35256 42515.35694 42515.36353 42515,36791 42515.37464 -0,363 -0.360 -0,370 -0.362 -0,355 0, 1479 0,1430 0.1593 0.1528 0. 1452 0,1255 0.1167 0.1120 0.0969 0.1084 42515,37902 42515,39826 42515.40159 42515.40638 42515.41062 -0.361 -0.357 -0.351 -0.3 59 -0.363 0. 1509 0. 1358 0.1225 0. 1291 0. 1282 0.0802 0.1260 0.0898 0.1123 0,1099 42518.07935 42518,08373 42513,09039 42518.09505 42518, 10192 -0,409 -0,401 -0,405 -0.400 -0.395 0. 1574 1 5 95 0. 1534 0.1624 0. 1471 0,1340 0.1217 0.1269 0.0895 0.1195 42518. 10536 42518,11289 42518, 11678 42518.12616 42518. 13095 -0.385 -0.387 -0.377 -0.389 -0.374 0. 1498 0. 1518 0. 1428 0. 1599 0. 1574 0,107 0.1278 0.1052 0. 1132 0.1156

PAGE 168

157 APPENDIX Continued HELIO. MJD D(v) D(b-v) D(u-b) *42518. 15678 42518. 16157 42518. 16817 42518.17254 42518.17935 -0.366 -0.342 -0.356 -0.344 -0.345 0.1530 0. 1385 0. 1441 0. 1 463 0. 1388 0,0833 0.0903 0.1048 0.0840 0.1158 42518. 18379 42513. 19101 42518.19560 42518.20268 42518.20782 -0,332 -0.334 -0.326 -0,325 -0,324 0. 1318 0. 1386 0.1335 0. 1323 0. 1354 0.0842 0.0972 0.0897 0,0908 0.0729 42518.23907 42518.24393 42518.25122 42518.25580 42518.25421 -0.289 -0.281 -0.287 -0.275 -0.262 0.1274 0. 1192 0.1215 0. 1230 0. 1101 0.0837 0.0849 0.1155 0. 1053 0.0862 42518.26900 42518.27789 42518.28247 42518.28983 42518,29441 -0.270 -0,2 49 -0.255 -0.257 -0,262 0.1238 0. 1228 0. 1183 0.1252 0. 1209 0.0795 0.0752 0.0788 0.1050 0.0964 42518.30115 42518.30629 425 18. 31315 42518.31782 4 2518.33 559 -0.257 -0.250 -0,250 -0.240 -0,269 0. 1353 0. 1115 0. 1184 0. 1160 0.1137 0.1132 0.1026 0.1005 0.0961 0.1052 42518.34094 42518,34740 42518.35219 42518.35893 42518.36405 -0.2 49 -0.255 -0.257 -0.261 -0.273 0. 1151 0.1264 0. 1269 0.1209 0. 1218 0.0737 0.1135 0.0948 0.1186 0.0830 42518.37649 42518,38101 42518.38823 42518.39392 425 18.39823 -0,260 -0,261 -0,270 -0.265 -0.275 0. 1385 0. 1054 0. 1245 0. 1034 0. 1176 0.0775 0.0801 0.1136 0.1099 0.1051 42518,40420 42519.09015 42519.09460 42519, 10723 42519.11210 -0.265 -0.449 -0.448 -0.432 -0.428 0. 1174 0.1723 0. 1764 0.1517 0. 1481 0.1058 0.1143 0.0887 0.1332 0.1267 4251S. 12050 42519.12501 42519. 13376 42519.13821 42519.14779 -0.444 -0.433 -0.442 -0.442 -0.439 0.1682 0. 1558 0.1669 0. 1663 0. 1708 0.1462 0.1484 0.1265 0.1239 0.1056 42519,15258 42519.16057 42519.16550 42519,17397 42519.17355 -0.435 -0.440 -0.443 -0.443 -0.434 0. 1592 0. 1613 0. 1626 0.1733 0. 1559 0.1167 0,1254 0.1234 0.1398 0.1318 42519, 18813 42519,19313 42519.23751 42519.24299 42519.25098 -0.435 -0.440 -0.4 40 -0.427 -0,441 0.1647 0, 1631 0. 1620 1 533 0.1757 0.1242 0.0998 0,1395 0.1113 0,1184

PAGE 169

158 APPENDIX Continued HELIO. MJD D(v) D(b-v) D(u-b) 42519.25723 42519.26598 42519.27112 42519.28049 42519,28619 -0.428 -0.438 -0.439 -0,436 -0.429 0.1603 0.1710 0. 1616 0.1698 0. 1678 0.0999 0.1195 0.1212 0.1272 0.0916 42519.31348 42519.31834 42519.32591 42519.33091 42519.33827 -0.431 -0.428 -0.439 -0.425 -0.447 0.1724 0.1634 0. 1654 0, 1641 0.1792 0.1282 0.1057 0.1314 0.1099 0.1314 4251S. 34355 42519.35084 42519.35563 42519,36264 42519.36334 -0.434 -0.427 -0.420 -C.440 -0.426 0. 1601 0.1537 0. 1473 0.1655 0. 1628 0.1150 0.1265 0.1131 0.1468 0.1283 42519,37688 42519.38146 42519.39063 42519.39549 42522. 17525 -0.430 -0.410 -0.450 -0.427 -0.326 0. 1678 0. 1509 0.1802 0. 1554 0.1447 0,1505 0.1098 0.1305 0.1076 0.1188 42522.18115 42522. 13893 42522.19400 42527. 14928 42527.15435 -0.314 -0.336 -0,321 -0,334 -0,331 0. 1401 0.1423 0. 1288 0,1229 0. 1398 0.0903 0.1254 0.1240 0.0992 0.0724 42527. 16206 42527.16665 42527.17533 42527.13026 425 27.22630 -0,344 -0,367 -0.371 -0.357 -0.373 0. 1428 0, 1472 0. 1701 1 473 0. 1502 0.1208 0.1096 0.0732 0.0476 0.1031 42527.23157 42527,24261 42527,24768 42534. 20243 42534.20771 -0,352 -0.343 -0,349 -0.371 -0,403 0, 1241 0,1098 0. 1392 0.1292 0.1543 0.1132 0,1306 0.1397 0,1435 0.1029 42534.21437 42534.21868 42534.22507 42534.22 972 42534.23680 -0.401 -0.396 -0.3 97 -0.395 -0.389 0.1622 0. 1494 0.1560 0. 1541 0.1615 0.1064 0. 1191 0.1078 0.1258 0.162 8 42843.31458 42843.31819 42843.33083 42843.33389 42843,35681 -0.299 -0,294 -0.299 -0.279 -0,296 0. 1283 0.1067 0. 1287 0, 1360 0. 1672 0.1125 0,1267 0.1196 0.0908 0.0600 42843.36215 42843.37819 42843.38375 42855.13603 42855. 14221 -0.282 -0.318 -0,316 -0.346 -0.354 0. 1246 0. 1728 0. 1324 0.1430 0, 1704 0.0698 0.0479 0.093 9 0.1498 0.1179 42855.15061 42855. 15610 42855,16555 42855. 17075 42855.13145 -0.343 -0.342 -0.340 -0.347 -0,334 0. 1617 0. 1457 0. 1320 0. 1537 0. 1310 0.1199 0.1106 0.1217

PAGE 170

APPENDIX Continued 159 HELIO. MJD D(v: D(b-v)' D(u-b; 42855,18680 4285519443 42855,19902 42855.20603 42855,21048 -0.338 -0.344 -0.345 -0.339 -0.3 44 0, 1607 0.1424 0. 1364 0, 1467 0.1410 0.1047 0,1324 0,1337 0.0982 0.1153 42855.21825 42855.22284 42855.23207 42855,23566 42855.24360 -0.338 -0.341 -0,336 -0.336 -0.333 0.1351 0. 1478 0,1260 0. 1436 0.1457 0.1145 0.1146 0.1358 0,1133 0.1084 42355.24805 42855.28707 42855.29159 42855,29902 42855.30374 -0.346 -0.328 -0.327 -0.335 -0.336 0. 1578 0.1327 0, 1332 0.1522 0.1400 0.0895 0.1123 0.0851 0.1031 0.0973 42855.31214 42855.31700 42855.37631 42855.38096 42855.39964 -0,333 -0.327 -0.325 -0.309 -0,347 0.1345 0. 1385 0. 1384 0. 1291 0. 1444 0.1189 0,0874 0.1239 0.1243 0.1129 42855.40450 428 55.4176 3 42855.42478 42855.43457 42861.12929 -0.339 -0,333 -0.336 -0.328 -0.249 0. 1429 0,1579 0. 1454 0. 1395 0. 1502 0.0992 0,1031 0.0933 0.1282 0.0963 42861.13519 42861.14262 42851,14790 42861.16019 42861. 16485 -0,217 -0.196 -0.171 -0,108 -0.085 0.1378 0. 1497 0,1577 0. 1787 0.1864 0.1018 0.1247 0.1135 0,1426 0.1414 42861,17241 42861.17721 42861.18200 42861. 18679 42861.19228 -0,037 -0.002 0.026 0,056 0.077 0. 1788 0, 1952 0. 1891 0.2059 0.2161 0.1545 0.1726 0. 1703 0.1623 0.1746 42861.19707 42861.20304 42861.20860 42861.21644 42861.22471 0.131 0.190 0.217 0.284 0.350 0.2357 0.2287 0.2695 0.2803 0.3049 0,1809 0.1953 0.1881 0,2074 0,2414 42361,22915 42861.23436 42861.23823 42861,24026 42861.24200 0.384 0,434 0.450 0.481 0.505 0,3155 0.3365 0.3378 0.3651 0.3772 0,2954 0,2948 0,2952 0.3073 0.3017 42861,24679 42861.24866 42861.25339 42861.25526 42861.25151 0,544 0,557 0.5 97 0,622 0.664 0.3882 0.3907 0.3982 0.4130 0,4519 0.3472 0-3559 0.3734 0.3603 0.3823 42861.26332 42861.26811 42861.26991 42861.27533 42861.27901 0.695 0.720 0,729 0.769 0,785 0.4506 0.4848 0.4876 0.4904 0.5088 0,4060 0.4548 0,4669 0.4735 0.4987

PAGE 171

160 APPENDIX Continued n/u ,,\0 nt., u\0 HELIO. MJD D(v)'' D(b-v)^ D(u-b 42861.29311 0.804 0-5172 0-5302 42861.29783 0.829 0.5113 0-5095 42861.30304 0.835 0.5137 0.5287 42861.31151 0.824 0.5263 0.5194 42861.31401 0.835 0.5311 0.5225 42861.35818 0.845 0.5400 0-5164 42861.36276 0.844 0.5190 0,5188 42861.36734 0.838 0.5326 0.5166 42861.37158 0.850 0.5074 0.5125 42863.17247 -0.402 0.1571 0.1262 42863.18303 "O.^^ R*ll^2 R'^^Ii 42863.19219 -0.403 0.1624 0.1089 42870.163 5 -0.334 0.1425 0,1418 42870: 6780 -0.330 0.1472 0.1058 42870.17197 -0.326 0.1409 0.1119 42870.18322 "0.336 0.1407 0.1420 4287C. 18760 -0.331 0.1418 0.1310 42870.19204 "0.326 M^tl^ 0.1236 42870.19648 -0.321 0.1332 0.1124 42870.20121 -0.325 0.1455 0.1032 42870.20579 -0.327 0.1435 0.1202 42870.21787 "0.329 0.1^26 0.1140 42870.22211 -0.323 0.1342 0.0971 42870.22600 "0.328 O.^^^J ^'HIS 42870.24447 -0.330 0.1466 0.1210 42870.25655 "0.327 0.1309 0.1232 4287C. 26086 -0.328 0.1359 0.1103 42870.27752 -0.332 0.1414 0.1294 42870:29405 -0.322 0.1438 0. 013 42870.29850 -0.323 0.1352 0.1001 42870.30468 "0.327 0.1326 0.1219 42870.31891 -0.322 0.1330 0.1140 42871.09480 0.480 0.3855 0.2669 42871.10327 0.411 0.2S58 0.2865 42871.10751 0.366 0.2921 0.2448 42871.10751 0.366 0.2921 0.2448 42871.11084 0.344 0.2784 0.2277 42871111084 0.344 0.2784 0.2277 42871.11709 0.292 0.2490 0.2244 42871.12126 0.263 0.2330 0.2049 42871.12557 0,225 0.2257 0.1711 42871,13050 0.186 0.2231 0.1725 42871.13772 0.135 0.2058 0.1816 42871.14244 0.105 0.1953 0.1611 42871,14663 0.074 0.1881 0.1562 42871,15675 0.002 0.1847 0.1372 42 871. 6563 -0.036 0.1580 0.1270 42871,16966 -0.058 0.1525 0.1254 42871.17383 -0.085 0.1502 0.1281 4287i:i7799 -01107 0.1578 0.1100 42871.13716 "0.141 0.1306 0.1175 42871.19181 -0.157 0.1377 0.0932 42871 19688 -0.174 0.1365 0.0939 42871,20633 -0.206 0.1256 0.1078 42371.21091 -0.216 0.1267 0,0999

PAGE 172

161 APPENDIX Continued HELIO. MJD D(v) D(b-v) D(u-b) 42871.21494 42871.22008 42871.22473 42871ft22924 42871ft23376 -0.224 -0.235 -0.247 -0.248 -0.243 0.1239 0. 1210 0. 1270 0. 1254 0. 1204 0, 1094 0,1130 0,1120 0.1148 0,1047 42871,23862 42871,24904 42871.25362 42871.25758 4287 1ft 26466 -0.2 47 -0.257 -0.246 -0.248 -0.248 0ft1252 0. 1258 0. 1246 Oft 1250 0.1198 0,1008 0,1050 0,0905 0,0945 0,0928 42871ft26897 42871ft27452 42871.27549 42871.28001 42871.28494 -0.243 -0.244 -0.242 -0.237 -0.240 0. 1156 0. 1202 0. 1179 0.1129 0. 1219 0,0946 0,1003 0,0985 0,0852 0.1066 42871.28966 42871.29410 42871.31334 42371.31716 42871.32612 -0.238 -0.237 -0,244 -0.240 -0.241 0. 1157 0, 1142 0. 1203 0. 1097 0,1204 0,0938 0,0729 0.0758 0.0855 0.0855 42871.33473 42371.34702 42871.35278 42871.35751 42871.35473 -0.246 -0.240 -0,230 -0.236 -0.236 0, 1014 0,1201 0, 1133 0,1194 0. 1147 0,0822 0,0735 0,0610 0,075 8 0.0835 42871.36917 42871.37376 42873. 10129 42873.10824 42873, 11580 -0,239 -0,241 -0.433 -0.435 -0.432 0, 1169 0. 1122 0. 1763 0, 1579 0.1580 0.0808 0,0831 0.1541 0,1269 0,1219 42873.12289 42873.13060 42873.13844 42873, 14712 42873.15421 -0,418 -0.401 -0,417 -0,420 -0.419 Oft 1480 0.1391 Oft 1437 0.1591 0, 1532 0,1144 0,1320 0.0954 0,1157 0.0910 42873,16615 42873. 17337 42873.18435 42873.19254 42873.30240 -0.392 -0.398 -0.396 -0.373 -0.301 0. 1444 0. 1509 0.1517 0. 1373 0ft1178 0.0926 0.1231 0.1393 0.1328 0,1083 4 2873.31059 42873. 31504 42873,32031 42873.32747 42873,33240 -0.301 -0,293 -0,281 -0,292 -0.285 0. 1289 0.1203 Oft 1184 0, 1157 01148 0,0708 0,0919 0.0825 0.0731 O.0953 42873.34066 42873.34427 42873.34858 42873.35427 42373.37969 -0.286 -0.285 -0.284 -0.290 -0.279 0,1226 0,1210 0. 1377 Oft 1201 0,1046 0.0994 0.1028 0.0864 0.0759 0.0905 42380.18382 42880. 18792 42880,19632 42880,20014 4288C. 20973 -0,334 -0.329 -0.306 -0.311 -0.313 0, 1359 0. 1362 0. 1382 0, 1337 0. 1314 0.1096 0.102 6 0,0760 0.1068 0.1194

PAGE 173

162 APPENDIX Continued HELIO. MOD D(v) D(b-v) D(u-b) 42880.21341 -0.291 0, 1065 0. 1173 42880. 22243 -0.285 0.1354 0,0664 42880,22505 -0.283 0. 1390 0.0842 42880.24271 -0.298 0.1254 0.1186 42880,24667 -0.301 0. 1202 0. 1 40 3 42880,25618 -0.322 0.1375 0.1212 42880,25972 -0.320 0. 1401 0.1405 42880,26757 -0.329 0. 1255 0.1095 42880.27111 -0.333 0, 1356 0. 1043 42880.28875 -0.286 0. 1025 0.0900 42880.29715 -0.266 0.1577 0.1156 42880.30479 -0.288 0. 1568 0.0441 42880.31639 -0.243 0. nsi 0.0929 42880.32472 -0.214 0.1403 0.1008 42880.33208 -0.220 0. 1452 0.1146 42880,34021 -0.164 0, 1712 0.1432 42880,34889 -0.111 0.1708 0.1330 42880.35778 -0.074 0. 1681 0.1032 42880.36542 0,003 0. 1783 0.1396 42880.37333 0.017 0,1708 0.1571 42880.38167 0.087 0.2102 0.1980 42880,39055 0.242 0,2441 0.1616 42880.39271 0.258 0, 2740 0.1286 42886.10481 -0.236 0.1188 0.0745 42886.11210 -0.240 0. 1243 0.0978 42886.12057 -0.241 0.1126 0.0920 42886.13488 -0.232 0. 1132 0.0796 42886.14162 -0,233 0. 1173 0.0785 42886. 14481 -0.245 0. 1230 0.0913 42386. 15182 -0.232 0.1118 0.0963 42886.15585 -0.236 0. 1126 0.0663 42886. 16224 -0.241 0. 1137 0.0853 42886.16613 -0,233 0, 1122 0, 0750 42886. 17175 -0.242 0,1260 0,0898 42886.17573 -0.245 0.1157 0.0896 42888. 18550 -0.240 0, 1098 0.1040 42886.18939 -0.237 0. 1138 0. 1027 42886. 19641 -0.237 0.1089 0,105 8 42886.20036 -0.237 0. 1129 0.0840 42886,20627 -0.252 0. 1232 0.0952 42888.21015 -0.255 1 235 0.1025 42886.21668 -0.241 1 1 83 0.0893 42886.22052 -0.247 0. 1191 0.0841 42888.22904 -0.255 0. 1225 0.1052 42886.23328 -0.255 1 254 0.0949 42886,24397 -0.254 0,1257 0.0869 42886.24779 -0.260 0. 1254 0.0900 42886,25390 -0.261 0. 1181 0.0834 42886.25765 -0.251 0. 126 0.0833 42886.26404 -0.249 0.1213 0.0795 42886.25772 -0.2 55 0. 1206 0.1004 42886,27362 -0.257 0. 1195 0.1100 42886.27737 -0.257 0, 1203 0.0958 42886.28342 -0.257 0. 1174 0,0889 42886,28703 -0.258 0. 1246 0.090 1 ^Hf-t-J-^Hr, Jr-li. — ,•

PAGE 174

APPENDIX Continued 163 42886.34612 42886.35279 42886,35932 42887.10672 42887.11477 42887. 12151 42887. 12783 42887.13463 42887.14873 42887. 15547 42887. 16186 42887.16574 42887.17026 42887. 17359 42887.19109 42887.19762 42887.25456 42887.26083 42887.26741 42887.27394 42887.28046 42887.28657 42887.30275 42887.30886 42887.31518 42887.32185 42887.32852 42887.34879 42887.35546 42887.36199 42887.36546 42887.36997 42887.37351 42887.37747 42887.33324 42887.38671 42887.39275 42887.39615 42887.4 0060 42887.40344 42888.10654 42888. 11342 42888,12071 42888, 12724 42888.13244 42888. 13626 42888.15286 42888. 16029 42888. 18654 42888. 17015 42888.17411 42888. 17321 42888.18966 42888,19439 42888.20015 -0.288 -0.2 40 -0.255 -0.412 -0,387 -0.404 -0.396 -G.401 -0.404 -0.405 -0.395 -0.411 -0.407 -0,390 -0,411 -0.413 -0.417 -0.417 -0.407 -0.410 -0.417 -0.412 -0.422 -0,428 -0.416 -0.387 -0,423 -0.412 -0.406 -0.423 -0.419 -0.425 -0.428 -0.422 -0.424 -0.429 -0,4 25 -0.431 -0.4 29 -0,421 -0.402 -0.415 -0,408 -0.396 -0.394 -0.3 97 -0.399 -0.396 -0.399 -0.394 -0.399 -0.383 -0,400 -0.399 -0.395 0. 0. 0. 0. 0. 1308 1523 1171 1628 1524 0. 1610 0.1450 0.1521 0. 1418 0.1495 0. 1320 0. 1582 0. 1471 0.1475 0. 1537 0.1587 0. 1505 0.1584 0. 1445 0.1417 0. 1511 0.1556 0. 1561 0.1683 0. 1546 0. 1631 0. 1534 0,1550 0.1576 0.1639 0, 1607 0.1717 0, 1726 0,1653 0. 1638 0. 0. 0. 0, 0. 1711 1722 167 1450 1252 0, 1507 0.1501 0. 1644 0. 1652 0. 1490 0. 0, 0. 0. 0. 0. 0. 0. 0. 0, 1390 1491 1527 1569 1646 1567 1425 1543 1487 1512 0.0791 0,0691 0,0609 0.1008 0.1116 0.1037 0.1044 0.0792 0.1004 0.1048 0.0953 0.1173 0.1298 0.1063 0.1446 0.1180 0. 1134 0.1192 0.1029 0.1014 0. 0, 1090 1135 1117 1145 1270 0.0946 0.0975 0.084 4 0.1614 0,1523 0.1317 0.1104 0. 1263 0,1586 0.1145 0, 0. 0, 0, 0, 0: 1514 1185 1361 0870 ,0811 1476 ,1227 ,1141 ,1096 ,1087 0.1167 0.0995 0.0998 0,1115 0.1076 0. 0. 0, 0, 0, 1162 1270 1166 1071 1163

PAGE 175

164 APPENDIX Continued HELIO. MJD D(v) D(b-v) D(u-b) 42888.20404 42888.20897 42888.21633 42888.28053 42388.28783 -0.380 -0.395 -0.394 -0.384 -0.3 80 0, 1511 0, 1569 0,1598 0, 1612 0, 1430 0.1054 0.1106 0.1068 0.1080 0.1143 42888,30307 42888.30972 42888,31625 42888.32278 42888.32949 -0.375 -0.387 -0.374 -0.380 -0.376 0, 1563 0.1535 0.1576 0.1555 0.1431 0,1062 0.1228 0,1174 0,1331 0,1091 42895-25188 42895.26097 42895.26756 42895.27903 42895.23492 -0.234 -0.233 -0.237 -0,225 -0.227 0. 1039 0. 1168 0.1212 0. 1187 0. 1176 0,0838 0,0817 0.0934 0,0895 0.0768 42895.28929 42895,29321 42895.30073 428 95,30443 42895.32025 -0.231 -0.235 -0.229 -0.228 -0,233 0. 1136 0.1187 0. 1163 0.1200 0. 1167 0.0669 0.0900 0.0931 0.0733 0.0794 42895.32455 42895,32856 42895.33687 42895,34 057 42896.09400 -0.228 -0.234 -0.234 -0,228 -0.298 0.1045 0. 1205 0.1164 0. 1091 0.1263 0.0842 0.0720 0.072 7 0.0898 0.1028 42896,10305 42896.10945 42896.11725 42896. 12442 42896.12799 -0,294 -0.294 -0.294 -0.298 -0.295 0. 1280 0. 1313 0. 1241 0.1226 0. 1190 0.1001 0.0856 0.0922 0.0871 0.1054 42896,13448 42896.13851 42896. 14530 42896.16311 42896. 15902 -0.306 -0.307 -0.301 -0.307 -0.306 0.1300 0. 1267 0.1271 0. 1285 0. 1353 0.1018 0.0960 0.1210 0,1203 0.1040 42896. 17234 42896, 17616 42896.18190 42896, 18737 42896.19308 -0.313 -0.314 -0.310 -0.324 -0.317 0. 1398 0.1296 0. 1324 0.1377 0. 1304 0.0868 0,0916 0.0913 0,1083 0.103 8 42896. 19672 42896.20071 42896.20699 42896.21085 42895.23005 -0.318 -0.312 -0.316 -0.318 -0,315 0.1360 0. 1358 0.1295 0. 1352 0.1321 0.1222 0.1087 0.123 5 0.1289 0.1110 42896.23584 42896.24045 42896.24713 42896,25042 42896.25399 -0.326 -0,325 -0.325 -0.322 -0,323 0. 1365 0. 1406 0. 1268 0,1303 0. 1353 0,1230 0,1169 0.1045 0.1104 0.0922 42896.25815 42896.26424 42896.26833 42896.27405 42896.27765 -0,330 -0,331 -0,328 -0,3 28 -0.331 0. 1308 0. 1402 0. 1465 0. 1350 0. 1453 0.0900 0.0979 0.1014 0.1214 0.1160

PAGE 176

165 APPENDIX Continued n/u ,.\0 n^,_h^o HELIO. MJD D(v) D(b-v) D(u-b 42896.29512 -0*326 M??R n'lO^I 42896,29865 -0*325 R' H§? n nq^u 42896.30481 -0-330 0. 262 0-??^J 42896,30874 -0-335 0-:^321 HSJ 42896.31223 -0,334 0.1314 0.1004 42896.31913 "0.338 0.1453 0.0928 42896.32314 "0-336 0.1385 0.1109 42896.32708 "0.335 0.1244 0.1018 42896.33822 "0.338 0.1471 0.0995 42896.34394 -0,334 0.1297 0.1255 42896.34758 "0.338 0.1462 0.1104 42896,35154 -0.334 0.1448 ^-H^ll 42396.36159 "0.351 0.1d60 ^^'Ul^ 42896.36527 "0.328 0.1233 2'?^H4 42901.20461 -0.367 0.1472 0.1397 42901.21110 "^.354 0.1502 I'VM 42901.21545 "0.373 0.1463 S'IRIq 42901.21893 -0.358 0.1399 0.104y 42916 13336 -0.411 0.1459 0.1261 42916,14186 -0.413 0.1508 0.1182 42916.15241 -0.406 0.1416 0,1236 42916 15907 -0:406 0,1474 0. 264 429 16.16592 "0.,'^18 0.1586 0.1439 42916.17155 -0.417 0.1554 0.1089 42916:17833 -0.410 0.1416 0.1177 42916.18483 -0.407 0.1482 0.1189 49Q16 20194 -0.409 0.1483 0.1481 42916.21087 -0.435 0.1702 0.0909 429 16:21757 -0,414 0.1575 0.1034 42916.23540 -0.413 0.1316 0.1344 42916.24184 "0.^13 0.1447 0.1349 li^qifi 24814 -0.417 0.1526 0.1402 42916:25454 -01417 0,1597 0.1416 42916.26195 "0.417 0.1595 0.0932 42916.27646 -0.419 0.1555 0.1101 42916.28391 "0.^26 0,1718 0.1436 42916.29142 "0.,it23 0.1587 2-2^2^ 42916.30851 '^'VJ ^llil n'nltl 42916.31511 -0.386 0.1558 0.0858 42916.32238 -0.412 0.1722 0.0943 42917.11234 -0-356 0.1274 0.1122 429 17.12217 -0,362 0.1378 0. 007 42917,12868 -0.360 P.1506 9*Aq^^ tt9qi7 17549 -0.358 0.1366 0.0954 429 17:20 162 -0.353 0.1446 0.0894 42917.20900 "0.356 0. ^^^^ S-iii7 tiOQ M 75502 -0.357 0.1529 0.111/ 429 17.26143 -0:339 0.1516 0.1304 429 17.26886 "0.339 0.1332 0.1170 42917.27527 -0.353 0.1432 0.0923 429 17.23219 "0.339 0.1366 0.0928 42917,31007 "0.331 0.1444 0.1400 42917.32093 "0.330 0.1374 0.0847 42923.11231 "0.325 0.1434 0.1162 42923.11965 -0.325 0.1355 0.1202

PAGE 177

166 APPENDIX Continued HELIO. MJD D(v) D(b-v) D(u-b) i|2923. -13857 -0-312 0-1^58 0-?988 U9q23, 14416 -0*321 0.1135 Q'JlfS 42929:08054 -0.220 0,0865 0.1040 42929,08740 -0.225 0.1128 0.0731 42929109774 -0,225 0.1118 0.0767 ioq^q 10410 -0,223 0.1215 0,0731 lilll: 10825 -0:228 0.1260 0.0644 tiV2l*]?il3 =§:li3 S: iii tliU 42929:12158 -01230 0.1182 0.0938 ii?qyQ 17494 -0.220 0.1127 0,0839 42929.12859 -0 221 0:i067 0-0654 42929 14194 -0.213 0.1142 0.0437 apq??* 14538 -0:219 0.0992 0.0435 42929:14861 -0.226 0:1118 0.0580 42929,15432 "0.220 0.1172 0*0753 42929.15784 -0.231 0.1266 O'O^^I 42929.16190 -0-224 0.1211 0,0775 42929.16521 -0.224 0.1067 0.0717 42929,16861 -0.228 0.1160 0.0743 ii9q9q 17393 -0.230 0.1189 0.0691 42929.17738 -0.225 0.1189 0.0550

PAGE 178

LIST OF REFERENCES Anderson, J., and Popper, D. M. 1975, Astron. Astrophys. 39, 131. Arnold, C. N., and Hall, D. S. 1973, lAU Inf. Bull. Var. Stars No. 842. Atkins, H. L., and Hall, D. S. 1972, Pub. A.S.P. 84, 638. Batten, A. H. 1973, Binary and Multiple Systems of Stars (Oxford: Pergamon) Bidelman, W. P. 1954, Ap. J. Suppl 1, 175. Biermann, P., and Hall, D. S. 1976, in lAU Symposium No. 73 Structure and Evolution of Close Binary Systems eds. P. Eggleton et al (Dordrecht: Reidel). Blanco, C, and Catalano, S. 1970, Astron. Astrophys. 4^, 482. Bopp, 8. W. 1975, lAU Inf. Bull Var. Stars No. 1175. 1978, private communications' -* Bopp, B. W., Espenak, R., Hall, D. S., Landis, H. J., Lovell, L. P., and Reucroft, S. 1977, A.J. 82, 47. NV Cash, W., Bowyer, S., Charles, P., Lampton, M., Garmire, G., and Riegler, G. 1978, Ap. J. (Letters) in press. Catalano, S., and Rodono, M., 1967, Mem. Soc. Ast. Italiano 38, 2. 1968, in lAU Colloquim No. 4 Non-Periodic Phenomena in Variable Stars ed. L. Detre (Budapest^ Academic Press), p. 435. 1974, Pub. A.S.P., 85, 390. Ceraski, L. 1914, A.N., 197, 256. Chambliss, C. R. 1976, Pub. A.S.P. 88, 762. — ^,vvV Charles, P. A. 1978, private communications*. Chen, K-Y., and Rekenthaler, D. A. 1965, Q.J. Florida Ac. Sci. 29, No Chisari, D., and Lacona, G. 1965, Mem. Soc. Ast. Italiano 36, 463. — — ~vvvv Conti, P. S. 1967, Ap. J. 149, 629. 167

PAGE 179

168 Eaton, J. A. 1977, lAU Inf. Bull. Var. Stars No. 1297. Eggen, 0. J. 1955, Pub. A.S.P. 57, 315. Field, J. V. 1969, M.N.R.A.S. 144, 419. Gadomski, J. 1926, Cir. Obs. Cracovie No. 22. Gibson, D. M., and Hjellming, R. M. 1974, Pub. A.S.P. 86, 552. Gibson, D. M., Hjellming, R. M., and Owen, F. N. 1975, Ap. J. (Letters), 200, L99. Glebocki, G. and Stawikowski, A. 1977, Acta Ast. 27, 225. Gratton, L. 1950, Ap. J. Ill, 31. 1 JUM-— Gray, D. F. 1976, The Observation and Analysis of Stellar Photospheres (New York: Wiley), p. 388. Hall, D. S. 1967, A.J., 72, 301. 1972, Pub. A.S.P. 84, 323. — Iff. 1975a, Acta Ast. 25, 215. Hi** 1975b, Acta Ast. 25, 225. 1976, in lAU Colloquim No. 29 Multiple Periodic Variable Stars ed. W. S. Fitch (Dordrecht: Reidel), p. 287. 1977, Acta Ast. 27, 281. 1978, private communications*, Hall, D. S., Henry, G. W., Burke, E. W., and Mull ins, J. L. 1977, lAU Inf. Bull. Var. Stars No. 1311. Hall, D. S., Montle, R. E., and Atkins, H. L. 1975, Acta Ast. 25, 125. Hall, D. S., Richardson, T. R., and Chambliss, C. R. 1967, A.J, ,, 81, 1138. Hardie, R. H. 1952, in Astronomical Techniques ed. W. A. Hiltner (Chicago University of Chicago Press), p. 178. Hearnshaw, J. B., and Oliver, J. P. 1977, lAU Inf. Bull. Var. Stars No. 1342. Herbst, W. 1973, Astron. Astrophys. 26, 137. Hiltner, W. A. 1947, Ap. J. 106, 481. Hoffmeister, C. 1915, A.N. 200, 177.

PAGE 180

159 I 1919, A.N., 208, 258. Joy, A. H. 1930, Ap. J. 72, 41. Keller, G., and Limber, D. N. 1951, Ap. J. lU, 637. Kron, G. E. 1947, Pub. A.S.P. 59, 251. landis, H. J., Lovell, L. P., Hall, D. S., Henry, G. W., and Renner, T. R. 1978, A.J. 83, 175. Li Her, W. 1978, invited address to AAS in Madison, Wise. Ludington, E. W. 1978, Bull. AAS 10, 418. Maggini, M. 1915, Pubbl Oss Arcetri Fasc. 34. Markworth, N. L. 1977, Ph.D. Dissertation, University of Florida at Gainesville. Merrill, J. E. 1950, rnntr^._Prin ceton Univ. Obs. No. 23. Mergentaler, A. 1950, Wroclaw Contr .No. 4, Milone, E. F. 1958, A^, 73, 708. 1975a, in lAU Col1)oquim No. 29, Multiple Per iodic Variable Stars, ed. W.'s. Fitch (Dordrecht: Rei del), p. 321. 1976b, Ap. J. Suppl 31, 93. — lUM. 1977, A.J., 82, 998. Miner, E. D. 1955, Ap. J. 144, 1101. Montle, R, E. 1973, M.A. Thesis, Vanderbilt University, Nashville, Tennessee. Mullan, D. J. 1974, Ap. J. 192, 149. 1976, Ap. J. 204, 818. Naftilan, S. A. 1975, Pub. A.S.P. 87, 321. Naftilan, S. A., and Drake, S. A. 1977, Ap. J. 215, 508. Nelson, B., and Duckworth, E. 1968, Pub. A.S.P. 80, 562. Oliver, J. P. 1971, Bull. AAS 3, 14. — mi 1973, in lAU Symposium No. 51 Extended Atmospheres a nd Circumstellar Matter, ed. A. H. Batten (Dordrecht: Reidel), p. 279.

PAGE 181

170 1974, Ph.D. Dissertation, University of California at Los Angeles. 1975, Pub. A.S.P. 87, 695. 1976, Rev. Sci Inst., 47, 581 Owen, F. N., Jones, T. W., and Gibson, D. M. 1976, Ap. J. (Letters) 210, L27. Owen, F. N., and Spangler, S. R. 1977, Ap. J. (Letters) 217, L41. Payne-Gaposchkin, C. 1939, Proc. Am. Philosph. Soc 81, 189. Pfeiffer, R. J. 1978, Bull. AAS 10, 418. Pfeiffer, E. F., and Koch, R. H. 1973, Bull. AAS ^, 345. 1977a, Pub. A.S.P. 89, 147. 1977b, lAU Inf. Bull. Var. Stars No. 1250. Plavec, M. 1967, 3.A.C. 18, 334. Plavec, M., i.and Smetanova, M. 1959, B.A.C. jD, 192. Plavec, M., Smetanova, M., and Pekny, A. 1961, B.A.C 12, 117. Popper, D. M. 1961, Ap. J. 133, 148. 1967, Ann. Rev. Astr. Ap., 5, 85. 1970, in lAU Colloquim No. 6 Mass Loss and Evolution in Close Binaries ed. K. Gyldenkerne and R. M. West (Copenhagen: Copenhagen University Observatory), p. 13. 1974, Bull. AAS, 6, 245. Popper, D. M., and Ulrich, R. K. 1977, Ap. J. (Letters) 212, L131. Rhombs, C. G., and Fix, J. D. 1977, Ap. J. 216, 503. Rucinski, S. M. 1977, Pub. A.S.P. 89, 280. Sadik, A. R. 1978, lAU Inf. Bull Var. Stars No. 1381. Schneller, H. 1928, A.N. 233, 361. Sitterly, B. W. 1930, Contr. Princeton Univ. Obs. No. 11. Spangler, S. R. 1977, A^, 82, 169. >*x

PAGE 182

171 Spangler, S. R., Owen, F. N., and Hulse, R. A. 1977, A^, 82, 989, Struve, 0. 1946, Ann, d' Astro ph.ys. 9, 1. 1948, Ap. J. 108, 155. t**/****^ Townley, S. D. 1915, Pop. Astr. 23, 25. Ulrich, R. K., and Popper, D. M. 1974, Bu1 1 AAS _, 5, 461. Walker, M. F. 1978, Pub. A.S.P. 89, 874. Walter, F., Charles, P., and Bowyer, S. 1978a, in press. _. 1978b, submitted to Nature Weiler, E. J. 1975a, Bull. AAS 7, 267. 1975b, lAU Inf. Bull. Var. Stars No. 1014. / 1978a, M.N.R.A.S. 182, 77. 1978b, private communications*. White, N. E., Sanford, P. W., and Weiler, E. J. 1978, submitted to Natlili Wielen, R. 1974, lAU Highlights of Astronomy Z, 395. Wood, D. B. 1971, A.J. 76, 701. 1972 A Comput er Program for Modeling Non-Spherical Eclipsing — 8i]^i?7'star Systems GSFC X-llU-y2-4y3 (Greebelt, Maryland: (.oddard Space Flight Center) Wood, F. B. 1945, Contr. Princeton Univ. Obs. No. 21, 10. Young, A., and Koniges, A. 1977, Ap. J. 211, 836. Notes for list of references: Talk given at the lAU Comm. 42-sponsored RS CVn Workshop, Socorro, New Mexico, April 5-7, 1978.

PAGE 183

BIOGRAPHICAL SKETCH On 17 December 1949, Elwyn Whit Ludington was born to Berchel A. and Leona Inez Ludington in Eugene, Oregon. He attended public school in Eugene and spent the summer months of his teenage years with his uncle and aunt (Robert and Esther Ludington) on their farm in Idaho. Her married Nancy A. Butterfield in August 1970. After receiving a B.S. degree in electrical engineering from Oregon State University in June 1972 he moved to Gainesville, Florida, to study astronomy in the graduate program of the University of Florida. In November 1972 his son Philip Jay Ludington was born. In June 1978 he married Karen Paige Rockwell; three years after a divorce from his first wife. Shortly after their marriage he and Karen moved to Austin, Texas, where he had a postdoctoral research associateship in the Department of Astronomy at the University of Texas at Austin. The degree of Doctor of Philosophy from the University of Florida is expected to be conferred in December 1978. 172:

PAGE 184

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the d^ree of Doctor of Philosophy. p. Jahfi/ Piroiiver, vnct^^rman Ifesjziciate Professor of Astronomy I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. T.Q>y^ F. Bradshaw Wood Professor of Astronomy I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ''MwvJ'; ?'v^'V' -Vv Kwan-Yu Chen Professor of Astronomy and Physical Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Stanley S. Ballard ^ Distinguished Service Professor of Physics ill MiaRi*t.^*U*^ t'

PAGE 185

I certify that I have read this study and that in my opinion it confoms to acceptable standards of scholarly presentation and ^s fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ck^ fa^> Howard L. Cohen Associate Professor of Physical Sciences and Astronomy This dissertation was submitted to the Graduate Faculty of the Department of Astronomy in the College of Liberal Arts and ciences and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December 1978 Dean, Graduate School


xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID ENQ0592B6_GFE414 INGEST_TIME 2014-12-03T19:32:59Z PACKAGE AA00026434_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES