Citation
An Analysis of the Rossiter effect in algol-type eclipsing binary systems

Material Information

Title:
An Analysis of the Rossiter effect in algol-type eclipsing binary systems
Creator:
Twigg, Laurence William, 1951- ( Dissertant )
Wilson, Robert E. ( Thesis advisor )
Wond, Frank B. ( Reviewer )
Devinney, Edward J. ( Reviewer )
Oliver, John P. ( Reviewer )
Campbell, Hugh D. ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1979
Language:
English
Physical Description:
viii, 207 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Eclipses ( jstor )
Eclipsing binary stars ( jstor )
Emission spectra ( jstor )
Hertzsprung Russell diagrams ( jstor )
Light curves ( jstor )
Radial velocity ( jstor )
Spectroscopy ( jstor )
Stellar classification ( jstor )
Stellar rotation ( jstor )
Velocity ( jstor )
Astronomy thesis Ph. D ( lcsh )
Dissertations, Academic -- Astronomy -- UF ( lcsh )
Eclipsing binaries ( lcsh )
Stars -- Rotation ( lcsh )
Miami metropolitan area ( local )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
One of the fundamental parameters of a star is its rate of axial rotation. This parameter affects both the shape of the star and the distribution of light over the stellar surface. Thus, an accurate analysis of the light curve of an eclipsing binary system should include the effects of stellar rotation. In addition, the values of fundamental astrcphysical parameters such as mass, radius, and luminosity are usually found by combining the results of both photometric and spectroscopic analyses of an eclipsing binary system. Therefore, the correct treatment of stellar rotation (thus yielding a more accurate light curve solution) is necessary to ensure an accurate determination of the aforementioned fundamental parameters. To date, the primary means of determining the rate of stellar equatorial rotational velocities (V' q ) has been through an analysis of spectral line profiles. This type of analysis is limited both statistics (through the determination of V for standard stars) and instrumental iv (in that the error of the V derived for the system under analysis is approximately equal to the reciprocal dispersion cf the spectroscopic equipment used). Thus, one would like to find a second, independent method for determining V , which could be compared and contrasted with the value found from line profiles. Such an independent method of determining V for a component of an eclipsing binary system is available through the analysis of a spectroscopic phenomenon known as the Rossiter effect. The Rossiter effect is characterized by (sometimes very large) deviations in the radial velocity curve during the partial phases of an eclipse. These deviations are in a positive (red-shifted) sense during ingress, and a negative (blue-shifted) sense during egress. These deviations occur because, during these phases, the geometrical covering of part of the star being eclipsed leads to a doppler shift of the spectral lines of this star arising from axial rotation, as opposed to orbital motion. The present investigation uses such an analysis of this effect in order to determine V for che primary components of 19 Algol -type eclipsing binary systems. In addition, new analyses of the associated light curves and determination of new absolute parameters were carried out for these systems. Further, the radii of possible ring structures existing around the primary components in several systems were determined. Finally, evidence is presented indicating that for several suspect systems no extra light is present at second and third contact, unlike the results of an analysis of Y Psc by Walter. It is suggested that the inclusion in this study of rotation effects on the stellar figures removes the need for such extra light.
Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 202-205.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Laurence William Twigg.

Record Information

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University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
023340361 ( AlephBibNum )
06560929 ( OCLC )
AAL2855 ( NOTIS )

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AtN ANALYSIS OF THE ROSSITER EFFECT IN ALGOL-TYPE
ECLIPSING BINARY SYSTEMS













By

LAURENCE WILLIAM 'iIGG


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





U:ITVELSITY 'SI FLORIDA


1979


L
























DEDICATION


This dissertation is dedicated to my parents, whose love made

all things possible.














ACKNOWLEDGEMENTS

During the years of work needed for the completion of this dis-

sertation, innumerable people have given their time, encouragement and

advice. Only through their combined support were the opportunities afforded

and the determination implanted that enabled me to continue when the inev-

itable mountains of computer output threatened to engulf and smother me.

First among these people is Dr. R. E. Wilson, who chaired the

supervisory committee. Dr. Wilson suggested the dissertation topic, and

made available his vast knowledge of eclipsing binary stars and his inti-

mate knowledge of the Wilson-Devinney computer programs used for this

research. His sense of humor and guidance, which date back to my first

days as an undergraduate student, helped develop the self-reliance and

discipline necessary for success in any field of endeavor.

Dr. E. J. Devinney has also provided a guiding force since my first

days studying astronomy. It was his willingness to set aside other work

in order to read the first versions of the dissertation that allowed

this dissertation to be completed on schedule. His advice, astronomical

and nonastronomical, will always be appreciated.

Other members of the supervisory committee were Dr. F. B. Wood,

Dr. J. P. Oliver, and Dr. H. Campbell. I wish to thank them for reading

the various versions of the dissertation and making useful comments on

them.

Special thanks go to Dr. H. C. Siith, sho read and commented on

the dissertation as well as slttLng in on the final oral examination as











a proxy for Dr. Wilson. Thanks also are due Dr. J. E. Merrill for many

enlightening and enjoyable discussions on W UMa binary systems, or, as

Dr. Merrill has dubbed them, the "Vermin of the skies."

I wish to thank W. W. Richardson for making several excellent ink

drawings for this dissertation.

Extra special thanks go to Ms. P. Guida, who not only helped edit

and type the various drafts of the dissertation, but provided much needed

moral support at all times.

A graduate student is often only as determined as his graduate

companions. For providing a background conducive to good astronomy as

well as enjoyable living, I wish to acknowledge all my fellow graduate

students, in particular J. T. Pollock and G. L. Fitzgibbons.

Special thanks go to Mrs. Irma Smith for her valuable assistance

in the final preparation and typing of the dissertation.

I owe my greatest debt to my family, who not only provided contin-

ual encouragement, but gave me every opportunity to follow my astronomical

calling. I wish to express a very special thanks to my parents for their

support, both moral and monetary, which allowed me to succeed in my

chosen field.















TABLE OF CONTENTS


ACKNOWLEDGEMENTS . . . . . . .

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

Chapter

I. INTRODUCTION . . . . . . . . ... .

Overview of the Problem .. . . . .......
Determination of Equatorial! Rotational Velocities .


The Rossiter Effect .. . ....
Algol-Type Eclipsing Binary Systems
Purpose of this Investigation . .


Page



vli


II. METHOD OF ANALYSIS . . . . . . ... . .

III. DISCUSSION OF INDIVIDUAL SYSTEM .......S.. ..

X Tri . . . . . .
Y Leo . . . . . . . . . . . .
RZ Cas . . . . . . . . . . . .
ST Per . . . . . . . . . ...
RX Hya. . . . . . . . . . . . .
W UMi . . . . . . . . . . ...
iW Cyg . . . . . . . . . . . .
RW Gem . . . . . . . . . . . .
TX 'UMa . . . . . . . . . . . .
TV Cas . . . . . . . . .
AQ Peg . . . . . . . . . . . .
SW Cyg . . . . . . . . . . . .
Y Psc . . . . . . . . . . .. .
Del ........................
RY Gem . . . . . . . . . . . .
U Sge . . . . . . . . . . ..
;U Ce . .. . . . . . . . ..
RY Per.............
RZ Set . . . . . . . . . . . .

IV. RESULTS AND CONCLUSIONS . . . . . . . . .


General Discussion. .
Detailed Discussion .
Suggestions for Further


Work . . . . . . .












TABLE OF CONTENTS--Continued

Page

APPENDIX A. ........ .... . ... ... . .. 82

APPENDIX B. . .......... ....... . . . 127

APPENDIX C .. . . .. . . . . . . . . 174

APPENDIX D. ........... . . . . ... . 189

REFERENCES . . .... ................. . 202

BIOGRAPHICAL SKETCH ... . .. .. . ... . . 206















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


AN ANALYSIS OF THE ROSSITER EFFECT IN ALGOL-TYPE
ECLIPSING BINARY SYSTEMS

By

Laurence William Twigg

December 1979

Chairperson: Robert E. Wilson
Major Department: Astronomy

One of the fundamental parameters of a star is its rate of axial

rotation. This parameter affects both the shape of the star and the

distribution of light over the stellar surface. ihus, an accurate

analysis of the light curve of an eclipsing binary system should include

the effects of stellar rotation. In addition, the values of fundamental

astrophysical parameters such as mass, radius, and luminosity are

usually found by combining the results of both photometric and spectro-

scopic analyses of an eclipsing binary system. Therefore, the correct

treatment of stellar rotation (thus yielding a more accurate light

curve solution) is necessary to ensure an accurate determination of the

aforementioned fundamental parameters.

'o date, the primary means of determining the rate of stellar

equatorial rotational velocities (Ve) has been through an analysis of

spectral line profiles. Ihis type of analysis is limited both statisically

(through the determination of V for standard stars) and instrumentally
e
(in that the error of the V derived for the system under analysis is
e
approximately equal to the reciprocal dispersion cf the s-ectroscopic

1]i











equipment used). Thus, one would like to find a second, independent

method for determining Ve, which could be compared and contrasted with

the value found from line profiles.

Such an independent method of determining Ve for a component of

an eclipsing binary system is available through the analysis of a spec-

troscopic phenomenon known as the Rossiter effect. The Rossiter effect

is characterized by (sometimes very large) deviations in the radial

velocity curve during the partial phases of an eclipse. These deviations

are in a positive (red-shifted) sense during ingress, and a negative

(blue-shifted) sense during egress. These deviations occur because,

during these phases, the geometrical covering of part of the star being

eclipsed leads to a doppler shift of the spectral lines of this star

arising from axial rotation, as opposed to orbital motion. The present

investigation uses such an analysis of this effect in order to determine

V for the primary components of 19 Algol-type eclipsing binary systems.

In addition, new analyses of the associated light curves and determin-

ation of new absolute parameters were carried out for these systems.

Further, the radii of possible ring structures existing around the pri-

mary components in several systems were determined. Finally, evidence is

presented indicating that for several suspect systems no extra light is

present at second and third contact, unlike the results of an analysis of

Y Psc by Walter. It is suggested that the inclusion in this study of

rotation effects on the stellar figures removes the need for such extra

light.














CHAPTER I

INTRODUCTION

Overview of the Problem

The study of eclipsing binary systems is usually carried out by

either a photometric or spectroscopic analysis of the light received

at the earth. These approaches yield characteristic yet overlapping

sets of parameters describing the system under study. Thus, while

each type of analysis may yield a value of the orbital eccentricity, e,

only the spectroscopic work will yield a value of Ki, the semiamplitude

of the radial velocity curve. Likewise, only the photometric analysis

of one or more light curves will yield a value for i, the orbital inclina-

tion. When both methods are combined, one then obtains a complete set

of absolute parameters, and thus a full physical description of the

system in terms of astrophysically interesting quantities (mass, radius,

etc.) is possible.

Many eclipsing binary systems have been analyzed both spectro-

scopically and photometrically, as described above, thus giving astron-

omers a large fraction of their data on stellar masses, radii, and lumi-

nosities. In addition, another fundamental parameter of a star is its

rate of axial rotation. There are many reasons why this parameter is of

interest. First, rotation has a direct effect on the shape of the star.

If reliable phctometric elements (and hence absolute elements) are to be

obtained, the model employed in analyzing the light curves should be

able to take into account the effect of rotation on the shape of the

component stars, in addition to the gravitational effects. Also,










distortion of the stars) due to tidal and rotational effects will result

in a nonuniform effective temperature over the stellar surfacess, a

phenomenon yielding a nonuniform light distribution, known as gravity

darkening, which will affect the photometric solution. If one knows the

rate of rotation and can determine the value of astrophysically inter-

esting parameters such as the linear limb darkening coefficient, x, or

the gravity darkening exponent, g (using a model including rotation

effects, etc.), one can then compare these numbers with those from the

several existing theoretical model atmospheres for rotationally flattened

stars. In this way, it is possible to determine which theory best fits

the observations. Finally. a knowledge of the rotation rate of a star

in an eclipsing binary system may yield important information on the

evolutionary status of the system. In particular, a binary system in

which one component shows a large stellar rotation value, coupled with

evidence of a gas stream between components implying a slow rate of

mass transfer may indicate recent large scale mass and angular momentum

transfer. In such a case, the large rotation rate implies that the

newly acquired rotational angular momentum has not been transferred back

into orbital angular momentum via, for instance, tidal braking. Thus

for many reasons it is useful to know the stellar rotation rate.

Determination of Equatorial Rotational Velocities

Traditionally, the method used to obtain V sin i, the projected

equatorial rotational velocity of a star, is to match the observed line

profile of some selected spectral line with the line profile of the cor-

responding spectral line of some standard star. The standard

star is usually a star of virtually the same spectral and luminos-

ity class as the star of interest. The standard stars are of











two types. Primary standard stars are those whose V have been determined

(usually through statistical means) to be either approximately equal to

zero, or equal to some fundamental lower bound characteristic of a particu-

lar spectral and luminosity class. Secondary standard stars have had

their Ve determined through matching their line profiles with the line

profiles of the primary standards which have been numerically rotationally

broadened a known amount. By the same process of theoretically broaden-

ing the line profiles of the standard stars and comparing the results

with the "unknown" line profile, a value of V sin i can be derived for
e

the star being investigated.

While this method has been carried out for many stars, it has

two problems when applied to stars in eclipsing systems. The first is

that the accuracy of V sin i determined by this method is approximately

the same (in kin/see) as the reciprocal dispersion used (in A/mm) in record-

ing the spectrum. Thus for an error of 10 km/sec one must use a recip-

rocal dispersion of 10 R/mm. Since one does not want to make too long

an exposure when observing many eclipsing binary systems (due to smearing

of the line profiles by orbital doppler shift), this limits accurate

results to the brighter eclipsing systems, or the moderately bright

(9 -12m long-period systems where exposure times can be made correspond-

ingly longer, and where a telescope of suitable light gathering power is

available. Work of this sort has beer carried out by Koch, Olson, and

Yoss (1963), Olson (1968), Van den Heuvel (1970), Nariai (1971), Levato

(1974), and Maliama (1978), mostly at reciprocal dispersions of 16 3/.a

to 50 i/mm. Secondly, the method relies heavily on statistical studies

to pick out primary "standard" stars (V sin iOC), and it presupposes











that the residual broadening of the lines of these primary standard

stars (mostly due to spherically symmetric macro- and microturbulence)

is characteristic of all the stars of that particular spectral and luminos-

ity class. Since stars in a binary system may have very large effects

on one another, and almost all standard stars are single stars, the usual

methods for determining rotational broadening may not apply. One should

note, however, that the results of different authors' investigations of

the same star using the above technique usually agree to within the

quoted errors (sometimes 50 km/sec). it is thus natural to seek an

independent method of determining Ve for stars in eclipsing binary

systems, which could then be compared and contrasted with the results

obtained from the line-profile matching method.

The Rossiter Effect

Such a method does, in fact, exist, and is based on a spectro-

scopic rotation effect known as the Rossiter effect. In a 1909 spectro-

scopic study of the eclipsing binaries A Tau and 6 Lib, F. Schlesinger

(1910) interpreted certain anomalies found in the radial velocity curves

of these stars as due to the rotation of the star being eclipsed. He

concluded that the departures from the expected radial velocity curves

during the partial phases of the primary (deeper) eclipse were due to the

star in front geometrically blocking part of the surface of the star

behind. These were in a positive sense (red shift) during ingress and in

a negative sense (blue shift) during egress. This effect is seen as an

asymmetry in the distribution of rotationally doppler shifted light

emanating from the eclipsed stellar disk. Assume that the rotation of the

stars is in the same direction as the orbital motion of the binary.











During ingress, the approaching limb of the star being eclipsed would

be hidden from view, and the resultant line profile would change from

symmetric to asymmetric, with the blue side of the line being modified

as shown in Figure 1. After totality (if it exists), the reverse will

occur. Note that there are no physical constraints placed upon the

stars involved. As long as the eclipsed star contributes enough light

so that its spectrum can be observed, any eclipse-caused asymmetry will

result in a corresponding asymmetric spectral line. Looking at Figure 1,

it is evident that a measurement of the position of the line with respect

to some laboratory standard line (whether measuring some weighted mean

line center, or simply setting on the deepest part of the profile) will

measure not an orbital doppler shift ( equal to the y velocity, V i.e.,

the velocity of the system toward or away from the sun, during primary

eclipse), but a doppler shift related to Ve. Thus a careful analysis of

the Rossiter effect should yield a value of Ve .

This effect was next reported in studies of 3 Persei (Algol) by

McLaughlin (1924) and B Lyrae by Rossiter (1924), both of whom attributed

the effect to stellar rotation. In 1931, 0. Struve and C. T. Elvey

(1931) confirmed Schlesinger's hypothesis by computing the asymmetric

line profiles expected for Algol (during primary eclipse and assuming

synchronous rotation, Porbit = P rotation'for the primary component)
orbit rotation
and comparing them with the observed profiles; the agreement between the

two was excellent.

All eclipsing binary systems should show the Rossiter effect,

although its magnitude and duration will certainly be a function of each

system's geometry and physical properties (i.e., period, etc.). The























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effect should be large and relatively easy to observe in a class of

eclipsing binary systems called Algol-type systems, which will now be

discussed.

Algol-Type Eclipsing Binary Systems

The classical Algol systems are characterized by the following

properties: (1) a deep primary eclipse, sometimes reaching 4-5m in

depth in the blue, (2) orbital periods ranging from 1 to 20 days, and

(3) spectral classes of A V or B V for the primary components, and G

or K (III or IV) for the secondary components. Photometric analyses

show that the deep primary eclipse is an occultation, wherein the larger,

cooler G or K subgiant passes in front of the smaller, hotter A or B

main sequence star. Thus the secondary eclipse (which in U, B, and V is

usually very shallow) is a transit eclipse. Using the spectroscopic and

photometric data, and assLuing that the secondary component fills its

limiting Roche lobe (as period changes and emission line activity suggest

it does), it was found that the secondary component was the less massive

component of the systems studied. This situation, where the larger,

cooler, less massive but more highly evolved star is accompanied by a

smaller, hotter, more massive main sequence component represents the

classical Algol paradox. Its resolution lies with the generally accepted

picture of stellar evolution that, because stars expand as they evolve,

the more massive star in a close binary system may expand to fill its grav-

itational Roche lobe first. Further expansion will lead to runaway, large

scale mass transfer from the original primary component to the original

secondary. This self-sustaining mass transfer will continue until after

the mass ratio,q, reverses. At some time after this, the rapid phase

of mass transfer will end, and be replace.- by a slow phase of mass











transfer, which now proceeds on the nuclear time scale of the original

primary (now the secondary component). The presence of either continuous

or intermittent gas streams between components is thus predicted. One

is then left with a more massive main sequence component (the original

secondary), and an evolved but less massive subgiant component (the

original primary) filling its inner Roche critical surface and slowly

transferring mass to the new primary component. This seems a reasonable

explanation of the Algol Paradox (cf. Crawford, 1955), and suggests that

because angular momentum as well as mass is transferred to the original

secondary, the current primary components of these systems may be rotat-

ing with a higher than synchronousvalue of V .

In many binary systems the rotational and orbital periods of the

component stars are thought to be equal, the condition of synchronous

rotation. Usually a mechanism such as tidal braking is cited to explain

this, wherein the rotational angular momentum is transferred into orbital

angular momentum via the gravitational drag induced through the distor-

tion of the outer envelope of an asynchronously rotating component.

However. due to the mass and angular momentum transfer described above,

the outer envelope of the primary components in Algol systems canspin

asynchronously, since the angular momentum transfer is large, and, during

the rapid phase of mass transfer, is on a much shorter time scale than

the tidal braking mechanism described above (for derails see Wilson and

Stothers, 1974). The degree of asynchronous rotation will be related to

the initial orbital parameters, initial stellar masses, and the stage

of evolution being observed (i.e., rapid phase or slow phase of mass

transfer).











It is thus possible to predict that the primary components of

Algol-type eclipsing binary systems may show a larger-than-synchronous

Rossiter effect. The most likely candidate Algol systems exhibiting this

effect would be those which are in the beginning of the slow phase of

mass transfer. Observations made later than this will exhibit a reduced

Ve of the primary component due to tidal synchronization. Observations

made earlier than this will encounter difficulty observing the spectral

lines of the primary component due to the presence of a thick "cocoon"

structure surrounding the primary during and immediately after the

stage of rapid mass transfer, as in 6 Lyrae (Wilson, 1974) and V356 Sgr

(Wilson and Caldwell, 1978).

Following consideration of all the points noted above, 19 Algol-

type eclipsing binary systems were selected for study. These systems

also possessed sufficient spectroscopic data to make a combined study

possible. The size of the Rossiter effect for these systems varies

from extremely large (U Cep, RY Per), to less than synchronous (W UMi, X

Tri). The systems range in period from 0.9 to 16 days. The bulk of the

spectroscopic data is provided by the extensive spectroscopic studies of

eclipsing binaries made by 0. Struve in the 1940's. The photometric

data range from modern UBV photoelectric observations to photographic

observations made by Gaposchkin (1953). Further discussion of the

selected data is made in the next chapter.

Purpose of This investigation

The major aims of this dissertation are as follows:

1. Derivation of V for the 19 systems under study, both to
e
provide new data, and to provide an independent measure of V

to be compared with the published data from line profile work.











2. Re-solution of the light curves of these systems, taking

into account the effect of rotational distortion of the

primary components.

3. Determination of new absolute elements for these systems.

4. Determination of the extent to which the limiting rotational

lobe is filled. The limiting rotational lobe is that potential

surface within the inner critical Roche surface,for faster

than synchronous rotation, for which the gravitational force

is equal to the centrifugal force at the intersection of the

surface with the line of centers.

5. Discussion of the possible evolutionary status of these

systems, and explanations of their other observed properties.

The next chapter deals with the selection and analysis of the data

chosen for this study.














CHAPTER II

METHOD OF ANALYSIS

A description of the method of analysis is now presented.

The two primary computer programs used in this study were the

Wilson-Devinney light curve program (hereafter LCP) and differential

corrections program (hereafter DCP). Both of these programs have been

extensively described in the literature (cf. Wilson and Devinney, 1971,

1973, and Wilson and Biermann, 1976). The LCP calculates monochromatic

light curves based on an input set of system parameters. The DCP uses

a starting set of system parameter values, and any number of observed

light curves, and calculates corrections to the starting parameter

values. A list of parameters to be differentially corrected is supplied

to the DCP program, along with any number of parameter subsets. In this

way, the method of parameter subsets (Wilson and Biermann, 1976) is used

to overcome any correlation problems between adjusted parameters. The

system parameters used by the two programs are the orbital inclination,

i, the mass ratio, q(= 2i/1), the value of the stellar surface potentials,

01 and Q2' the polar temperatures, T1 and T., the gravity darkening

exponents, g, and g2, the linear limb darkening coefficients, xl and x2,

the fractional luminosities, L1 and L2, the bolometric albedos, A1 and

A2, the wavelength(s) of observation, X, the amount of third light, 1,

and the ratio of the rotation rate to the synchronous rate, F.

in addition to the above, the two programs recognize a mode integer.

Specification cf the mode allows the program to incorporate any special











constraints one might feel should be included. As an example, the

solutions presented here for the 19 Algol systems were carried out in

mode 5. This mode specifies the condition that the secondary component

exactly fill its inner critical surface (see previous discussion of

Algol systems in Chapter I).

Finally, the LCP, in addition to calculating theoretical light

curves, also calculates the radial velocity curves for each component.

The velocities which are computed are dimensionless, and contain the

factor 2nP/a, where P is the orbital period and a is the separation

of centers.

The procedure used in this study is an iterative one, since a

computer program for the simultaneous solution of photometric and

spectroscopic data is not yet available (although the basic principles

for such a program have recently been discussed, Wilson, 1979). A

general outline of the method used for obtaining Ve for the 19 Algol

systems is given below.

1. The LCP was used to compute, via trial and error, an initial,

fairly close fit to the light curvess, and thus a first set

of parameters describing the system.

2. The parameters found in (1) were supplied to the DCP along

with the light curve(s), and an initial guess of the value

of F (which comes from an inspection of the observed radial

velocity curve). Several runs of the DCP were made until a

good fit to the light curve(s) was achieved. The progress

of the solution process was followed by running the LCP with

the new, updated parameter values, and plotting the resultant

light curve versus the observed points after each run of the

DCP.











3. The theoretical radial velocity curve calculated after the

last DCP run in (2) (i.e., from the last LCP run) was then

plotted against the observed radial velocity curve in order

to check the amplitude of the Rossiter effect. To do this,

the observed velocities were transformed into dimensionless

velocities. Note that at phase 0.25, the value of the theo-

retical dimensionless velocity and the value of the semi-

amplitude of the observed radial velocity curve, K will be

equal except for the multiplicative constant mentioned

previously (2TrP/a). Thus, knowing K1 and the dimensionless

velocity at phase 0.25, the constant factor can be determined.

Once this factor is known, it is possible to transform the other

observed velocities into dimensionless velocities. Corrections

for the value of V and any possible phase shifts between the

spectroscopic and photometric data were also taken into

account.

4. In most cases, the initial guess of F and hence the amplitude

of the Rossiter effect was incorrect in (3). LCP runs were

then carried out for different values of F, until the correct

amplitude was achieved. This new value of F was put back into

the DCP and the solution of the light curve carried out for the

new value of F.

5. Through the iterative process outlined in (4), the prelimi-

nary solutions converge to a light curve solution and a value

of F such that both the amplitude of the Rossiter effect is

correct, and a good fit to the light curves) is obtained. For

the final DCP runs, the fit to the light curve was carried out











until the corrections for the adjusted parameters were less

than or approximately equal to their associated probable

errors. Also, although only the basic parameters i, q, 01,

T2, and L1 were adjusted during the iterative process, an

attempt was made during the final runs to adjust xl, g1, and

A2 for stars with no complications in the light curve and

good observational phase coverage.

6. The final light curve solution yielded a final value of

Vtheo at phase 0.25. As explained, value of the factor for

transforming Vobs into Vtheo could now be obtained. Remember-

ing that this factor = 2TP/a, and knowing P very accurately,

we can solve for a (in km) (if P is in seconds and K1 is in

km/sec) through the following equation:

S= [(K.P/I2Vtheo,0.25)] (1)

7. From the LCP, a value of rl,side (= side radius of the primary

component in terms of the separation of centers, a) is also

computed. With a from (6), R1, the side radius of the primary

component in km, is computed.

8. With R1 from (7), and the relation Ve( = 27R1/P, the svn-
I e(syn) 1
chronous equatorial velocity of the primary is calculated.

Finally, using the final value of F, the value of V is
e
arrived at from the equation Ve = Ve(yn)'F.

Having summarized the computer programs used in this study, and the

general method used for determining Ve, a review of the problems which

arose during the solution process is now appropriate. A summary of the

problems found in analyzing the photometric data will be done first.










The quality and quantity of photometric data for each system varied

greatly. When possible, two- or three-color photoelectric light curves

were used. For several systems only one-color photometric data were

available. In one case the only available light curve was the photo-

graphic light curve by Gaposchkin (1953). While the accuracy of the

photographic light curves is lower than the photoelectric light curves,

they should suffice for a first survey such as this work. When pos-

sible, 50-100 normal points per light curve were used.

A major problem for many systems was the presence of distortions

at certain phases of the light curves. The majority of these distortions

can be described as extra light added to the "undisturbed" light curve

between phases 0.08 and 0.35. Since gas streams are almost certainly

present for most of these systems, and disk structures may also exist,

it is not surprising that many light curves show distortions of the

nature described above (a description of the light curve distortions

for individual systems is included in Chapter III). When obviously

disturbed sections of the light curve were present, the distorted regions

were excised. In addition, the U light curves for several systems were

not used because many authors have reported distortions of these light

curves near second contact. Thus it is hoped that the effect of distor-

tions on the solution process was minimized.

It should be noted here that the assumption was made that the

effective wavelength of observation for the photographic light curves

was approximately 4100 S (see Arp, 1961).

Spectroscopically many problems are evident in these determina-

tions of rotational velocities. Foremost of these is the definition

of the "center" of an asymmetric spectral line. The LCP calculates a









mean line center, where the mean is calculated by weighting the radial

velicty of each grid area on the star by the light emitted from that area

in the observer's direction. Thus, effects due to limb and gravity darken-

ing, rotational flattening, etc., are automatically taken into account. An

assumption made here is that the intrinsic line profile is narrow as com-

pared to the rotational broadening function. While this assumption would be

important if one were going to match theoretical and observed line profiles,

it does not directly affect the measurement of the line centers (except that

the wider the profile, the harder it will be to determine the center of the

line).

It was noticed, however, that when the initial spectroscopic results

for several systems were plotted, the onset of the observed Rossiter effect

came later than the theoretical time of onset, and ended earlier than

expected! An explanation for this effect results directly from the assump-

tion that most observers, when trying to determine the line center of an

asymmetric line, apparently simply choose the deepest part of the profile

as the center of the line (Abt, 1979). However, as outlined in Figure 2,

identification of the deepest part of the line as the center will not

measure a line shift (due to the Rossiter effect) during the initial and

final phases of the eclipse. In order to test this, the LCP program was

modified to print the expected line profile for values of phase during

which the rotation effect would be present. A new graph of the rotation

effect, as it would seem if the deepest part of the line were used to

define the line center, was constructed. The result, shown in Figure 3,

confirms the aforementioned hypothesis. Note that the crmlitude of the

Rossiter effect was not affected. For this reason the primary fitting

criterion was that the ampliLude of the theoretical and observed Rossiter

effect match.























0 03
4 0, o4


- 0i 03t '0 U H


C3 aU 9z o 03 H
'A F- "- L
SZ 3 3 T-i Ln 3H


3 00 3 3


Q -00 i -C 3
a n o3 V) 0 3 -
a ec i



S 03 0 0 0 0 3
4-4c C C-)

oC4 3u ca
4a ao
. C $ 4 i
to e 0 a 34
) 0U 0 2 0- 0 U) 04)





or3.) o U) n 0
0-0 0 0 Mj 4
O 0 c 'a
O l *H i *3 >








03 o 3 0 0




S 0 L)- ,- -- -) '-A
U0C 03 *-, *k4-4
-l o >o o m a z >

23 0 = U) r, ) (4- 1) C) *

03 O 0= --
3 03 0003 0
F- iu 4 0 -3 0 U 0
033 O- 0 0 cO


03 CI 0 03-' F- 03 zi


d F 00 0 C 0 00
*ri (U * 0

0,-H.-- 0c^F-U-03
03 03 03 (- 3 U) 0 ) 03 3



,0 O.,,3Q U) 0 3 0303
- 03 4-' a 0 03 -
3 e'U O SU

aa tl E-> a 3 3i

G O a C a >
H O- .rl X y -C 3
HO~~od8HcR











































































































__ ___ aI _Y__I.


_ _1 I IC


__ _I

















E





V -D 0 1 =
'1. oJ C C C


r C3 .1 0 -r


44000 10
tHl C C 4




03 -: 0 a


) 04 00


C0 C
C4r-C0 C
C O C - C


.4C4 -



0 OC 0 0
.. 00 00








U -C 0
0 '0U >T0 -






CO C U) -4
OC Cr CU 44








44,0 0 C.2




d C U)

U C (0 ) C 0
O i Ci










CC c
-4 0 144
c0 0 U C

0 0 C C CO
'H C -C C

4C D OD 0


C a0 0
CO . -i Y ) CC










.P I
'O 0 ^ y Q-
(U~e ~ '0 -
c-3 C, m iU












s? -


i I fi


4 *4



0'\


4


C,



C I'









/j


/


-~I


I -0 '--- --- --S


'3


S' 'o


30'0-


Si'


OIc

la


I


u,

1)
C =




- C
^. 0


in
Ir,


-r
I~


Se'0


SL'


so'o-


s5z-


, d i .





'I
9 'N I

.4'

q\I
3'






a


N'i


N'


--











A further problem exists in the interpretation of the observed

Rossiter effect as a unique velocity; that is, different spectral lines

show effects of different amplitudes. In particular, the higher excita-

tion lines such as lie I and He II sometimes show a rotation effect

double that for the hydrogen lines. As suggested by Hansen and McNamara

(1959) for RZ Sct, and Hiltner (1946) for RY Per, this circumstance is

probably due to either (a) the hydrogen lines arising in a more slowly

rotating disk or envelope structure around the primary, while the helium

lines arise in the true stellar photosphere, or (b) the normal stellar

hydrogen lines are severely modified by absorption and/or emission in the

aforementioned disk structure, thus making the velocities determined

from these lines unreliable. In any case, it would seem that the He

lines and other higher excitation lines are more accurate indicators of

the rotation velocity of the stellar envelope. For this reason, the

radial velocity measurements of the He I, He II, and Mg II lines were

used whenever possible in this study. For systems whose published radial

velocities represent an average of all measured lines, the results of

such work very likely yield only lower bounds to V .
e
Near the bottom of primary eclipse, where the light of the secondary

component may become equal to or even exceed that of the primary component,

one might need to consider the role of possible line blending (if it

occurs) on the observed line profiles of the primary component, and thus

on the determination of the line center. Further, the light curve solu-

tions show that for most of the partial phases the light of the primary

is much greater than that of the secondary. Thus tnis effect would only

operate during a small time interval. In addition, it is known that,

in almost every zase studied here, the secondary is of a later, much











cooler spectral type than the primary; hence it has a much different

spectrum. Thus it is unlikely that, except for a few very weak lines

that are near the lines normally measured, any significant blending

of spectral features of the two stars will occur. For several systems,

the presence of such weak lines of the secondary probably accounts for

the presence of measured radial velocities for the primary component

during a total eclipse. When this effect was recognized, affected data

points were eliminated from the analysis.

There most certainly is a problem with emission lines from the

stream or disk modifying the line profiles. It would be expected that

the systems which show a large Rossiter effect, disturbed light curves,

and prominent emission lines at certain phases are those systems which

display the largest radial velocity distortions and large scatter

throughout their radial velocity curves. This is in fact the case.

Systems such as U Cep, AQ Peg, RZ Sct, RY Per, SW Cyg, and U Sge all

exhibit such behavior. The amount of scatter and distortion introduced

into the radial velocity curve through such emission line effects (and/

or absorption, which may also exist) will be a complicated function of

system-stream-disk geometry and physical parameters (e.g., the density

and temperature of the gas stream) (see Parise, 1979). In more tractable

cases, the velocity curve outside of eclipse can be recovered (see

Hardie, 1950), in which case an accurate value of K1 may be obtained, as

previously mentioned. Several actions may be taken in order to minimize

the influence of the effects mentioned above: (1) Because the higher

excitation lines of He and Mg are probably more indicative of the stellar

surface rotation (due to relatively larger modification of the H profiles










through absorption and/or emission in the stream-disk structure), only

these (and similar) lines should be (and were) used whenever possible,

(2) Reconstructed radial velocity curves, for which an attempt to remove

the effect of emission/absorption has been carried out, should be utilized;

and (3) Direct matching of observed and theoretical line profiles, whereby

direct comparison might shed light on distortions of the line profile due

to extraneous emission/absorption, should be employed. Unfortunately, U Cep

is the only system for which (2) has been carried out, and both (2) and (3)

would require microdensitometer tracings for all the spectroscopic data--a

task outside the scope of this work. It should be noted, however, that

at the phases corresponding to the maximum of the Rossiter effect (i.e.,

just before primary minimum), one should expect mostly emission from

either the ring or a hot spot where the gas stream hits the disk structure

(if it exists). Thus, if the emission falls at the same wavelength as the

rotationally modified absorption feature, one should expect line filling

to occur, and thus the measured effect will be smaller. This topic will

be discussed again in Chapter III as it pertains to individual systems.

Finally, another source of error is that of line smearing due to

long exposure times. For several of the systems studied, the Rossiter

effect goes through an entire cycle in only 70 minutes. If care is not

taken, and long exposure times are used, the line profile will be smeared,

and the effect washed out. Comments on this problem as it pertains to

individual systems will be made in Chapter III.

In summary. the problems with the spectroscopic data fall into

two main classes: (1) Those which, through blending or smearing, tend

to lessen the amplitude of the Rossiter effect, and (2) those which








25


distort the radial velocity curve, thus making the derived value of K1

uncertain. However, since the prime objective of the fitting process

is to match the amplitude of the Rossiter effect, the value of Ve found

should be, at worst, a lower bound to the true value. In the next

chapter the observational data utilized for the individual systems will

be discussed in detail.















CHAPTER III

DISCUSSION OF INDIVIDUAL SYSTEMS

In this chapter the observational data used in this study will

be discussed. For each system a summary of the spectroscopic and

photometric data used is given. Comments on the derived values of

the temperature of the secondary component, T2, the ratio of rotation

rate to the synchronous rate, F, and the presence of possible period

changes are also presented. Further discussion of the systems studied

as pertains to the equatorial rotational velocity, Ve, derived absolute

elements, etc., will be presented in Chapter IV. Table I gives the

basic observed parameters for each system. Table II lists the spectro-

scopic elements used in this study. Table III presents the results of

the photometric analysis for the wavelength independent parameters.

Table IV lists the results of the photometric analysis for the wave-

length dependent parameters. Figures A-1 to A-20 (see Appendix A) show

the fits to the spectroscopic data, and Figures B-1 to 8-22 (see Appendix

B) show the theoretical fits to the individual light curves. The ab-

scissa for all figures is orbital phase. For Figures A-1 to A-20, the

ordinate is velocity, V, in dimensionless units. The ordinate for Fig-

ures B-1 to B-22 is light level.

X Tri

The spectroscopic work of Struve (1946b) was used for this investi-

gation. 'he spectral type of the primary component is A3 V. The derived

value of T2 implies G2 III or G3 IV for the spectral type of the second-

ary component. This is in good agreement with the spectral type of G3

given by Struve, who states that some blending with the A3 spectrum

26











TABLE I

BASIC SYSTEM DATA


Spectral Spectral
HD (BD*) Period Class Class
Name Number (Days) Component 1 Component 2


X Tri 12211 0.9715 A3 V G3 IV
Y Leo +260 1981* 1.6861 A3 V K3 IV
RZ Cas 17138 1.1953 A3 V K1 IV
ST Per 18541 2.6484 AS V K1 IV
RX Hya 78014 2.2816 A8 V KO IV
W UMi 150265 1.7012 A3 V G9 IV
WW Cyg 227457 5.3177 B8 V G4 III
RW Gem 250371 2.8655 B5 B6 V FO III
TX UMa 93033 3.0633 B8 V F7 FS III
TV Cas 1486 1.8127 B9 V Gl IV
AQ Peg +120 4653* 5.5483 A2 V Kl IV
SW Cyg 191240 4.5728 A2 V K3 IV
Y Psc 221700 3.7659 A3 V K2 IV
W Del 352682 4.8060 AO B9.5 V KO IV
RY Gem 58713 9.3009 A2 V KO III Ki IV
U Sge 181182 3.3806 B8.5 V GS III
U Cep 5679 2.4930 B7 V G8 III
RY Per 17034 6.8636 B4 V FO III
RZ Sct 169753 15.1902 B2 II AO II III











TABLE II

SPECTROSCOPIC DATA


Name P (Days) log P Kl(km/sec) y(km/sec) e f(m)


X Tri 0.9715 -0.013 110.0 -05.0 0 0.134
Y Leo 1.6861 0.227 60.0 +.0.0 0 0.038
RZ Cas 1.1953 0.078 68.0 -40.0 0 0.041
ST Per 2.6484 0.423 33.0 -50.0 0 0.008
RX Hya 2.2816 0.358 40.0 00.0 0 0.015
IV UMi 1.7012 0.231 86.6 -17.9 0 0.110
IW Cyg 3.3177 0.521 68.0 +08.0 0 0.108
RW Gem 2.S655 0.457 68.5 +00.3 0 0.950
TX UMa 3.0633 0.486 51.8 +00.5 0 0.128
TV Cas 1.8127 0.258 88.0 +50.0 0 0.012
AQ Peg 5.5483 0.744 35.0 -08.0 0.24 0.023
SW Cyg 4.5728 0.660 43.0 -01.0 0.30 0.033
Y Psc 3.7659 0.576 37.0 +06.0 0.12 0.019
W Del 4.8060 0.682 30.0 +19.0 0.20 0.013
RY Gem 9.3009 0.968 27.1 +11.8 0.16 0.018
U Sge 3.3806 0.529 68.0 -10.1 0.04 0.088
U Cep 2.4930 0.397 85.0 00.0 0 0.160
RY Per 6.8636 0.837 36.0 -26.0 0.21 0.033
R2 Set 15.1902 1.182 36.5 -14.5 0 0.077










TABLE III

WAVELENGTH INDEPENDENT PARAMETERS


a a a
Name i gl 2 A1

X Tri 88.18 + 0.30 1.00 0.32 1.00
Y Leo 85.68 z 0.30 1.00 0.32 1.00
RZ Cas 82.00 + 0.07 1.00 0.32 1.00
ST Per 87.42 0.42 1.00 0.32 1.00
RX Hya 83.47 1.50 1.00 0.32 1.00
W UMid 85.21 0.25 1.00 0.50 1.00
NW Cyg 87.68 0.17 1.00 0.32 1.00
RW Gem 1 87.35 0.21 1.00 0.32 1.00
RW Gem 2 86.71 0.13 1.00 0.32 1.00
TX UMa 82.45 0.15 1.00 0.32 1.00
TV Cas 77.79 1.32 1.00 0.32 1.00
AQ Peg 83.57 0.16 1.00 0.32 1.00
SW Cyg 83.66 0.12 1.00 0.32 1.00
Y Psc 87.00 0.06 1.00 0.32 1.00
W Del 86.56 0.25 1.00 0.32 1.00
RY Gem 83.92 0.51 1.00 0.32 1.00
U Sge 87.12 0.17 1.00 0.32 1.00
U Cep 83.35 0.54 0.99C_ 0.30 0.44Ci 0.22 1.00
RY Per 82.42 0.17 1.00 0.32 1.00
RZ Sct 1 81.84 1.50 1.00 1.00 1.00
RZ Set 2 80.72 1.80 1.00 1.00 1.00


aExcept where noted, these parameters were not adjusted.

Not adjusted--found from associated values of n1 and Q.

Cparameter adjusted for this system.

Not solved by author (see Devinney and Sutton, 1979).













TABLE III--Extended


Aa Ti(K) T,( K) 1 2a


0.19c9 0.0
0.50
0.50
0.50
0.50
1.00
0.50

0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.52c: 0.04
0.50
1.00

1.00


3 9,730
9,260
9,730
9,260
8,000

8,750
14,500
16,400
16,400
13,400
12,400

9,730
9,730
9,260
10,800
9,730
13,000
13, 600
17,500

22,700
22, 00


5553 20
4292 50
4744 35
4800 60
4358 = 800

5000 40
5490 45
7000 30
7007 : 26
5823 76
5666 400
4216 24
4305 18
4572 13
4933 50
4703 170
5263 11

4824 120
6540 50

S953 90
9050 200


- -


10.264 0.11

9.3685 0.54


+


4.257
5.105
4.760
5.655
5.010
3.223
5.008
5.436
5.503
u.444
5.845
S.820
7. 863
5.474
6.839
10.607
5.527
8.773
S.767


0.03
0.03
0.02
0.11
0.28
0.01
0.05
0.06
0.04
0.07
0.40
0.14
0.09
0.02
0.17
1.50
0.03
0.12
0.11


3.157c 0.02
2.557
2.612
2.228
2.161
2.S635c 0.01
2.464
2.576
2.564
2.430
2.700
2.387
2.489
2.346
2.225
2.150
2.645
2.998
2.428












TABLE III--Continued


b b
Name q r r r b
Name rl,pole 1,side 1,point

X Tri 0.634 .006 .270 .002 .272 .002 .279 .003
Y Leo 0.342 .005 .210 .001 .213 .001 .214 + .001
RZ Cas 0.368 + .002 .227 .001 .233 .001 .235 + .001
ST Per 0.198 + .003 .183 + .004 .184 + .004 .185 .004
RX Hya 0.172 .040 .207 + .012 .211 .013 .211 + .013
W UMid 0.464 = .003 .351 + .001 .363 + .001 .383 .002
WW Cyg 0.299 .003 .212 .002 .215 .002 .217 + .002
RW Gem 1 0.351 .004 .196 + .002 .207 .002 .208 .002
RW Gem 2 0.345 .003 .194 .002 .198 .002 .199 + .002
TX UMa 0.284 .003 .162 + .002 .164 + .002 .164 .002
TV Cas 0.411 .090 .184 + .014 .188 .015 .189 + .015
AQ Peg 0.265 .005 .117 .002 .123 + .002 .123 + .002
SW Cyg 0.310 i .004 .132 .002 .138 .002 .139 .002
Y Psc 0.247 + .002 .191 + .001 .193 .001 .194 .001
W Del 0.197 + .004 .151 .004 .151 + .004 .152 .004
RY Gem 0.167 + .050 .095 + .014 .097 + .014 .097 .014
U Sge 0.384 + .008 .196 + .001 .219 .002 .221 .002
U Cep 0.565 .030 .139 .002 .177 + .009 .179 + .009
RY Per 0.283 .007 .118 .002 .137 .003 .138 + .003
RZ Sct 1 0.247 + .011 .100 + .001 .136 .007 .137 .008
RZ Sct 2 0.211 .080 .109 .006 .122 .010 .122 .011












TABLE III--Extended


r b r b r b b
r,back 2,pole r2,side r2,point 2,back


.277 .003 .319 .333 .440 .365
.214 .001 .271 .282 .380 .315
.234 .001 .276 .288 .387 .320
.185 .00 .232 .242 .331 .274
.211 .013 .223 .232 .318 .264
.374 .002 .292 .304 .401 .337
.216 .002 .261 .272 .368 .304
.208 .002 .273 .284 .383 .317
.198 .002 .271 .283 .381 .315
.164 : .002 .257 .268 .363 .300
.188 .015 .285 .297 .398 .329
.123 .002 .252 .263 .356 .295
.139 .002 .264 .274 .371 .307
.194 .001 .247 .257 .350 .290
.152 .004 .232 .241 .330 .273
.097 .014 .221 .322 .316 .262
.221 .002 .285 .297 .398 .330
.179 .009 .309 .323 .429 .355
.138 .003 .257 .267 .362 .300
.137 .008 .251 .261 .355 .294
.122 .010 .236 .246 .336 .278







TABLE IV
WAVELENGTH DEPENDENT PARAMETERSa


Light
Name Curve xe(() L1 L2b x1 x2


X Tri V 5500 .8498 .0018 .1502 .33 .06 .71
B 4400 .9097 .0024 .0903 .51 .07 .81
Y Leo V 5500 .9426 .0056 .0574 .57 .07 .46
B 4400 .9772 .0064 .0229 .44 .07 .53
red 8000 .8611 .0064 .1389 .08 r .10 .33
RZ Cas V 5500 .9210 .0035 .0790 .46 .05 .44
B 4400 .9634 .0030 .0366 .43 .05 .53
U 3650 .9796 .0028 .0204 .41 .06 .40
ST Per R 6940 .8308 .0163 .1692 .38 .31 .61
I 8760 .7691 .0179 .2309 .30 = .23 .50
RX Hya pg 4100 .9714 .0470 .0286 .45 .60 1.00
W UMi V 5500 .9450 .0023 .0550 .33 .05 .500
B 4400 .9780 .0023 .0220 .49 .04 .500
U 3650 .9887 .0022 .0113 .47 .04 .500
IWV Cyg V 5500 .9357 .0026 .0643 .34 .12 .65
B 4400 .9708 .0029 .0292 .42 .12 .78
U 3650 .9840 x .0031 .0160 .36 .12 .84
RW Gem i V 5500 .8354 .0016 .1646 .40 .06 .59
RW Gem 2 V 5500 .8330 .0017 .1670 .40 .06 .59
TX UlMa blue 4500 .9046 .0066 .0954 .40 .10 .85
TV Cas pg 4100 .9260 .0464 .0740 .48c .85
AQ Peg V 5500 .8818 .0041 .1182 .30 .14 .85
B 4400 .9536 .0042 .0464 .40 .15 1.00
SW Cyg V 5500 .8852 = .0027 .1148 .01 .13 .85
B 4330 .9497 .0028 .0503 .26 .11 1.00
Y Psc V 5500 .9178 .0010 .0822 .44 .03 .83
B 4400 .9631 .0013 .0369 .51 .03 1.00
W Del V 5500 .8885 .0035 .1115 .23 .20 .71
B 4400 .9484 .0027 .0516 .47 .18 .86
RY Gem pg 4100 .9018 .0080 .0982 .57c .95
U Sge y 5470 .9048 .0096 .0952 .17 .16 .68
b 4670 .9376 .0127 .0624 .20 = .28 .82
v 4110 .9588 .0134 .0412 .25 .26 .93
u 3500 .9780 + .0111 .0220 .20 .16 .86
U Cep V 5500 .8789 .0283 .1211 .35 .35 .77
S 4300 .9458 .0362 .0542 .62 .27 .93










TABLE IV--Continued


Light
Name Curve A (R) L Lb x xc

RY Per V 5500 .7535 .0131 .2465 .33 .61
T 4400 .8529 .0151 .1471 .42 .71
RZ Sct 1 V 5400 .5858 .0321 .4142 .29C .47
E 4250 .6852 .0472 .3148 .36c .59
RZ Set 2 V 5400 .6347 .0420 .3653 .29c .47
B 4250 .7424 .0450 .2576 .36c .59

aNo third light was found (within the probable error) for any of the
systems studied.
parameter not adjusted in mode 5.

Parameter was net adjusted.

No adjustment necessary to value found by Markworth (1977).











exists on the plates taken during primary minimum (totality lasts

approximately 12 minutes). The radial velocity curve is symmetric, and

shows a small, less-than synchronous (F=0.6) Rossiter effect. No emis-

sion lines are present. Figure A-I shows the fit to the radial velocity

curve.

The modern BV light curves of Bozkurt, Ibanoglu, GUlmen and

GUdUr (1976) were used for the photometric analysis. These light curves

exhibit excellent phase coverage and small scatter throughout. Because

the mode 5 solution gave a very poor fit out of eclipse, a mode 2 solu-

tion was tried, which resulted in a. good fit to the light curves, as

shown in Figure B-1. A periodic representation of the time-of-minima

data was found by Rafert (1977). This is probably a light-time effect

due to a third (unseen) member of the system.

Y Leo

By assuming a circular orbit and a value of F = 1.5, an excellent

fit to the radial velocity curve is achieved. Struve's (1945) impression

that the light of the A3 V primary is still visible during mid-primary

eclipse (i.e. that primary eclipse is partial) is supported by the present

work. The derived value of T2 implies a spectral class of K2 III or

K3 IV. The exposure times were short enough that line smearing should

not have been a problem. As mentioned earlier, the radial velocity

curve of this star was used to test the effect of measuring the deepest

part of the line profile as the line center, instead of using a weighted

mean (see Figures 2, 3 and A-2). There is evidence for period changes

in this system, although the exact nature is in question. A value of

F = 1.5 was used for the final photometric analysis.











The photometric analysis was carried out using the B, V, and

red ( e = 8000 R, 3000 A wide bandpass) light curves of Johnson (1960)

(see Figures B-2 and B-3). As a check on the assumption of using mode

5 for these systems, a trial run of the DCP in mode 2 (identical to

mode 5 except that the lobe-filling constraint on the secondary is relaxed)

provided corrections indicating that the secondary did fill its Roche

lobe. No complications are evident in the light curves other than an

indication that the ingress shoulder of primary eclipse is slightly low.

Evidence for period changes is summarized by Rafert (1977).

RE Cas

Spectroscopically this system has been studied by Jordan (1914)

and Horak (1952), the latter work being used for the present investiga-

tions (89 observations at 40 R/mm at 3933 ) The spectral type is

given as AO (Horak) to A3 V (Chambliss, 1976). The derived value of

T, suggests a secondary spectral classification of KO III or Kl IV. No

emission lines were noted by Horak. Both branches of a moderately

large rotation effect are seen. A value of F = 1.6 gives a satisfactory

fit to the rotation effect, as can be seen in Figure A-3.

Many photoelectric light curves exist, the most modern being the

studies of Chambliss (1976) and Lee and Lee (1977). The UBV normal points

of Chambliss were used in this study. A solution of the 3 light curves,

using approximately 75 normal points for each light curve, was carried

out, resulting in excellent fits to the light curves (see Figures B-4

and B-5). A variable light curve is suspected for this system (Chambliss,

1976). Rafert (1977) has discussed the evidence for period changes in

this system, emphasizing the probable filling of the secondary's Roche

lobe.











ST Per

The spectroscopic data used were that of Struve (1946b). He and

Hill et al. (1975) agree on an A3 V classification for the primary

component. The value of 1' found implies a spectral type of KO III or

K1 IV, in agreement with the classification by Weiss and Chen (1976).

The radial velocity'is characteristic of a circular orbit, with the

Rossiter effect being evident for the egress phases of primary eclipse.

No data were taken during ingress. A value of F = 1.35 was used for the

final photometric analysis. Figure A-4 shows the final fit to the

spectroscopic data.

The photometric analysis of this star was carried out using the

RI photometry of Weiss and Chen (1976). Approximately 50 normal points

in each color were used. While there is appreciable scatter in the

original observations, the use of judiciously chosen normal points

allowed a solution to be found with little difficulty. Figure B-6 dis-

plays the final fit to the light curves. A discussion of the evidence

for period changes is given by Rafert (1977).

RX Hya

The spectroscopic data of Struve (1946b) were used for the analysis

of this system. The spectral type of the primary is AS V, making it

the "latest" spectral type primary studied. The value of T2 derived in

the photometric solution implies a secondary spectral type of KO IV or

G8 III. The radial velocity curve is symmetric, with a pronounced

rotation effect present (F = 2.0). Struve states that during mid-primary

eclipse, "the metallic lines look slightly stronger, but the spectrum

is still essentially that of the brighter, AS, star." The later than











normal spectral type of the primary and the latter statement of Struve

may point to blending problems near primary eclipse, perhaps affecting

the amplitude of the Rossiter effect. No emission lines are noted by

Struve. The fit to the radial velocity curve is shown in Figure A-5.

The light curve used was the photographic light curve of

Gaposchkin (1953), it being the only light curve available. Figure B-7

shows the fit for this partially eclipsing system. The scatter of the

light curve is typical of photographic light curves. A mode 2 solution

was also attempted for this system. The results showed a marked prefer-

ence for the secondary completely filling its Roche lobe. A limited

amount of data implies a period change for this system (Rafert, 1977).

W UMi

This star was included as an example of a system whose radial

velocity curve showed a synchronous Rossiter effect. A new solution of

the UBV photoelectric observations of Devinney, Hall and Ward (1970),

using the Wilson-Devinney programs, has recently been carried out by

Devinney and Sutton (1979). The results of this study have been kindly

communicated by Dr. E. J. Devinney (1979) ahead of publication. This

latter solution shows the system to be either semidetached, or detached

with the secondary very close to its Roche lobe. Their solution was

carried out with F = 1.0. The final elements communicated by Dr. Devinney

were used in the LCP to produce the theoretical radial velocity curve

shown in Figure A-6 plotted against the observations of Sahade (1945).

It would seem from Figure A-6 that the primary component (A3 V) may be

rotating slower than the synchronous rate. In order to test this (to











the first order), the LCP was used to calculate a new theoretical radial

velocity with F = 0.75. The values of all parameters except q, were

kept at their F = 1.00 value. i was adjusted so that the side radius

of the primary component was kept constant. The result is shown in

Figure A-7. While the shape is still not quite right, the fit is superior

to the theoretical F = 1.0 radial velocity curve. If real, the low rota-

tion rate of the primary component could be explained by (1) a system in

pre-main sequence contraction, such that the spin of the primary com-

ponent has not been synchronized through, for instance, tidal effects,

or (2) a systemwell past even the slow phase of mass transfer (i.e., no

gas streams are present), with the "new" primary (by virtue of the orig-

inal phase of rapid mass transfer) now expanding off the main sequence,

so that its rotational rate has slowed to conserve angular momentum.

No emission lines are noted by Sahade.

NW Cyg

The spectroscopic data used for this were that of Struve (1946b).

ie describes the spectrum of the primary as 38 V, and that of the second-

ary as approximately G, although the faintness of the system during

primary eclipse (V = 13.3) made the observation during this time very

difficult. A moderate rotation effect is present although data were

taken only during ingress, and the radial velocity curve is character-

istic of a circular orbit. No emission lines are noted by Struve, although

the same problem mentioned above would make their detection very difficult

if the emission is weak. The derived value of T2 implies a spectral type

for the secondary of G5 IV or G4 III, in agreement with Struve's estimate.

A value of F = 1.55 was found to give the best agreement with the ampli-

tude of the Rossiter effect, and the resulting fit is shown in Figure A-8.











The three-color UBV light curves of Hall and Wawrukiewicz (1972)

were used for -the photometric analysis. The individual points were

used instead of normal points. The fit to the light curve is shown

in Figures B-8 and B-9. The solution does confirm the low value of xl

found by Hall and Wawrukiewicz (1972). The suggestion that "extra"

light is present at second and third contact (due to a hot spot on the

primary) is not supported by an 0 minus C plot of the residuals. The

presence of period changes (cf. Rafert, 1977) and a "spun-up" primary

(in addition to the arguments presented by Hall and Wawrukiewicz) do

not favorthe pre-main sequence contraction state of evolution suggested

by Field (1969).

RW Gem

The spectroscopic work of Struve (1946b) was used in analyzing

this star. Except for 3 questionable points near phase 0.96, the radial

velocity curve is well represented by a circular orbit, with an excellent

fit to the amplitude of the Rossiter effect being achieved with F = 2.1

(see Figure A-9). The spectral type of the primary component has been

given as B5 V (Struve, 1946b) and B6 V (Lucy and Sweeney, 1971). The

spectral type of the secondary was given by Struve as roughly FS sub-

giant and FO IV by Lucy and Sweeney (1971). The derived value of T2

is consistent with an FO II-III classification. The revised values of

K! and y given by Lucy and Sweeney were used in the fitting procedure.

No emission lines are noted by any of the above authors.

The V light curve of Tremko and Vetesnik (1974) was used for the

photometric analysis. No other photoelectric data were available, although

a photographic light curve by Gaposchkin (1953) does exist. The published











normal points were used, although a second solution was made after the

normal points between phases 0.1 and 0.4 were removed. There is a defin-

ite distortion of the light curve at these phases. The difference

between the two solutions is not as large as would be expected (see

Tables III and IV, RW Gem 1 and 2). The fit to the observed light curve

is shown in Figure B-10. There is evidence of period changes in this

system (Rafert, 1977).

TX UMa

The spectroscopic observations of Hiltner (1945) were used in the

present investigation. Other spectroscopic work has been carried out by

Swensen and McNamara (1968). The spectral type of the primary is B8 V.

According to Hiltner, the spectral class of the secondary component is

gF2. However, a more recent study (UCLA Observatory Report, 1976) gives

a classification of GO III-IV. This is in agreement with the classifi-

cation of F8-F7 III found from the derived value of T,. The radial

velocity curve appears symmetric, as the value of e = 0.029 derived by

Hiltner suggests. The observations of Swensen and McNamara (1968) indi-

cate a variable shape for the radial velocity curve, although this may

reflect differences in the measuring technique used by the different

authors. The magnitude of the rotational disturbance is unequal during

the partial phases of primary eclipse, it being smaller during ingress

and larger during egress from primary eclipse. A value of F = 2.0 gave

a satisfactory "average" fit to the data. No emission lines have been

reported for this system. Figure A-10 shows the fit to the spectroscopic

data.

Of the light curves available in the literature, the blue photo-

electric light curve (Xe = 4500 A) of Huffer and Eggen (1947) was used











for this analysis. Other work has been published by Koch (1961), and Hill

and Hutchings (1973). Forty-seven normal points were used for this

investigation. The fit to the light curve is shown in Figure B-Il. The

derived value of q = 0.29 fortuitously agrees with the value of 0.27

found by Grenwing and Herczeg (1966) from an analysis of the slope of

the radial velocity curve of the secondary component during primary

eclipse. Rafert (1977) has summarized the evidence for period changes

in this system.

TV Cas

The spectroscopic work of Sahade and Struve (1945) was used in the

present investigation. The spectral type of the primary is given as

B9. The secondary spectrum is not observed, although the derived value

of T, implies a spectral type of G2 III or G1 IV. A small to moderate

Rossiter effect is seen during the egress phases from primary minimum.

Although the data are sparse, a circular orbit is indicated, with a

value of F = 2.1 giving a satisfactory fit to the rotation effect (see

Figure A-11).

Several authors have published light curves for this system.

A recent paper by Walter (1979) gives a thorough and detailed discussion

of this system, as well as presenting a new set of observations. One

notes that the light curves are variable, and that there is definite

evidence for period changes in this system. It was noted that the

photographic light curve of Gaposchkin (1953), which is based on 2631

plates, represents a "mean" light curve when compared to the other pub-

lished blue light curves. Thus, in view of the quantity and quality

of the spectroscopic data, and in the interest of avoiding problems due











to asymmetries, the Gaposchkin light curve was used in the present

study (see Figure B-12). The results of the present study match the

previously reported results of other authors' analyses very closely and

thus confirm that the photographic light curve represents a mean light

curve of the system. The cause of the periodic fluctuations present in

the light curves is thought by Walter (1979) to be due to a gas stream

between components, and a hot spot present on the primary component.

Although no emission lines were seen by Sahade and Struve (1945), their

small number of observations coupled with the intermittent nature of

the light curve asymmetries does not make this surprising. Evidence for

period changes is summarized by Rafert (1977).

AQ Peg

The spectroscopic data of Struve (1946a) were used for this investi-

gation. The spectral type of the primary component is A2 V. The spectral

type of the secondary, which is seen during the total phase of primary

eclipse, is given as GS. This is in fair agreement with the type KO III

or K1 IV given by the derived value of T,. The latter is in good agree-

ment with the secondary spectral type of K2 IV found by Hall (1979) from

(B-V)o. The emission seen during primary eclipse is indicative of a

ring around the primary component. Red-shifted emission components for

the H, Mg, and Ca II lines are seen during ingress to primary eclipse.

Near central eclipse the emission is composed of two unequal components,

the stronger being the red-shifted, and the weaker being the violet-

shifted emission lines. During egress, the red-shifted emission lines

disappear, while the violet-shifted components become stronger. The

radial velocity curve is asymmetrical (leading to a value of e = 0.24),











and large scatter near phase 0.6 is especially noticeable. Both of these

effects are probably due to the effects of the gas stream and the ring

structure present. A very large Rossiter effect is present, with an

excellent fit to the rotational disturbance being achieved with F = 6.7

(see Figure A-12). A photographic light curve by Gaposchkin (1953) and

UBV photoelectric photometry by Hall (1979) exist. The BV light curves

of the latter were used for this study. Except for a slight asymmetry

in primary eclipse and a disturbed region near phase 0.1 in the V light

curve, the BV light curves are free of large distortion. At some

phases, the scatter may be larger than expected by Hall (1979) and is

probably due to the complicated nature of the system. Of interest here

is the plot (see Figure C-l in Appendix C) of the 0 minus C residuals

in primary eclipse. As with Y Psc, no excess light near second or third

contact was found. Indeed, the rounded bottom, which according to Hall

is due to emission from circumstellar matter, is well fit by the model

used here, which includes the effect of rotational flattening (see

Figure B-13). Hall (1979) cites evidence for period changes in this

system.

SW Cyg

The spectroscopic data of Struve (1946b) were used for this study.

The skewed, distorted shape of the radial velocity curve is obvious

(especially between phases 0.45 and 0.75), and is responsible for the

value of e = 0.3 found by Struve. Thus, as with the other system show-

ing similar distortions, the value of K1 must be viewed with caution.

A large rotation effect is present during egress from primary eclipse,

making a value of F = 5.0 necessary in order to achieve a satisfactory











fit. Figure A-13 shows the fit to the observed radial velocity curve.

The spectral type of the primary is A2 V. According to Struve, the

spectral type present at mid-eclipse is approximately KO. This is in

good agreement with a spectral class of K2 III or K3 IV found from the

derived value of T2. Emission lines are present throughout primary

eclipse. In phase order, Struve reports the presence of (1) a weak

red-shifted emission feature for Ii B, no violet-shifted component,

(2) strong red-shifted emission present in H B and H y, (3) slightly

weaker red-shifted emission in H B, (4) strong violet-shifted emission

in H 8 and H y, and (5) weak violet-shifted emission in H 3. This

definitely indicates an emission ring structure around the primary com-

ponent. No velocity measurements for the emission lines are given.

The light curves used are the BV light curves of Walter (1971)

(see Figure B-14). Additional light curves are published by Wendell

(1909), and most recently Hall and Garrison (1972). Walter, and Hall

and Garrison give detailed analysis of the available light curves. The

model of Hall and Garrison deals with a partial ring structure which

intersects the primary instead of encircling it. They also state that

a "protuberance" must be present on the primary in order to explain an

excess of light in the V band during certain phases. Walter prefers a

model with absorption in the gas stream from the secondary to the primary,

the absorption being strongest during the ingress phases of primary

eclipse. In addition, extra light is present at some phases due to the

presence of a hot spot on the primary component. All authors agree that

the disturbance of the U light curve near second contact is due to light

from either a hot spot on the primary, or a hot spot in the ring structure











where the gas scream intersects it. Figure C-2 shows a plot of the 0

minus C residuals during primary eclipse taken from the present work.

Again, while systematic trends may show the presence of absorption or

extra light during ingress and egress from primary eclipse, no definite

evidence of residual light at second and third contact is apparent.

Thus, the "protuberance" needed by Hall and Garrison to supply extra

light in V at some phases may simply be an artifact of their model,

which does not include corrections for rotational flattening of the

primary. A discussion of evidence for period changes is given by

Rafert (1977).

Y Psc

The spectroscopic data of Struve (1946b) were used to study

this system. The primary component is of spectral type A3 V ("with

many sharp lines present"), and the derived value of T', implies a spectral

type of K1 III or K2 IV, in agreement with Struve's estimate of KO. Tne

theoretical fit to the radial velocity curve is shown in Figure A-14.

The value of e = 0.12 found by Struve is probably due to the obvious

distortion of the radial velocity curve by a gas stream, whose presence

is implied by an H 3 violet-shifted emission feature seen during egress

from primary eclipse. The distortion of the radial velocity curve is

especially pronounced between phases 0.5-0.7 (as in SW Cyg, U Sge and

other systems thought to contain gas streams); i.e., when the observer

sees the light of the primary component through the gas stream. A good

fit to the amplitude of the Rossiter effect is given with F = 1.65.

The photoelectric data of Walter(1973a, 1973b) were chosen for

this analysis (see Figure 8-15). A photographic light curve by Gaposchkir

(1953) also exists. This system is one of several for which Walter has











hypothesized a bright hot spot on the primary component in order to

explain "extra light" present at second and third contact. Figure C-3

shows a plot of the 0 minus C residuals for primary eclipse from the

present analysis. The effect seen by Walter is not evident on the plot.

This is probably due to the difference in shapes assumed for the stars

by the two models used. In particular, the Russell-Merrill method used

by Walter does not take into account rotational flattening. The fact

that the Wilson-Devinney model, which does include the effects of rota-

tion, does not predict extra light at second and third contact, as did

Walter's Russell-Merrill modeling, probably shows the necessity of model-

ing this effect when analyzing the light curves for these systems. Pos-

sible period changes are discussed by Rafert (1977).

W Del

The spectroscopic data used in this study are that of Struve (1946b).

The radial velocity curve is skewed and shows large scatter at some

phases. This is reflected in the "classical" value of e = 0.2 found by

Struve. The spectral type of the primary is AO V-B9.5 V (Struve, 1946b),

and Hill et al. (1975). The derived value of T, implies a spectral type

for the secondary of GS III or KO IV, in fair agreement with Struve's

estimate of G5 subgiant. A red-shifted H 3 emission component is easily

seen during ingress from primary eclipse, and faint H B violet-shifted

emission is seen during egress from primary eclipse. The H emission

seen, and evidence of period changes in this system (Rafert, 1977,

Plavec, 1960) point to a gas stream and an asymmetric ring structure.

The stronger red-shifted emission component may also indicate a hot spot

on the trailing edge of the primary component. The pronounced Rossiter











effect has a satisfactory fit with F = 1.7. Since the radial velocities

given are averages of all lines, this value of F is probably an under-

estimate. The fit to the radial velocity curve is shown in Figure A-15.

The photoelectric data used for this system are that of Walter

(1970). A photographic light curve by Gaposchkin (1953) also exists.

The deep primary minimum (2.6 in V, and 3s4 in B) is definitely asymmetric

as pointed out by Walter. This appears in the present solution as long

runs of systematically positive or negative residuals in primary eclipse.

A likely explanation is that extra light from a hot spot on the primary

or ring structure is present during egress from primary eclipse. The

fit to the light curves is shown in Figure B-16.

RY Gem

The spectroscopic work of McKellar (1949), carried out at disper-

sions of 50 a/mm and 135 R/mm, supplied the data for the present analysis.

Spectroscopic work has also been carried out by Gaposchkin (1946) and

Wyse (1934). The spectral types given are A2 V and K2 subgiant. The

latter agrees well with the value of T, derived in this work, which

implies a spectral type of KO III or K1 IV. Wyse (1934) noted violet-

shifted emission in H for plates taken during totality. McKellar notes

double emission at mid-primary, and violet-shifted H 3 emission during

egress from totality and during the latter phases of totality. The

double emission is seen in H 6 to H i, and in K of Ca II. The emission

lines yield a velocity of particles in the ring of + 200 km/sec with

respect to the system. Thus this system probably contains a gas stream

and a ring structure similar to AQ Peg and RZ Set. Out of eclipse the

radial velocity curve shows severe distortion and large scatter at most











phases. Both of these are due to the above mentioned stream-ring struc-

ture. The value of K1 is thus suspect, and may be in error up to 25%.

Figure A-16 shows the fit to the observed radial velocity curve.

The only light curve available was the photographic light curve of

Gaposchkin (1953) (see Figure B-17). The scatter is large between phase

0.3-0.45, and the light curve is asymmetric, with the points between

phases 0.65 and 0.75 being low. The value of q is therefore fairly

uncertain. Period changes have been observed for this system (cf. Rafert,

1977).

U Sge

The spectroscopic data of both Struve (1949) and McNamara (1951a)

were used in this study. McNamara's work was done at a dispersion of

26 R/mm, and 75 /nmm at minimum light, while that of Struve was done

at 40 b/mm (with a few plates at 10 a/mm). The spectral type of the

primary component is B8.5 V, and that of the secondary component G3 III.

The latter agrees perfectly with the classification of G3 III found

from the derived value of T,. A detailed discussion by the above men-

tioned authors points out the following: (1) the radial velocity

curves given by the He lines and the H lines are different, as in the

cases of RY Per and TZ Sct, (2) the rotation effect is larger for the

He and Mg lines than for the H lines (see McNamara, 1951b), (3) sporadic

emission lines are present during primary eclipse, and (4) "satellite"

H lines, as seen in g Lyrae are present. The fact that the distortions

are not nearly as large as in, for instance, RY Per (as seen by the

derived value for U Sge of e = 0.04) and in the presence of sporadic

emission activity indicates a variable ring and gas stream structure in











the system. Only the He line measurements of Struve and the mean velocity

of all lines except H and Ca for McNamara's data were used for the present

work. A final value of F = 4.2 gave a satisfactory fit to the Rossiter

effect, as shown in Figure A-17.

The excellent uvby photometry of McNamara and Feltz (1976) was used

for the photometric analysis (see Figures B-18 and B-19). Recent

photometry of this system has also been published by Cester and Pucillo

(1972). Approximatley 50 normal points in each color were used for the

analysis. Of interest here is the value of q = 0.41 found by the

present work. Recent infrared spectroscopy by Tomkin (1979) indicates

a value of 0.33. Although no correlation problems were indicated by the

DCP, trial runs were made in both mode 2 and 5 wherein the value of

q was set to 0.33 and not adjusted. The results gave much inferior fits

to the light curves. Perhaps the difference between the photometric and

spectroscopic values of q lies in the fact that the large temperature

difference between components can lead to severe modification of the

spectral lines of the secondary, and thus to the resultant value of q.

In support of the mode S solution for this system is the fact that

in addition to the emission activity the period of this system is known

to be variable (Rafert, 1977).

U Cep

A great deal of work, both spectroscopic and photometric, has

been done on this system. A complete summary of the spectroscopic work

can be found in a recent article by Batten (1974). The radial velocity

curve is extremely distorted, as can be seen in Figure A-18. However,

Hardie (1950) has published an interesting article in which the radial











velocity measurements for the H lines (using Struve's 1943 radial velocity

measurements) have been "corrected" for distortions present in the line

profiles. The corrected radial velocity curve yields a value of e = 0.0,

which is in accord with the value implied by the photometry. The new

value of K1, 85 km/sec, is quite different from the older value of 120

km/sec. This difference leads to a large change in the mass function

from 0.41 to 0.16. Batten (1974) gives the spectral type of the primary

component as B7 V, and that of the secondary as G8 III-IV. The latter

agrees well with G8 III or KO IV found from the derived value of T2.

The large amplitude of the Rossiter effect necessitated a value of

F = 8.0. The large amount of data on emission-line activity in this

system is summarized by Batten (1974). The theoretical fit to the

radial velocity curve is shown in Figure A-19. The fit during egress from

primary eclipse is not good, and may be due to the reconstruction tech-

nique used by Hardie during these phases, or to problems measuring the

line centers at such times.

The photometric history of this system is summarized in the recent

work of Markworth (1977). He attempted a Wilson-Devinney solution of

his UBV light curves and achieved a satisfactory fit to them. For this

analysis, he assumed a value of F = 5.0. However, the theoretical radial

velocity curves calculated using the parameter values found by Markworth

(1977), and a value of F = 5.0, resulted in too small a Rossiter effect.

Consequently, the BV light curves of Markworth were reanalyzed using a

value of F = S.0 and using the parameter values of Markworth as the

starting values for the analysis. The result is shown in Figure B-20.

Cf interest in the new results are the lower value of q found (0.57











versus 0.64), and the higher value of g and lower value of g2 found.

However, the distorted nature of the light curves makes the determin-

ation of such insensitive parameters such as g2 and A1 very uncertain.

The intermittent nature of the emission activity and the distortions

(sometimes very large) in the light curves indicate that sporadic mass

transfer events are taking place in this system. The large amount of

data on the nature of the period changes seen in this system are sum-

marized by Rafert (1977).

RY Per

The 62 spectroscopic observations of Hiltner (1946) were used for

this analysis. Wyse (1934) gives the spectral types as B6 and FS.

Hiltner gives the spectral type of the primary as B4 V, and states that

the He lines are more diffuse than the H lines. The secondary's spectrum

is visible on seven plates taken during primary minimum. Hiltner gives

the secondary's spectral type as "F5 with giant characteristics."

Another study (UCLA Observatory Report, 1976) gives FO III as the

secondary's spectral classification. These estimates correspond well

with the derived value of 66000 K. The radial velocity curve is asym-

metric, and displays large scatter throughout. An extremely large

rotation effect is present, which leads to a final value of F = 10.0.

As discussed by Hiltner, the more interesting aspects of the spectro-

scopic data are: (1) The amplitude of the Rossiter effect is 2-3 tines

larger for the He lines as for the H lines (an effect discussed in

Chapter II), (2) Both the amplitude and y velocities are different for

the radial velocity curves of the two lines, and (3) There is a marked

difference between the two radial velocity curves between phases 0.90 to

0.95. These effects can be explained by the modification of the normal











hydrogen line profiles by emission and/or absorption in the gas stream/

ring structure thought to be present. Thus the He velocities are thought

to be nore indicative of the true stellar rotation rate. Strangely, no

mention is made of the presence of emission lines, although Hiltner does

mention the appearance of "satellite" hydrogen lines (such as are seen

in B Lyrae), which are thought to be caused by absorption in a thick

stream silhouetted against the B4 primary component. There is an indi-

cation of polarization (1%) of the light of this system. The fit to the

radial velocity data is seen in Figure A-20.

Several photographic light curves exist for this system, as well

as an excellent visual light curve (e.g. Gaposchkin, 1953, and Wood,

1946). However, Dr. D. Popper (1979) kindly provided his new UBV light

curves. The BV light curves were used for the analysis, as it was

suspected that the U light curve was asymmetric in primary eclipse. The

fit to the photoelectric data is shown in Figure B-21. There is evidence

that the light curve is variable between phases 0.08 and 0.50, as seen

in Figure B-21. No period changes are suspected for this system (Wood,

1946), although the data are sparse.

RZ Set

The spectroscopic data of Neubauer and Struve (1945) and Hansen

and McNamara (1959), the latter work being the more extensive, were

used in this investigation. The radial velocity curve exhibits a dis-

torted shape, large scatter throughout, a large disturbance present from

approximately phase 0.85 to 0.90, and doubling of the hydrogen absorption

lines during eclipse. Both red- and blue-shifted emission components

are present for the hydrogen lines during eclipse. The very large











Rossiter effect present was fit with a value of F equal to 15. This

system not only shows the previously discussed effect of the He lines

implying higher values of Ve than the H lines, but there is definite

evidence that the higher excitation He lines show a larger rotational

disturbance than the lower excitation He lines! Thus there is clear

evidence for a substantial stream/disk structure in this system.

Another interesting facet of this system is the odd behavior of the

hydrogen emission components during eclipse. In contrast to most other

systems, the red-shifted emission component is weaker during ingress to

eclipse and stronger during egress from eclipse (and vice versa for the

blue-shifted component) All lines show pronounced asymmetric profiles

during eclipse (cf. Hansen and McNamara, Figures 3 and 4). Although

Hansen and McNamara attributed this to modification of the line profiles

by emission/absorption arising in the stream/disk structure, the con-

tinuous variation and the shape exhibited in the above mentioned figures

are what would be expected for a normal rotation effect. However, such

emission/absorption effects are seen at many phases, although at those

phases the line profile changes are usually nonsystematic, and the

resultant line profiles are very complicated.

Hansen and McNamara (1959) give the spectral type of the primary

component as B2 II, and AO II-III for the spectral type of the secondary

component. The latter is in excellent agreement with the value of T,

found in this study. Due to the aforementioned distortions of the

radial velocity curve, the value of K1 is probably accurate to only

+ 20%. Figure A-21 shows the fit to the Rossiter effect for solution

one (see below).











The B and V light curves of Wilcken, McNamara, and Hansen (1976)

were utilized in this study. Unfortunately, the large distortions

present at almost acl phases of the light curve rendered the solution

results questionable. Two types of solutions were attempted. For

solution one, the observed points between phases 0.05 and 0.45 were

removed from the solution process. This was done under the assumption

that the points in this phase range were high due to added light from

a hot spot on either the primary component or at a possible junction of

the ring or disk and the gas stream between components. Similarly for

solution two, all points between phases 0.70 and 0.95 were removed from

the solution process. In this case it was hypothesized that the ingress

shoulder of primary eclipse was low due to absorption of light by the

stream/disk structure. Tables III and IV display the unexpectedly simi-

lar results for both solutions. Because solution two gave a poorer fit

to the light curve, solution one was adopted as the preferred solution,

although in view of the large distortions present in the light curve,

it must be considered tentative. The value of Ml found was low, but

not unreasonably so. The situation is probably even more complicated

than this simple dichotomy presented here, i.e., both large scale absorp-

tion and added lignt from a hot spot are probably distorting the light

curves! Much more work needs to be carried out for this interesting

system. Evidence for a-, increase in the period of this system has

been given by Karentnikov (1967).







56



Having summarized the basic information concerning the systems

studied, the next chapter presents a detailed discussion of the results

obtained in this investigation.














CHAPTER IV

RESULTS AND CONCLUSIONS

The purpose of this final chapter is to present the results of

this investigation, and discuss these results both generally and with

regard to the individual systems. The general discussion is presented

first.

General Discussion

The Hertzsprung-Russell Diagram

Figure 4 shows a Hertzsprung-Russell Diagram (hereafter HRD) which

displays the positions of the systems investigated in this work, the

position of the Zero Age Main Sequence (hereafter ZAMS), the position

of the Terminal Age Main Sequence (hereafter TAMS), and the areas popu-

lated by stars in luminosity classes III and IV. The values of M the

absolute visual magnitude, for the components of the systems studied were

calculated in the following way. The LCP calculates the value of the

surface area of each component, using the separation of centers as the

unit of length. Since the separation of centers in kilometers is known

(Table V), a radius for each component, R, (which represents the radius

of a sphere with the same surface area), can be calculated. This value

of R, and the known value of the stellar effective temperature, Te., are

then used in the following equation, which yields a value of log (L,/L0)

(where L. is the stellar luminosity, and L is the solar luminosity).

log(L,/Lg) = 2 log(R,/Rg) + 4 log(Te,/Te) (2)

















S.
00
- *vi
0.
o 00
ri *v ; a)






to a ,041 -
a r- 0 421 *0 C
-"-44 -0 -3
















-no
S04-4 >0 .0

- 3 41 -0
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C -C -3 ?




















00440 O N
-1* H c
Z o -o .



S*H 0
-n o-.-- S.0
























o'dP 0
i 'n r 3

-^ 0 <-; I 0
S0 0 0 0t
VIi 3 3 r



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0 000
ac c i a0

3 0 30 0 0


N 0,4. -J- ^1 4: ^ *




S. 0 0; 0^ 0.-

-r 04-4 3] 14 .
'(4l 4-t 0 0j '- ?


O(- 0y -^ 0 0

^- c -' n
rt')QU0SV]








,--0 S CS.***
0. 0 O. 0 0 -

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ON 0)p
3 vi ^" 3 S sd *









0" + 0I :> 2 421 >
Xri0 t JU ^








- -- -4 O-n




*r200>4 0.^ -
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2 00 0 0




4-4 0-0 -l 0 C,42


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--- -r L O3 r 0










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HI
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x I
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- C0- 3'- S O h 05 CO'5 0




















- Un M: c 4 N t r ,:') 1: 1 C) N C' C) tn Z 0 N
U: tl' C -. C') 10 V) vi tC N C') N CA] C') tIN rC


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cw cc r[- Cn c) --: C- c, cc cc .T Ln l- Lo C),
rq t' N C' -) C) C') C') C') In 14C) C'








C) 'C) (^ cc -c- C) NM N cc cil N^ N^ C), .) C
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A value for IM was then calculated through the relations:

h~bol, = 4.72 -2.5-log(L,/L) 3)
and,

M = BDol,. Bolometric Correction (4)

The values of the Bolometric Corrections and Mbol, were taken from

Harris (1963). The values of L,, R,, and Mv,* are given in Table

VI for the primary components, and Table VII for the secondary com-

ponents. The positions of the indivudal systems in the diagram will

be discussed in a later section.

Equatorial Velocities

The primary aim of this dissertation was the derivation of V
e
for the 19 systems selected. These values are given in Table V. The

major source of error in the derived value of Ve for systems possessing

photoelectric observations lies in the value of K1 used. The error in

Ve should be proportional to that in KI. In the case of U Cep, as

previously shown, this may reach a factor of 25%! However, the low mass

found for the primary component of U Cep may indicate that the signifi-

cant reduction of K1 found for this system via the "reconstruction"

technique of Hardie (1950) may have been too large. In most cases, however,

the derived values of Ve appear to be reliable, since the derived masses

for many of the systems are in good agreement with the values expected

for the associated spectral types. The above statement is justified

because the masses depend on K ', whereas the value of Ve depends linearly

on K1. Thus, any large error in K, will immediately appear as a large
I' i-
deviation in the expected value of the derived masses. It is interesting

that the large distortions of the radial velocity curves present in some











TABLE VI

ABSOLUTE ELEMENTS--PRIMARY COMPONENTS


Name R1,,[R) log(R1 ,) log(Te, ) LI ,(L) log(L1,*) My


X Tri
Y Leo
R2 Cas
ST Per
RX Hya
W UMi
;vl Cyg
RW Gem
TX UMa
TV Cas
AQ Peg
SW Cyg
Y Psc
W Del
RY Gem
U Sge
U Cep
RY Per
a
R2 Sct


1.51
1.67
1.39
1.92
2.33
3.42
4.25
2.95
2.27
2.05
2.22
2.23

2.67
2.61
3.28
5.22
1.90
2.80

6.-17


0.178
0.222
0. 113
0.283
0.367
0.533
0.629
0.470
0.355
0.312
0.347
0.348
0.427
0.417
0.516
0.508
0.279
0.447

0.311


3.988
3.967
3.988
3.967
3.903
3.967
4.161
4.215
4.127
4.093
3.988
3.988
3.967
4.033
3.988
4.114
4.134
4.243
4.356


17.9
18.0
15.1
23.9
19.6
75.9
706.9

555.3
146.40
87.8
39.2
39.3
46.4
82.1
85. 1
261.5
109.0
648.6

9,811.2


1.254
1.256
1.180
1.379
1.293
1.880
2.S49
2.745
2.166
1.944
1.593
1.5935
1.667
1.914
1.930
2.417
2.037
2.812

3.992


1.84
1.78
2.01
1.47
1.60
0.22

-1.36
-0.75
0.16
0.52
0.99
0.98
0.75
0.34
0.15
-0.36
0.49
-0.73

-3.03


results for solution RZ Set 1 are


probably more accurate than the results


presented,
RZ Set 2.


only the


for


as they are












TABLE VII

ABSOLUTE ELEMENTS--SECONDARY COMPONENTS


Name R2 ,*( ) log(R2,,) log(Te ,) L2, (L) logL,
2,* a ~ L10


X Tri
Y Leo
RZ Cas
ST Per
RX Hya
W UMi
WW Cyg
RW Gem
TX UMa
TV Cas
AQ Peg
SW Cyg
Y Psc
I Del
RY Gem

U Sge
U Cep
RY Per
R- Scta


1.82
2.29
1.79
2.62

3.00
2.71
5.66
4.39
5.85
3.37
5.02
4.67
5.70
4.34
8.33
4.74
3.89
6.02
14.48


0.260
0.360
0.254
0.418
0.477
0.432
0.753
0.642
0.585
0.527
0.701
0.669
0.569
0.637
0.921
0.675
0.590
0.779
1. 161


3.745
3.633
5.676
3.672
5.695
3.683
5.740
5.846
. 765
3.753
5.625
3.653
3.660
3.693
3.672
3.721
3.683
3.816
3.952


2.8
1.6
1.4
3.0
4.8
3.6
25.7
41.0
15.0
10.5
7.0
6.6
5.3
9.8
30.0
15.2


58.6
1152.9


0.444
0.197
0.159
0.472
0.680
0.554
1.410
1.615
1. 177
1.014
0.847
0.816
0.723
0.993
1.477
1. 182
0.860
1.768
3.062


3.71
4.77
4.69
3.91
3.29
3.59
1.41
0.75
1.84
2.29
5.00
3.22
3.13
2.51
1.39
1.97
2.84
0.36
.7


Only the results for solution RZ Set 1 are presented, as they are
probably more accurate than the results for RZ Set 2.











systems (e.g. SW Cyg) do not seem to have greatly affected the associated

values of K1, as shown by the values of the derived masses. The author

estimates that an error of 10% is a realistic upper limit to the errors

in Ve. This value may be 20% for those systems which possess only

photographic light curves, due to the uncertain values of q found in

these cases.

A comparison should be made between the values of V found in

this study, and those values available in the literature found from line

profile analysis. Table VIII shows such a comparison for 10 systems

for which values of Ve sin i are available. For W UMi and U Cep the

values are comparable for the two methods. For TV Cas, W Del, Y Psc, RZ Sct,

RZ Cas, U Sge, and TX UMa the values found in the present study are

higher than the line profile values by factors of 1.6 to 2.6. The

value of Ve for TX UMa found in this study is uncertain due to the afore-

mentioned difference in the magnitude of the rotation effect during

ingress into and egress from eclipse. If a value of F = 3 is used (which

would fit the amplitude of the Rossiter effect during egress from primary

eclipse), then a value of V = 114 km/sec results--a value in good accord

with the value found by Mallama (1978). The result fund for RY Per

must be viewed with caution, as will be discussed later. Thus it is

seen that the results from line profile analysis yield values of V
e
equal to or greater than the values given by the rotation effect. This

might be explained by hypothesizing that the assumed rotational velocities

of the standard stars are systematically underestimated.











TABLE VIII

COMPARISON OF V 's FOUND BY ROSSITER EFFECT AND LINE PROFILE ANALYSIS
e



V (present V (line profile
Name study)(km/sec) analysis)(km/sec) Reference


TV Cas 122 70 Van den Heuvel (1970)
RY Per 219 280 Van den Heuvel (1970)
W UMi 71 75 Van den Heuvel (1970)
W Del 58 30 Van den Heuvel (1970)
Y Psc 60 37 Van den Heuvel (1970)
U Cep 337 310 Olson (1968)
RZ Cas 93 82 Olson (1968)
RZ Scta 365 240 258 Van den Heuvel (1970)
U Sge 201 88 Olson (1968)
TX UMa 76 123 Mallama (1978)


aOnly the results for solution RZ Set 1 are presented, as they are
probably more accurate than the results for RZ Set 2.










Mass Determination

Table IX gives the derived values of M,1' M2' and Mtot. These

masses were determined from the equations:

M, = f(m)/sin i (1/q + 1)2 (5)

and,

i1 = M2/q (6)

For those systems with photoelectric light curves, the major

source of error is in the value of K1 used. The value of K1 enters

the above mass equations through the mass function:

f(m) = 1.0385 x 10' P K(7)

It can be seen that the error in K. is given by:

A(K3) = 3KI2 AK1 (3)

Thus, the fractional error is:

ACK )/K = 3AK1/K] (9)

Therefore, a 10% error in K1 gives a 30% error in f(m), and hence in the

mass values. So, 30% is adopted as a reasonable upper limit to the

error in the masses.

There is good agreement in the derived values of Al found for the

A2-A3V primary components. These values lie between 1.5 and 2.0, with

an average mass of 1.73 for the seven systems with reliable masses.

The values of 14 for the AO-B3 spectral class primaries is in good agree-

ment with the expected values (see Underhill, 1966, pp. 140-143) with

the exceptions of U Cep and RY Per. The value of U1 for U Cep is lower

than expected (2.21.4 vs. 3.5,' ), but not totally unreasonable. As

noted, this is probably due to an overcorrection in the value of K1

found by Hardie (1950). The value of 11 found for RY Per is extremely




















o ^- crr- (N cc c m 'cc -2 cc icn c) '0 v) -, r- ( -
cc cc 0c N- c n cc N- 7c n (4 cc c Gc Ni c' t; (













cc cc N- c -' cc Cc cc -T t c r c o nc cc Lo c c-A
C~ cc rcc crc cc-i -)' -^ cc cca cc cci co cc r- -n cc- (








c I n -0 c- cc cc -cc (N (N (N -C) cc :o (N cc

'c- N-- ccn ^ -- cc ^ CJ C-i cc cci cc ^r^ *- cc ^- '-

3- -i r ( o- c - n N (N q


S0 c C C 00C 0


C)~ Z (NCc c~
n cc -l (N -3 c

cc c c c c c


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0c c


x c cx c c cc c cc cc t c cc cc r
0 0 00 -- i








rl- ol U cc 0 Nl z- cc L c c c rN LN OCc rc


0 0 00 00 C0 0 0 0C 0 0 0 ' 0







- N r- N c c r Lr)c o C c dc r(N cc c (c M cc
35^603 3033= 303f)


~m~MI3U~C3n 1~


C) o cc S ^1
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r-
x o>- c c c c 3 x
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low for a spectral classification of B3, and is probably due to the

inaccurate values of q and K1 characterizing this system.

The discordant masses found for RY Gem and RX Hya should be viewed

with caution because they are due to values of q found from the analysis

of photographic light curves. The high values of 1 found for W UMi

and WW Cyg, coupled with their positions in the HRD, point to evolution-

ary effects.

All the reliable masses reported here are lower than the values

quoted by Allen (1964). One straightforward explanation for this is

inappropriate weighting given to stellar masses predicted by theory, as

opposed to observed dynamicall" values.

The total masses for these systems are also of interest. Van den

Heuvel (1970) has studied the rotation of primary components of 23 Algol

systems through line profile analysis. He concludes that (a) for systems

with a period < 5 days and primary spectral types of B8 or later, the

deviation from synchronous rotation is small for 14 out of 15 systems

studied, and (b) primaries of spectral type B8 or earlier rotate, on

the average, at twice the synchronous rate regardless of the value of

the period. He attempts to explain these results as due to the differ-

ences in Case A and Case B mass exchange. For Case B evolution (i.e.,

the Roche limit is reached after the end of core hydrogen burning, but

before helium burning) one expects Algol-type systems to be produced

(Kippenhahn et al., 1967, and Refsdal and Weigert, 1969) for (original)

primary masses of2.S3, or less, and total system masses of 4.5M or

less. On the other hand, Algol systems can be produced through Case A

evolution (i.e., the Roche limit is reached during core hydrogen burning)











for almost any initial mass for the (original) primary component. This,

plus other statistical evidence given by Van den Heuvel (1970), indicates

that the Algol systems with B8 or later primary components are probably

the result of Case B evolution, whereas the systems with primary com-

ponents of spectral class B8 or earlier are the result of Case A evo-

lution. (For another facet of this apparent dichotomy of systems,

see Devinney, 1973.) Van den Heuvel thus explains the two conclusions

given above as follows: For Case B evolution, the rapid phase of mass

transfer is short lived, the amount of mass transferred is relatively

small as compared to Case A, and there is no long lasting stage of slow

mass transfer during which large amounts of mass and angular momentum

are transferred to the "new" primary component. Thus, synchronization

through tidal braking can start immediately after the phase of rapid mass

transfer. For Case A evolution, not only is there relatively more mass

and angular momentum transferred during the rapid phase of mass transfer,

but there also exists a long phase of slow mass transfer during which

significant amounts of mass and angular momentum are constantly trans-

ferred to the "new" primary component, thus keeping it in a prolonged

state of asynchronous rotation. Thus, following Van den Heuvel's scenario,

one would expect to have a much higher probability of finding a Case A

system in an asynchronous state of rotation as compared to the Case B

systems.

On the other hand, it should be pointed out that (a) for Case B

mass exchange, helium ignition in the "original" primary component will

cause this component to "break" contact and shrink within its limiting

Roche surface, and (b) for either Case A or B mass exchange, the slow











phase of mass transfer may not lead to the same "spinning up" of the

primary component. That is, the slow phase of mass exchange may be slow

enough so that, for shorter period systems, tidal braking can continually

resynchronize the rotation of the primary component (once the initial

asynchronism has been dealt with). With all these points in mind, the

results of this investigation are examined below.

The data presented in this study are consistent with the scenario

given by Van den Heuvel, with a few exceptions. An examination of

Table IX shows that for systems with M tot<3.5,1 and a period less than

5 days, the values of F range between 1 and 2 (except for the case of

SW Cyg, which has a period of 4.57 days). For systems with a primary

spectral type of B9 or earlier, Mtot is usually greater than 3.5' and

1.5 < F < 10.0. WW Cyg and W UbN probably have rotation ratios affected

by evolution off the main sequence. It is probable that AQ Peg, RY Gem,

SW Cyg, and Y Psc are Case B systems "caught" at or just past the rapid

phase of mass transfer. Thus we find them with low ,tot, a spectral type

of the primary component later than B9, but a high value of F, and a

ring-stream structure present.

Extra Light at Second and Third Contact

As mentioned in Chapter III, the idea has been suggested (Walter,

1973a) that for several systems extra light is present near second and

third contact. The source of this extra light has been identified with

either a hot spot on the primary component (Walter, 1973a), or a "pro-

tuberance" on the trailing side of the primary component (Hall and

Garrison, 1972). As an example, consider Walter's analysis of Y Psc.

His Figure 3 clearly shows extra light present at both second and third

contact, the amplitude of the effect being approximately equal to 0.02.











This should be compared to Figure C-1, which displays the analogous plot

for the present solution of Y Psc. One immediately sees that the current

analysis does not show the effect given by Walter's analysis. The other

figures in Appendix C display 0 minus C residual plots for 6 other sys-

tems for which extra light has been hypothesized. Considering the scatter

of points, there is no definite evidence of extra light at second and

third contact for W Del, WW Cyg, AQ Peg, and SW Cyg. The large scatter

and complicated behavior of the residuals seen in the 0 minus C plot for

U Cep (Figure C-6) is probably related to the disturbed nature of the

light curve present during this particular epoch of observation (see

Markworth, 1977). Figure C-7, which displays the results for U Sge, shows

definite evidence of absorption of light near first and fourth contact.

The cause of the discrepancies between the results presented here, and those

of previous authors is probably related to the inadequate description of the

stellar figures by models not taking into account asynchronous rotation.

Detailed Discussion

Discussion of Individual Systems

X-Tri.--Tne position of this system in the HRD shows the primary

component to be on the ZAMS, and the secondary component to be approxi-

mately I 2 below the region of luminosity class IV objects. The detached

nature of the final solution, the low values of F and A2 found, and the

fact that the period change data is indicative of a light time effect

rather than a mass transfer effect all point to a pre-main sequence

evolutionary state for this system.











Y Leo.--Y Leo is very similar to X Tri and RZ Cas in that the primary

is very close to the ZAMS, and the secondary is approximately 1m5 below

the luminosity class IV region. The evidence for erratic period changes

and the derived value of F = 1.5 indicate a system in the phase of slow

mass transfer.

RZ Cas.--The primary component of RZ Cas lies a little below the

ZAMS, and the secondary component lies about 1.4 below the luminosity

class IV region. The value of F = 1.6 and the period change information

indicate a system akin to Y Leo, i.e., in the phase of slow mass transfer.

ST Per.--ST Per is similar to the last three systems described.

An interesting point here is that even with a small value of F, the

Rossiter effect was still very evident. Since the synchronous velocity

is also low (37 km/sec), it is evident that the present method of

analysis should yield a much more accurate value of V than normal
e
spectroscopy carried out at 40 or 50 3/mm (i.e., an error of 40 to 50

km/sec!).

RX Hya.--The position of this system in the HRD would seem to

imply a system with its primary component evolved from the main sequence.

However, the derived value of i' is much too high. This is probably due

to the fact that a photographic light curve was used for the photometric

analysis. A change in q from 0.17 to 0.22 would give a mass in the

expected range. The value of F, period change data, and spectral type of

the primary hint that a more accurate value for q would lead to a solu-

tion similar to that for Y Leo and similar systems.

W UMi.--This system shows evidence of being in an evolved state.

The mass of the primary component and the position of the primary com-

ponent in the HRD support the picture of a primary which has evolved











away from the main sequence after the end of the phase of slow mass

transfer. The lower than synchronous value of F would then be explained

through the normal expansion of the primary during this evolutionary

phase, and normal tidal braking (see also Devinney and Sutton, 1979).

WW Cyg.--The primary component of this system is characterized by

a large mass and a low value of F. The secondary component lies in the

region populated by luminosity class III objects. The position of the

primary component in the HRD implies that it has evolved from the main

sequence. In view of the scenario for Case A evolution discussed

earlier, it may seem strange that the value of F is only 1.53. This

value of F probably indicates both the effect of tidal braking and the

effect of the expansion of the primary during its evolution off the main

sequence.

RW Gem.--The position of the components of this system in the

HRD reveal a primary near the ZAMS and a secondary found in the lumin-

osity class III area of the HRD. The mass of the primary component is

normal for its spectral type. Thus, this is a normal Algol system in

the slow phase of mass transfer.

TX UMa.--The placement of this system in the HRD is in accord

with the picture of a typical Algol system in the slow phase of mass

transfer. Similar to RW Gem, TX UMa has a primary on the ZAMS, and a

secondary in the luminosity class III area. The mass agrees with its

spectral type. More spectroscopic work is required in order to see if

the asymmetry in the amplitude of the Rossiter effect is real, and if

not, what the actual amplitude is.











TV Cas.--While similar to TX UMa in its placement in the HRD, the

mass found for the primary component of this system seems high for a

spectral type of B9. In view of the sparse spectroscopic data, and the

photographic light curve used, this value for M1 should be viewed as

tentative.

AQ Peg.--The position of this system in the HRD indicates a normal

main sequence primary component and a secondary component which lies in

the area populated by luminosity class IV objects. The derived mass of

the primary is normal for its spectral class. Along with SW Cyg, W Del,

RY Gem, RY Per, Y Psc, and RZ Sct, this system represents those Algol-

type binaries possessing a gas stream and a ring structure around the

primary component. A determination of the radius of the ring around the

primary can be made by utilizing the published descriptions of the behav-

ior of the emission features during primary eclipse. Using the parameters

determined in this study, Figure D-l (see Appendix D) was constructed.

This shows the system geometry at those phases for which emission lines

were observed. By correlating the presence (or absence) of red or

blue emission features with the position of binary components for several

different phases, one can deduce the distance from the primary component

at which the greater part of the emission is arising. This distance can

then be identified with the radius of the ring around the primary com-

ponent. In this case, a ring radius of 4 to 4.5 R is consistent with

the emission line behavior. As a consistency check, one can assume

Keplerian motion for the particles in the ring. Thus, the absolute mass

of the primary component can be calculated via the equation:











= vR in/G (10)
ring
where 1, is the mass of the primary, v is the velocity of the ring

particles, R is the ring radius, and G is the universal gravitation
ring
constant. In this case, the mass derived using equation 10 is in perfect

accord with that obtained by the method outlined earlier in this chapter

(a ring radius of 4.5R, gives perfect agreement).

SW Cyg.--This system is almost identical to AQ Peg as the HRD plot

shows. Once again, the description of the emission lines given by

Struve (1946b) allows one to deduce, using Figure D-2, the radius of the

ring around the primary component. In this case, a value near 3.5R is

indicated. This would predict a velocity for the particles in the ring

of 320 km/sec. Unfortunately, velocity measurements for the emission

lines were not published, thus confirmation of this ring radius must await

further work.

Y Psc.--This system falls in the same area of the HRD as the last

two systems. No values of Vemission sin i are available for this system,

and only a few plates show the emission activity. This system is par-

ticularly difficult for an analysis of the emission features, due to the

grazing configuration of eclipse, as shown in Figure D-3. Nevertheless,

a value of Ring = 3 to 3,.R seems to fit the available data.

W Del.--The location of this system in the HRD is typical for an

Algol system with a main sequence primary component and a luminosity

class III-IV secondary component. The mass of the primary component is

in accord with its spectral type. As with the previous three systems,

the emission line data were analyzed in order to deduce a value of

R ring Figure D-4 shows the system geometry at phases of interest. A
ring'











value of Ring = 4.OR is indicated, implying a value of Vemission =
ring 0 emission
340 km/sec. Once again, however, no published values for V
emission
were given by Struve (1946b).

RY Gem.--The HRD plot for this system shows a primary component
m,
approximately 1.3 above the main sequence. However, the value of M1

found for this system is much too high, and is probably affected by the

value of q found from the photographic light curve. In this case, a

better value of iI1 is found by using the description of the emission

line behavior to determine a value of Rring the value of V emission
ring emission
200 km/sec given by McKellar (1949), and using equation 10 to determine

a value of MI. Doing so yields a value of I = 1.7M in excellent agree-

ment with the results for the other A2-ASV primary components studied.

The apparent overluminosity of the primary is also uncertain due to the

photographic light curve solution. It is probable that a reasonable

value of q would lead to a small value of R,, and hence a lower value

of v More accurate results must thus await a photoelectric light

curve. In addition, the value of K1 is very uncertain, witness the large

distortions present in the radial velocity curve. A change of K1 from

28 km/sec to 21 km/sec would also bring the mass down to a reasonable

value, although the radius of the primary component would still be in

doubt.

U Sge.--The primary component of this system fits approximately

1 0 above the main sequence, while the secondary component lies in the

luminosity class III area. The derived mass for the primary component

is in good agreement with its spectral type. McNamara (1951a) has

measured the value of Vemission -sin i on two plates, and finds











V ss. -sin i = 280 km/sec. Figure D-6 shows the eclipse geometry.
emission
Unfortunately, the red-shifted emission component was not observed.

Thus, all that can be said is that a value of Rring = 6.OR (found from

the above value of Vemission sin i and the previously derived value of

M1 is compatible with the behavior of the blue-shifted emission com-

ponent. The sporadic nature of the emission and the position of the

primary component in the HRD argue that this system is in an evolved

state--probably near the end of the slow phase of mass transfer for

Case A evolution. Hence the high value found for F.

U Cep.--The primary component of this system lies very near the

ZAIMS, while the secondary is situated in the subgiant region of the

HRD. Possible reasons for the low value of 1 have already been dis-

cussed. The high value of V found for this system might lead one to
e
consider whether or not this star is filling or almost filling its

limiting rotational lobe (see Chapter I). If so, it would mean that

the primary component could not accept any further mass or angular

momentum from the secondary component until tidal braking has transferred

rotational angular momentum back into orbital angular momentum. In this

case, the matter which could not be accepted by the primary would be

forced to orbit around the primary, thus leading to a temporary ring

structure. This could then be cited as the cause of the sporadic emis-

sion and light curve anomalies seen in this system (Markworth, 1977;

Batten, 1974). The possibility of this type of double-contact binary

(i.e., the secondary filling its normal, synchronous Roche lobe, and the

primary filling its critical rotational lobe) has been discussed by

Wilson and Twigg (1979). Table V presents both the percentage of the











limiting rotational lobe filled by the primary component, and the per-

centage of the Roche lobe filled by the primary component. One sees from

Table V that only U Cep and RZ Sct are strong candidates for being double-

contact systems. However, one notes several systems that fill 40-70%

of their limiting rotational lobes. Considering that, as stated in

Chapter II the estimates for F given here are probably lower limits, it

is possible that further study will reveal more candidate double-contact

systems.

RY Per.--The primary component of this system lies on the ZAMS,

and the secondary is within the luminosity class III area of the HRD.

The low mass is probably due to the q found from the light curve solu-

tion. This is due to the large variability of the light curve between

phases 0.15 and 0.45 (very similar to RZ Set). In addition, the value

of K1 is very much in doubt. The value of f(m) calculated from K1 given

by the He lines is twice that of the value given by the H lines. Much

more detailed spectroscopic work must be done on this system before a

reliable set of absolute elements can be deduced.

RZ Sct.--As described earlier, the light curve solution, and hence

the absolute elements are very uncertain. However, solution one (see

Chapter III) does give a consistent picture of a 7 to 14Mi primary

located near the ZAMS, and a secondary component in the normal position

for an AO II-III star. Judging from the totally asymmetric light curve

and the distortions present in the radial velocity curve, this system

is probably in the last states of rapid mass transfer (e.g., V356 Sgr,

Wilson and Caldwell, 1978). The odd behavior of the emission components

of the H lines during eclipse indicates a retrograde ring around the











primary component. It appears that the particles leaving the vicinity

of L1, the inner Lagrangian point, possess an initial velocity toward

the leading side of the primary component, the velocity being large

enough to lend to the formation of the retrograde ring. This picture

is consistent with the presence of "extra" light, presumably due to a

hot spot where the stream intersects the ring structure, at phases just

after primary eclipse.

Suggestions for Further Work

The method outlined in this work can yield accurate values of both

V and the absolute elements of Algol-type binaries. As stated, the fit
e

to the amplitude of the Rossiter effect leads to values of Ve that are

equal to or greater than the values found by line profile analysis

techniques. I'hether the line profile method is underestimating V or

the rotation effect method is overestimating V can only be answered by

more work in this field. However, the consistent results for the masses,

especially for the A2-A3 starts, indicates (1) that the distortions present

in the radial velocity curves may not affect the value of K1 as severely

as previously thought, and (2) that the values of q derived from the

photometric analyses are reliable. As shown by ST Per, the amplitude of

the Rossiter effect can be moderately large even for low values of F.

For this reason it appears that this method will find its greatest use

in determining V for such cases as ST Per (i.e., systems with low equa-

torial rotational velocities and small departures from synchronous rota-

tion), since the lire profile method may give errors as large as the

amplitude of the radial velocity curve for these cases (see the discus-

sion of ST Per for such a case).











With the modification of the LCP for asynchronous rotation, and

its ability to generate theoretical line profiles, an even more accurate

method for determining V is available. Instead of fitting a gross

property of the radial velocity curve (such as the amplitude of the

rotation effect), and thus finding a single, best fitting value for F,

one could in principle generate theoretical line profiles at each phase

for which a spectroscopic observation is available. Then, one could

obtain densitometry tracings of the desired spectral lines, and match the

theoretical and observed profiles for each phase point. In this way,

several determinations of F are obtained, which can then be suitably

averaged for a final value. Therefore, (i) several independent determin-

ations of F can be made, (2) only those lines which one assumes arise in

the primary component are used, and (3) the effects of gas stream/disk

emission/absorption would be more obvious, and thus, hopefully, avoid-

able. Thus, a line fitting technique is used, but the underlying geo-

metric cause of the asymmetric profile is retained.

In summary, this work has shown that an accurate value of Ve (at

worst a lower bound) can be determined via a careful analysis of the

Rossiter effect in eclipsing binary systems of the Algol-type. This

investigation was somewhat limited in its scope by the availability of

computer time. Thus, not all light curves were analysed to their full

potential. However, it is hoped that the solutions and results contained

herein will be of some use as a guide to further, more refined analysis

(in particular, the line profile matching method outlined above.)





































APPENDICES














APPENDIX A

Appendix A contains figures showing the theoretical fits to the

observed Rossiter effect for the systems studied. For each figure, the

abscissa is orbital phase, and the ordinate is dimensionless velocity,

V Figure A-18 shows only the "uncorrected" radial velocity observa-

tions of U Cep, for comparison with Figure A-19 which shows the

"corrected" (Hardie, 1950) radial velocity observations and the theo-

retical fit to the Rossiter effect for U Cep.




































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PAGE 1

AN ANALYSIS OF THE ROSSl'TER EFFECT IN ALGOL-TYPE ECLIPSING BINARY SYSTEMS By LAURENCE WILLIAM TKIGG 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

PAGE 2

JiJ £ DEDICATION This dissertation is dedicated to my parents, whose love made all things possible.

PAGE 3

ACKNOWLEDGEMENTS During the years of work needed for the completion cf this dissertation, innumerable people have given their time, encouragement and advice. Only through their combined support were the opportunities afforded and the determination implanted that enabled me to continue when the inevitable mountains of computer output threatened to engulf and smother me. First among these people is Dr. R. £. Wilson, who chaired the supervisory committee. Dr. Wilson suggested the dissertation topic, and made available his vast knowledge of eclipsing binary stars and his intimate knowledge of the Wilson-Devirmey computer programs used for this research. His sense of humor and guidance, which date back to my first days as an undergraduate student, helped develop the self-reliance and discipline necessary for success in any field of endeavor. Dr. E. J. Devinney has also provided a guiding force since my first days studying astronomy. It was his willingness to set aside other work in order to read the first versions of the dissertation that allowed this dissertation to be completed on schedule. His advice, astronomical and nonastronomicai, will always be appreciated. Other members of the supervisory committee were Dr. F. B. Wood, Dr. J. P. Oliver, and Dr. H. Campbell. I wish to thank them for reading the various versions of the dissertation and making useful comments on them. Special thanks go to Dr. H. C. Smith, who read and commented on the dissertation as well as sitting in on the final oral examination as iii

PAGE 4

a proxy for Dr. Wilson. Thanks also are due Dr. J. E. Merrill for many enlightening and enjoyable discussions on W UMa binary systems, or, as Dr. Merrill has dubbed them, the ''Vermin of the skies. ! ' I wish to thank W. W. Richardson for making several excellent inkdrawings for this dissertation. Extra special thanks go to Ms. P. Guida, who net only helped edit and type the various drafts of the dissertation, but provided much needed moral support at all times. A graduate student is often only as determined as his graduate companions. For providing a background conducive to good astronomy as well as enjoyable living, 1 wish to acknowledge all ray fellow graduate students, in particular J. T. Pollock and G. L. Fitzgibbons. Special thanks go to Mrs. Irma Smith for her valuable assistance in the final preparation and typing of the dissertation. I owe my greatest debt to my family, who not only provided continual encouragement, but gave me every opportunity to follow my astronomical calling. I wish to express a very special thanks to my parents for their support, both moral and monetary, which allowed me to succeed in my chosen field.

PAGE 5

TABLE OF CONTENTS ACKNOWLEDGEMENTS . rage 111 ABSTRACT vii Chapter I. INTRODUCTION i Overview of the Problem 1 Determination of equatorial Rotational Velocities . . 2 The Rossiter Effect 4 Algol-Type Eclipsing Binary Systems 3 Purpose of this Investigation 10 II. METHOD OF ANALYSIS 12 III. DISCUSSION OF INDIVIDUAL SYSTEMS 26 X Tri 26 Y Leo 35 RZ Cas 36 ST Per 57 RX Hya ......... 37 W UMi 3g WW Cyg .'.'.'.'.'.'.'.'.'. 39 R»V Gem 4D TX UMa ..'..'.'.'.'.'. 41 TV Cas 42 AQ ?eg '.'.'.'.'. 45 SW Cyg 44 Y Psr At r; " 46 IV Del 47 RY ; ;em 43 L ! Sge 49 U Ce P SO RY P« 52 RZ Set 53 IV. RESULTS .AND CONCLUSIONS 57 General Discussion 57 Detailed Discussion i\ Suggestions for Further Work 79

PAGE 6

TABLE OF CONTENTS— Continued Page APPENDIX A 82 APPENDIX B 127 APPENDIX C 174 APPENDIX D. REFERENCES. 1< ( m: 5IOGRAPHICAL SKETCH 206 vi

PAGE 7

Abstract of Dissertation Presented tc the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy .AN ANALYSIS OF THE ROSS ITER EFFECT IN ALGOL-TYPE ECLIPSING BINARY SYSTEMS By Laurence William Twigg December 1979 Chairperson: Robert E. Wilson Major Department: Astronomy One of the fundamental parameters of a star is its rate of axial rotation. This parameter affects both the shape of the star and the distribution of light over the stellar surface. Thus, an accurate analysis of the light curve of an eclipsing binary system should include the effects of stellar rotation. In addition, the values of fundamental astrcphysical parameters such as mass, radius, and luminosity are usually found by combining the results of both photometric and spectroscopic analyses of an eclipsing binary system. Therefore, the correct treatment of stellar rotation (thus yielding a more accurate light curve solution) is necessary to ensure an accurate determination of the aforementioned fundamental parameters. To date, the primary means of determining the rate of stellar equatorial rotational velocities (V' q ) has been through an analysis of spectral line profiles. This type of analysis is limited both statistics (through the determination of V for standard stars) and instrumental iv (in that the error of the V derived for the system under analysis is approximately equal to the reciprocal dispersion cf the spectroscopic

PAGE 8

equipment used). Thus, one would like to find a second, independent method for determining V , which could be compared and contrasted with the value found from line profiles. Such an independent method of determining V for a component of an eclipsing binary system is available through the analysis of a spectroscopic phenomenon known as the Rossiter effect. The Rossiter effect is characterized by (sometimes very large) deviations in the radial velocity curve during the partial phases of an eclipse. These deviations are in a positive (red-shifted) sense during ingress, and a negative (blue-shifted) sense during egress. These deviations occur because, during these phases, the geometrical covering of part of the star being eclipsed leads to a doppler shift of the spectral lines of this star arising from axial rotation, as opposed to orbital motion. The present investigation uses such an analysis of this effect in order to determine V for che primary components of 19 Algol -type eclipsing binary systems. In addition, new analyses of the associated light curves and determination of new absolute parameters were carried out for these systems. Further, the radii of possible ring structures existing around the primary components in several systems were determined. Finally, evidence is presented indicating that for several suspect systems no extra light is present at second and third contact, unlike the results of an analysis of Y Psc by Walter. It is suggested that the inclusion in this study of rotation effects on the stellar figures removes the need for such extra light.

PAGE 9

CHAPTER I INTRODUCTION Overview of the Problem The study of eclipsing binary systems is usually carried out by either a photometric or spectroscopic analysis of the light received at the earth. These approaches yield characteristic yet overlapping sets of parameters describing the system under study. Thus, while each type of analysis may yield a value of the orbital eccentricity, s, only the spectroscopic work will yield a value of K.. , the semiamplitude of the radial velocity curve. Likewise, only the photometric analysis of one or more light curves will yield a value for i, the orbital inclination. When both methods are combined, one then obtains a complete set of absolute parameters, and thus a full physical description of the system in terms of astrophysically interesting quantities (mass, radius, etc.) is possible. Many eclipsing binary systems have been analyzed both spectroscopically and photometrically, as described above, thus giving astronomers a large fraction of their data on stellar masses, radii, and luminosities. In addition, another fundamental parameter of a star is its rate of axial rotation. There are many reasons why this parameter is of interest. First, rotation has a direct effect on the shape of the star. If reliable photometric elements (and hence absolute elements) are to be obtained, the model employed in analyzing the light curves should be able to take into account the effect of rotation on the shape of the component stars, in addition to the gravitational effects. Also,

PAGE 10

distortion of the star(s) due to tidal and rotational effects will result in a nonuniform effective temperature over the stellar surface(s), a phenomenon yielding a nonuniform light distribution, known as gravity darkening, which will affect the photometric solution. If one knows the rate of rotation and can determine the value of astrophysically interesting parameters such as the linear limb darkening coefficient, x, or the gravity darkening exponent, g (using a model including rotation effects, etc.), one can then compare these numbers with those from the several existing theoretical model atmospheres for rotationally flattened stars. In this way, it is possible to determine which theory best fits the observations. Finally, a knowledge of the rotation rate of a star in an eclipsing binary system may yield important information on the evolutionary status of the system. In particular, a binary system in which one component shows a large stellar rotation value, coupled with evidence of a gas stream between components implying a slow rate of mass transfer may indicate recent large scale mass and angular momentum transfer. In such a case, the large rotation rate implies that the newly acquired rotational angular momentum has not been transferred back into orbital angular momentum via, for instance, tidal braking. Thus for many reasons it is useful to know the stellar rotation rate. Determinati on of Equatorial Rotational Velocities Traditionally, the method used to obtain V sin i, the nrojected ' e equatorial rotational velocity of a star, is to match the observed line profile of some selected spectral line with the line profile of the corresponding spectral line of some standard star. The standard star is usually a star of virtually the same spectral and luminosity class as the star of interest. The standard stars are of

PAGE 11

two types. Primary standard stars are those whose V have been determined (usually through statistical means) to be either approximately equal to zero, or equal to some fundamental lower bound characteristic of a particular spectral and luminosity class. Secondary standard stars have had their V determined through matching their line profiles with the line profiles of the primary standards which have been numerically rctationally broadened a known amount . By the same process of theoretically broadening the line profiles of the standard stars and comparing the results with the "unknown" line profile, a value of V sin i can be derived for r e the star being investigated. While this method has been carried out for many stars, it has two problems when applied to stars in eclipsing systems. The first is that the accuracy of V_sin i determined by this method is approximately the same (in km/sec) as the reciprocal dispersion used (in A/mm) in recording the spectrum. Thus for an error of ± 10 km/sec one must use a reciprocal dispersion of 10 A/mm. Since one does not want to make too long an exposure when observing many eclipsing binary systems (due to smearing of the line profiles by orbital doppler shift), this limits accurate results to the brighter eclipsing systems, or the moderately bright (9 -12 ) long-period systems where exposure rimes can be made correspondingly longer, and where a telescope of suitable light gathering power is available. Work of this sort has beer, carried out by Koch, Olson, and Yoss (1965), Olson (1963), Van den Meuvel (1970), Nariai (1971), Levato (19,4), and Maliama (1978), mostly at reciprocal dispersions of 16 A/mm to 50 A/mm. Secondly, the method relies heavily on statistical studies to pick out primary "standard" stars (V sin i-0) , and it presupposes

PAGE 12

that the residual broadening of the lines of these primary standard stars (mostly due to spherically symmetric macroand microturbulence) is characteristic of all the stars of that particular spectral and luminosity class. Since stars in a binary system may have very large effects on one another, and almost all standard stars are single stars, the usual methods for determining rotational broadening may not apply. One should note, however, that the results of different authors' investigations of the same star using the above technique usually agree to within the quoted errors (sometimes ± 50 km/sec) . It is thus natural to seek an independent method of determining V for stars in eclipsing binary systems, which could then be compared and contrasted with the results obtained from the line-profile matching method. The Rossiter Effect Such a method does, in fact, exist, and is based on a spectroscopic rotation effect known as the Rossiter effect. In a 1909 spectroscopic study of the eclipsing binaries X Tau and 6 Lib, F. Schlesinger (1910) interpreted certain anomalies found in the radial velocity curves of these stars as due to the rotation of the star being eclipsed. He concluded that the departures from the expected radial velocity curves during the partial phases of the primary (deeper) eclipse were due to the star in front geometrically blocking part of the surface of the star behind. These were in a positive sense (red shift) during ingress and in a negative sense (blue shift) during egress. This effect is seen as an asymmetry in the distribution of rotationally doppler shifted light emanating from the eclipsed stellar disk. Assume that the rotation of the stars is in the same direction as the orbital motion of the binary.

PAGE 13

During ingress, the approaching limb of the star being eclipsed would be hidden from view, and the resultant line profile would change from symmetric to asymmetric, with the blue side of the line being modified as shown in Figure 1. After totality (if it exists), the reverse will occur. Note that there are no physical constraints placed upon the stars involved. As long as the eclipsed star contributes enough light so that its spectrum can be observed, any eclipse-caused asymmetry will result in a corresponding asymmetric spectral line. Looking at Figure 1, it is evident that a measurement of the position of the line with respect to some laboratory standard line (whether measuring some weighted mean line center, or simply setting on the deepest part of the profile) will measure not an orbital doppler shift (= equal to the y velocity, V , i.e.. the velocity of the system toward or away from the sun, during primary eclipse) , but a doppler shift related to V . Thus a careful analysis of the Rossiter effect should vield a value of V . e This effect was next reported in studies of 3 Persei (Algol) by McLaughlin (1924) and $ Lyrae by Rossiter (1924), both of whom attributed the effect to stellar rotation. In 1931, 0. Struve and C. T. Elvey (1931) confirmed Schlesinger' s hypothesis by computing the asymmetric line profiles expected for Algol (during primary eclipse and assuming synchronous rotation, P , . = P , for the primary component), J orbit rotation and comparing them with the observed profiles; the agreement between the two was excellent. All eclipsing binary systems should show the Rossiter effect, although its magnitude and duration will certainly be a function of each system's geometry and physical properties (i.e., period, etc.). The

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U CTj a, u o

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effect should be large and relatively easy to observe in a class of eclipsing binary systems called Algol-type systems, which will now be discussed. Algol-Type Eclipsing Binary Systems The classical Algol systems are characterized by the following properties: (1) a deep primary eclipse, sometimes reaching 4-5 in depth in the blue, (2) orbital periods ranging from 1 to 20 days, and (31 spectral classes of A V or B V for the primary components, and G or K (III or IV) for the secondary components. Photometric analyses show that the deep primary eclipse is an occultation, wherein the larger, cooler G or K subgiant passes in front of the smaller, hotter A or B main sequence star. Thus the secondary eclipse (which in 'J, B, and y_ is usually very shallow) is a transit eclipse. Using the spectroscopic and photometric data, and assuming that the secondary component fills its limiting Roche lobe (as period changes and emission line activity suggest it does) , it was found that the secondary component was the less massive component of the systems studied. This situation, where the larger, cooler, less massive but more highly evolved star is accompanied by a smaller, hotter, more massive main sequence component represents the classical Algol paradox. Its resolution lies with the generally accepted picture of stellar evolution that, because stars expand as they evolve, the more massive star in a close binary system may expand to fill its gravitational Roche lobe first. Further expansion will lead to runaway, large scale mass transfer from the original primary component to the original secondary. This self-sustaining mass transfer will continue until after the mass ratio, q, reverses. At seme time after this, the rapid phase of mass transfer will end, and be replaces by a slow phase of mass

PAGE 17

transfer, which now proceeds on the nuclear time scale of the original primary (now the secondary component) . The presence of either continuous or intermittent gas streams between components is thus predicted. One is then left with a more massive main sequence component (the original secondary) , and an evolved but less massive subgiant component (the original primary) filling its inner Roche critical surface and slowly transferring mass to the new primary component. This seems a reasonable explanation of the Algol Paradox (cf. Crawford, 19S5) , and suggests that because angular momentum as well as mass is transferred to the original secondary, the current primary components of these systems may be rotating with a higher than synchronous value of V . In many binary systems the rotational and orbital periods of the component stars are thought to be equal, the condition of synchronous rotation. Usually a mechanism such as tidal braking is cited to explain this, wherein the rotational angular momentum is transferred into orbital angular momentum via the gravitational drag induced through the distortion of the outer envelope of an asynchronously rotating component. However, due to the mass and angular momentum transfer described above, the outer envelope of the primary components in Algol systems can spin asynchronously, since the angular momentum transfer is large, and, during the rapid phase of mass transfer, is on a much shorter time scale than the tidal braking mechanism described above (for details see Wilson and Stothers, 1974) . The degree of asynchronous rotation will be related to the initial orbital parameters, initial stellar masses, and the stage of evolution being observed (i.e., rapid phase or slow phase of mass transfer) .

PAGE 18

10 It is thus possible to predict that the primary components of Algol-type eclipsing binary systems may show a larger -thansynchronous Rossiter effect. The most likely candidate Algol systems exhibiting thi; effect would be those which are in the beginning of the slow phase of mass transfer. Observations made later than this will exhibit a reduced \' e of the primary component due to tidal synchronization. Observations made earlier than this will encounter difficulty observing the spectral lines of the primary component due to the presence of a thick "cocoon" structure surrounding the primary during and immediately after the stage of rapid mass transfer, as in |3 Lyrae (Wilson, 1974) and V356 Sgr (Wilson and Caldwell, 1978). Following consideration of all the points noted above, 19 Algoltype eclipsing binary systems were selected for study. These systems also possessed sufficient spectroscopic data to make a combined study possible. The size of the Rossiter effect for these systems varies from extremely large (U Cep, RY Per), to less than synchronous (W UMi, X Tri) . The systems range in period from 0.9 tc 16 days. The bulk of the spectroscopic data is provided by the extensive spectroscopic studies of eclipsing binaries made by 0. Struve in the 1940's. The photometric data range from modern UBV photoelectric observations to photographic observations made by Gaposchkin (1953) . Further discussion of the selected data is made in the next chapter. Purpose of This Investigation The major aims of this dissertation are as follows: 1. Derivation of V for the 19 systems under study, both to provide new data, and to provide an independent measure of V to be compared with the published data from line profile work.

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11 2. Re-solution of the light curves of these systems, taking into account the effect of rotational distortion of the primary components. 3. Determination of new absolute elements for these systems. 4. Determination of the extent to which the limiting rotational lobe is filled. The limiting rotational lobe is that potential surface within the inner critical Roche surface, for faster than synchronous rotation, for which the gravitational force is equal to the centrifugal force at the intersection, of the surface with the line of centers. 5. Discussion of the possible evolutionary status of these systems, and explanations of their other observed properties. The next chapter deals with the selection and analysis of the data chosen for this study.

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CHAPTER II METHOD OF ANALYSIS A description of the method of analysis is now presented. The two primary computer programs used in this study were the Wilson-Devinney light curve program [hereafter LCP) and differential corrections program (hereafter DCP) . Both of these programs have been extensively described in the literature (cf. Wilson and Devinney, 1971, 1973, and Wilson and Bierraann, 1976} . The LCP calculates monochromatic light curves based on an input set of system parameters. The DCP uses a starting set of system parameter values, and any number of observed light curves, and calculates corrections to the starting parameter values. A list of parameters to be differentially corrected is supplied to the DCP program, along with any number of parameter subsets. In this way, the method of parameter subsets (Wilson and Biermann, 1976) is used to overcome any correlation problems between adjusted parameters. The system parameters used by the two programs are the orbital inclination, i, the mass ratio, q (=/£, /A/..) , the value of the stellar surface potentials. i"2, and fi_, the polar temperatures, T and T ? , the gravity darkening exponents, g 1 and g , the linear limb darkening coefficients, x, and x ? , the fractional luminosities, L 1 and L 9 , the bolometric albedos, A and A,, the wavelength(s) of observation, -\, the amount of third light, 1„, and the ratio of the rotation rate to the synchronous rate, F. In addition to the above, the two programs recognise a mode integer. Specification cf the mode allows the program to incorporate any special

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15 constraints one slight feel should be included. As an example, the solutions presented here for the 19 Algol systems were carried out in mode 5. This mode specifies the condition that the secondary component exactly fill its inner critical surface (see previous discussion of Algol systems in Chapter I) . Finally, the LCP, in addition to calculating theoretical light curves, also calculates the radial velocity curves for each component. The velocities which are computed are dimensionless , and contain the factor 2nP/a_, where P is the orbital period and a is the separation of centers . The procedure used in this study is an iterative one, since a computer program for the simultaneous solution of photometric and spectroscopic data is not yet available (although the basic principles for such a program have recently been discussed, Wilson, 1979) . A general outline of the method used for obtaining V for the 19 Algol systems is given below. 1. The LCP was used to compute, via trial and error, an initial, fairly close fit to the light curve(s), and thus a first set of parameters describing the system. 2. The parameters found in (1) were supplied to the DCP along with the light curve(s) , and an initial guess of the value of F (which comes from an inspection of the observed radial velocity curve) . Several runs of the DCP were made until a good fit to the light curve (s) was achieved. The progress of the solution process was followed by running the LCP with, the new, updated parameter values, and plotting the resultant light curve versus the observed points after each run of the DCP.

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14 3. The theoretical radial velocity curve calculated after the last DCP run in (2) (i.e., from the last LCP run) was then plotted against the observed radial velocity curve in order to check the amplitude of the Rossiter effect. To do this, the observed velocities were transformed into dimensionless velocities. Note that at phase 0.25, the value of the theoretical dimensionless velocity and the value of the semiamplitude of the observed radial velocity curve, K. , will be equal except for the multiplicative constant mentioned previously (2TrP/a_) . Thus, knowing K, and the dimensionless velocity at phase 0.25, the constant factor can be determined. Once this factor is known, it is possible to transform the othea observed velocities into dimensionless velocities. Corrections for the value of V and any possible phase shifts between the spectroscopic and photometric data were also taken into account . 4. In most cases, the initial guess of F and hence the amplitude of the Rossiter effect was incorrect in (5) . LCP runs were then carried out for different values cf F, until the correct, amplitude was achieved. This new value of F was put back into the DCP and the solution of the light curve carried cut for the new value of F. 5. Through the iterative process outlined in (4), the preliminary solutions converge to a light curve solution and a value of F such that both the amplitude of the Rossiter effect is correct, and a good fit to the light curve(s) is obtained. For the final DCP runs, the fit to the light curve was carried out

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15 until the corrections for the adjusted parameters were less than or approximately equal to their associated probable errors. Also, although only the basic parameters i, q, fi, T 2 , and L.. were adjusted during the iterative process, an attempt was made during the final runs to adjust x.. , g 1 , and Afor stars with no complications in the light curve and good observational phase coverage. 6. The final light curve solution yielded a final value of V , at phase 0.25. As explained, value of the factor for transforming V , into V . could now be obtained. Rememberobs theo ing that this factor = 2iTP/a, and knowing P very accurately, we can solve for a_ (in km) (if P is in seconds and fC is in km/sec) through the following equation: a= [(K 1 .P/2W theO)0 . 25 )] (1) 7. From the LCP, a value of r 1 . , (= side radius of the primarv ljSide r component in terms of the separation of centers, a) is also computed. With a from (6), R n , the side radius of the primary component in km, is computed. 8. With R, from (7), and the relation V , , = 2ttR,/P, the svn1 e(synj 1 chronous equatorial velocity of the primary is calculated. Finally, using the final value of F, the value of V is arrived at from the equation V = V , "F. e e(synj Having summarized the computer programs used in this study, and the general method used for determining V , a review of the problems which arose during the solution process is now appropriate. A summary of the problems found in analyzing the photometric data will be done first.

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16 The quality and quantity of photometric data for each system varied greatly. When possible, twoor three-color photoelectric light curves were used. For several systems only one-color photometric data were available. In one case the only available light curve was the photographic light curve by Gaposchkin (1955). While the accuracy of the photographic light curves is lower than the photoelectric light curves, they should suffice for a first survey such as this work. When possible, 50-100 normal points per light curve were used. A major problem for many systems was the presence of distortions at certain phases of the light curves. The majority of these distortions can be described as extra light added to the "undisturbed" light curve between phases 0.08 and 0.35. Since gas streams are almost certainly present for most of these systems, and disk structures may also exist, it is not surprising that many light curves show distortions of the nature described above (a description of the light curve distortions for individual systems is included in Chapter III). When obviously disturbed sections of the light curve were present, the distorted regions were excised. In addition, the U light curves for several systems were not used because many authors have reported distortions of these light curves near second contact. Thus it is hoped that the effect of distortions on the solution process was minimized. It should be noted here that the assumption was made that the effective wavelength of observation for the photographic light curves was approximately 4100 % (see Arp, 1961) . Spectroscopically many problems are evident in these determinations of rotational velocities. Foremost of these is the definition of the "center" of an asymmetric spectral line. The LCP calculates a

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mean line center, where the mean is calculated by weighting the radial velicty of each grid area on the star by the light emitted from that area in the observer's direction. Thus, effects due to limb and gravity darkening, rotational flattening, etc., are automatically taken into account. An assumption made here is that the intrinsic line profile is narrow as compared to the rotational broadening function. While this assumption would be important if one were going to match theoretical and observed line profiles, it does not directly affect the measurement of the line centers (except that the wider the profile, the harder it will be to determine the center of the line) . It was noticed, however, that when the initial spectroscopic results for several systems were plotted, the onset of the observed Rossiter effect came later than the theoretical time of onset, and ended earlier than expected! An explanation for this effect results directly from the assumption that most observers, when trying to determine the line center of an asymmetric line, apparently simply choose the deepest pari of the profile as the center of the line (Abt, 1979). However, as outlined in Figure 2, identification of the deepest part of the line as the center will not measure a line shift (due to the Rossiter effect) during the initial and final phases of the eclipse. In order to test this, the LCP program was modified to print the expected line profile for values of phase during which the rotation effect would be present. A new graph of the rotation effect, as it would seem if the deepest part of the line were used to define the line center, was constructed. The result, shown in Figure 3, confirms the aforementioned hypothesis. Note that the amplitude of the Rossiter effect was not affected. For this reason the primary fitting criterion was that the amplitude of the theoretical and observed Rossiter effect match.

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3 to 3 Ch u Pn a H CO O O O a cs h -d > '-m x,3 -a y a -h m •< ca to 3 +-> 4-1 3 10 6 -H -H _G 4H CD U J3 -3 H O a O a O O0 3 O S "" C 3VH CD O C U P £ 3 •> 3 4-> . CD O .< 3 i-H CD X CD rt 3 ^H fH rH cj a o a id u > H 4-1 3 +-» O 3 CD I CO U C JZ U JZ J=i CD +-> 3 3 CD O O C a, 4-> > CD d JZ S O 3 +-» r< 4-> CD CD X 00 O 3 O CO CD fn M +-> =0 to Mh CD CD Uh'HhUtJpiWfH CD 4-1 CD t3 CO X4-I O 4-1 a CD fn CD CO CM 3 u o, a 3 e CD -H OCD SO a a r< g ^< <-h 3 3, CD to +J JZ =0 CD 'Ji£ CD T) r~, a M CO CD CD PL, a. 3 s CD CD CD O CD a i— ( a .3 3

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19

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s

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Sft'Oco SO'OS5'0-

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A further problem exists in the interpretation of the observed Rossiter effect as a unique velocity; that is, different spectral lines show effects of different amplitudes. In particular, the higher excitation lines such as He I and He II sometimes show a rotation effect double that for the hydrogen lines. As suggested by Hansen and McNamara (1959) for R2 Set, and Hiltner (1946) for RY Per, this circumstance is probably due to either (a) the hydrogen lines arising in a more slowly rotating disk or envelope structure around the primary, while the helium lines arise in the true stellar photosphere, or (b) the normal stellar hydrogen lines are severely modified by absorption and/or emission in the aforementioned disk structure, thus making the velocities determined from these lines unreliable. In any case, it would seem that the He lines and other higher excitation lines are more accurate indicators of the rotation velocity of the stellar envelope. For this reason, the radial velocity measurements of the He I, He II, and Mg II lines were used whenever possible in this study. For systems whose published radial velocities represent an average of all measured lines, the results of such work verv likelv yield only lower bounds to V . j j j e Near the bottom of primary eclipse, where the light of the secondarycomponent may become equal to or even exceed that of the primary component one might need to consider the role of possible line blending (if it occurs) on the observed line profiles of the primary component, and thus on the determination of the line center. Further, the light curve solutions show that for most of the partial phases the light of the primary is much greater than that of the secondary. Thus tnis effect would only operate during a small time interval. In addition, it is known that, in almost every case studied here, the secondary is of a later, much

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cooler spectral type than the primary; hence it has a much different spectrum. Thus it is unlikely that, except for a few very weak lines that are near the lines normally measured, any significant blending of spectral features of the two stars will occur. For several systems, the presence of such weak lines of the secondary probably accounts for the presence of measured radial velocities for the primary component during a total eclipse. When this effect was recognized, affected data points were eliminated from the analysis. There most certainly is a problem with emission lines from the stream or disk modifying the line profiles. It would be expected that the systems which show a large Rossiter effect, disturbed light curves, and prominent emission lines at certain phases are those systems which display the largest radial velocity distortions and large scatter throughout their radial velocity curves. This is in fact the case. Systems such as U Cep, AQ Peg, RZ Set, RY Per, SW Cyg, and U Sge all exhibit such behavior. The amount of scatter and distortion introduced into the radial velocity curve through such emission line effects (and/ or absorption, which may also exist) will be a complicated function of system-stream-disk geometry and physical parameters (e.g., the density and temperature of the gas stream) (see Parise, 1979) . In more tractable cases, the velocity curve outside of eclipse can be recovered (see Hardie, 1950), in which case an accurate value of K, may be obtained, as previously mentioned. Several actions may be taken in order to minimize the influence of the effects mentioned above: (1) Because the higher excitation lines of He and Mg are probably more indicative of the stellar surface rotation (due to relatively larger modification of the H profiles

PAGE 32

24 through absorption and/or emission in the stream-disk structure) , only these (and similar) lines should be (and were) used whenever possible, (2) Reconstructed radial velocity curves, for which an attempt to remove the effect of emission/absorption has been carried out, should be utilized; and (3) Direct matching of observed and theoretical line profiles, whereby direct comparison might shed light on distortions of the line profile due to extraneous emission/absorption, should be employed. Unfortunately, U Cep is the only system for which (2) has been carried out, and both (2) and (5) would require micro densitometer tracings for all the spectroscopic data— a task outside the scope of this work. It should be noted, however, that at the phases corresponding to the maximum of the Rossiter effect (i.e., just before primary minimum), one should expect mostly emission from either the ring or a hot spot where the gas stream hits the disk structure (if it exists). Thus, if the emission falls at the same wavelength as the rotationally modified absorption feature, one should expect line filling to occur, and thus the measured effect will be smaller. This topic will be discussed again in Chapter III as it pertains to individual systems. Finally, another source of error is that of line smearing due to long exposure times. For several of the systems studied, the Rossiter effect goes through an entire cycle in only 70 minutes. If care is not taken, and long exposure times are used, the line profile will be smeared, and the effect washed out. Comments on this problem as it pertains to individual systems will be made in Chapter III. In summary, the problems with the spectroscopic data fall into two main classes: (1) Those which, through blending or smearing, tend to lessen the amplitude of the Rossiter effect, and (2) those which

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distort the radial velocity curve, thus making the derived value of K uncertain. However, since the prime objective of the fitting process is to match the amplitude of the Rossiter effect, the value of V found e should be, at worst, a lower bound to the true value. In the next chapter the observational data utilized for the individual systems will be discussed in detail.

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CHAPTER III DISCUSSION OF INDIVIDUAL SYSTEMS In this chapter the observational data used in this study will be discussed. For each system a summary of the spectroscopic and photometric data used is given. Comments on the derived values of the temperature of the secondary component, T , the ratio of rotation rate to the synchronous rate, F, and the presence of possible period changes are also presented. Further discussion of the systems studied as pertains to the equatorial rotational velocity, V , derived absolute elements, etc., will be presented in Chapter IV. Table I gives the basic observed parameters for each system. Table II lists the spectroscopic elements used in this study. Table III presents the results of the photometric analysis for the wavelength independent parameters. Table IV lists the results of the photometric analysis for the wavelength dependent parameters. Figures A-l to A-20 (see Appendix A) show the fits to the spectroscopic data, and Figures 8-1 to B-22 (see Appendix B) show the theoretical fits to the individual light curves. The abscissa for all figures is orbital phase. For Figures A-l to A-20, the ordinate is velocity, V, in dimensionless units. The ordinate for Figures 8-1 to B-22 is light level. X Tri The spectroscopic work of Struve (1946b) was used for this investigation. The spectral type of the primary component is A3 V. The derived value of T 7 implies C2 III or 63 IV for the spectral type of the secondary component. This is in good agreement with the spectral type of G5 given by Struve, who states that, some blending with the A5 spectrum 2 b

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27 TABLE I 5ASIC SYSTEM DATA

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23 TABLE II SPECTROSCOPIC DATA Name

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29 TABLE III WAVELENGTH INDEPENDENT PARAMETERS Name

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30 TABLE III --Extended

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31 TABLE III— Continued

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TABLE III— Extended 32 l,back

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TABLE IV WAVELENGTH DEPENDENT PARAMETERS* 53 Name

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34 TABLE IV--Continued

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55 exists on the plates taken during primary minimum (totality lasts approximately 12 minutes). The radial velocity curve is symmetric, and shows a small, less-than synchronous (F=0.6) Rossiter effect. No emission lines are present. Figure A-l shows the fit to the radial velocitycurve . The modern BV light curves of Bozkurt, Ibanoglu, GUlmen and GUdUr (1976) were used for the photometric analysis. These light curves exhibit excellent phase coverage and small scatter throughout. Because the mode 5 solution gave a very poor fit out of eclipse, a mode 2 solution was tried, which resulted in a good fit to the light curves, as shown in Figure B-l. A periodic representation of the time-of -minima data was found by Rafert (1977). This is probably a light-time effect due to a third (unseen) member of the system. Y Leo By assuming a circular orbit and a value of F = 1.5, an excellent fit to the radial velocity curve is achieved. Struve's (1945) impression that the light of the A3 V primary is still visible during mid-primary eclipse (i.e. that primary eclipse is partial) is supported by the present work. The derived value of T ? implies a spectral class of K2 III or K3 IV. The exposure times were short enough that line smearing should not have been a problem. As mentioned earlier, the radial velocity curve of this star was used to test the effect of measuring the deepest part of the line profile as the line center, instead of using a weighted mean (see Figures 2, 3 and A-2) . There is evidence for period changes in this sytem, although the exact nature is in question. A value of F = 1.5 was used for the final photometric analysis.

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36 The photometric analysis was carried out using the B_, V, and red (A = 8000 A, 3000 A wide bandpass) light curves of Johnson (1960) (see Figures B-2 and B-5) . As a check on the assumption of using mode 5 for these systems, a trial run of the DCP in mode 2 (identical to mode 5 except that the lobe-filling constraint on the secondary is relaxed) provided corrections indicating that the secondary did fill its Roche lobe. No complications are evident in the light curves other than an indication that the ingress shoulder of primary eclipse is slightly low. Evidence for period changes is summarized by Rafert ( 1977) . RZ Cas Spectroscopicaily this system has been studied by Jordan (1914) and Horak (1952), the latter work being used for the present investigations (39 observations at 40 A/mm at 5953 A) . The spectral type is given as AO (Horak) to A5 V (Chambliss, 1976). The derived value of T 7 suggests a secondary spectral classification of KO III or Kl IV. No emission lines were noted by Horak. Both branches of a moderately large rotation effect are seen. A value of F 1.6 gives a satisfactory fit to the rotation effect, as can be seen in Figure A-5. Many photoelectric light curves exist, the most modern being the studies of Chambliss (1976) and Lee and Lee (1977). The UBV normal points of Chambliss were used in this study. A solution of the 5 light curves, using approximately 75 normal points for each light curve, was carried out, resulting in excellent fits to the light curves (see Figures B-4 and B-5). A variaole light curve is suspected for this system (Chambliss, 1976). Rafert (1977) has discussed the evidence for period changes in this system, emphasizing the probable filling of the secondary's Roche lobe.

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57 ST Per The spectroscopic data used were that of Struve (1946b) . He and Hill et al . (1975) agree on an A5 V classification for the primary component. The value of T 9 found implies a spectral type of KO III or Kl IV, in agreement with the classification by Weiss and Chen (1976) . The radial velocity is characteristic of a circular orbit, with the Rossiter effect being evident for the egress phases of primary eclipse. No data were taken during ingress. A value of F = 1.55 was used for the final photometric analysis. Figure A-4 shows the final fit to the spectroscopic data. The photometric analysis of this star was carried out using the RI_ photometry of Weiss and Chen (1976). Approximately 50 normal points in each color were used. While there is appreciable scatter in the original observations, the use of judiciously chosen normal points allowed a solution to be found with little difficulty. Figure B-6 displays the final fit to the light curves. A discussion of the evidence for period changes is given by Rafert (1977). RX Hya The spectroscopic data of Struve (1946b) were used for the analysis of this system. The spectral type of the primary is AS V, making it the "latest" spectral type primary studied. The value of T 9 derived in the photometric solution implies a secondary spectral type of KO IV or GS III. The radial velocity curve is symmetric, with a pronounced rotation effect present (F = 2.0). Struve states that during mid-primary eclipse, "the metallic lines look slightly stronger, but the spectrum is still essentially that of the brighter, AS, star." The later than

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33 normal spectral type of the primary and the latter statement of St rave may point to blending problems near primary eclipse, perhaps affecting the amplitude of the Rossiter effect. No emission lines are noted by Struve. The fit to the radial velocity curve is shown in Figure A-5. The light curve used was the photographic light curve of Gaposchkin (1953), it being the only light curve available. Figure B-7 shows the fit for this partially eclipsing system. The scatter of the light curve is typical of photographic light curves. A mode 2 solution was also attempted for this system. The results showed a marked preference for the secondary completely filling its Roche lobe. A limited amount of data implies a period change for this system (Rafert, 1977) . W UMi This star was included as an example of a system whose radial velocity curve showed a synchronous Rossiter effect. A new solution of the UBV photoelectric observations of Devinney, Hall and Ward (1970), using the Wilson-Devinney programs, has recently been carried out by Devinney and Sutton (1979) . The results of this study have been kindly communicated by Dr. E. J. Devinney (1979) ahead of publication. This latter solution shows the system to be either semidetached, or detached with the secondary very close to its Roche lobe. Their solution was carried out with F 1.0. The final elements communicated by Dr. Devinney were used in the LCP to produce the theoretical radial velocity curve shown in Figure A-6 plotted against the observations of Sahade (1945) . It would seem from Figure A-6 that the primary component (A3 V) may be rotating slower than the synchronous rate. In order to test this (to

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59 the first order) , the LCP was used to calculate a new theoretical radial velocity with F = 0.75. The values of all parameters except q, were kept at their F = 1.00 value. 12 was adjusted so that the side radius of the primary component was kept constant. The result is shown in Figure A-7. While the shape is still not quite right, the fit is superior to the theoretical F = 1.0 radial velocity curve. If real, the low rotation rate of the primary component could be explained by (1) a system in pre-main sequence contraction, such that the spin of the primary component has not been synchronized through, for instance, tidal effects, or (2) a system well past even the slow phase of mass transfer (i.e., no gas streams are present) , with the '"new" primary (by virtue of the original phase of rapid mass transfer) now expanding off the main sequence, so that its rotational rate has slowed to conserve angular momentum. No emission lines are noted by Sahade. WW Cyg The spectroscopic data used for this were that of Struve (1946b) . He describes the spectrum of the primary as B8 V, and that of the secondary as approximately G, although the faintness of the system during primary eclipse (V = 13.3) made the observation during this time very difficult. A moderate rotation effect is present although data were taken only during ingress, and the radial velocity curve is characteristic of a circular orbit. No emission lines are noted by Struve, although the same problem mentioned above would make their detection very difficult if the emission is weak. The derived value of T-, implies a spectral type for the secondary of G5 IV or G4 III, in agreement with Struve' s estimate. A value of F = 1.55 was found to give the best agreement with the amplitude of the Rossiter effect, and the resulting fit is shown in Figure A-S.

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40 The three-color UBV light curves of Hall and Wawrukiewicz (1972) were used for the photometric analysis. The individual points were used instead of normal points. The fit to the light curve is shown in Figures B-8 and B-9. The solution does confirm the low value of x 1 found by Hall and Wawrukiewicz (1972) . The suggestion that "extra" light is present at second and third contact (due to a hot spot on the primary) is not supported by an minus C plot of the residuals. The presence of period changes (cf. Rafert, 1977) and a "spun-up" primary (in addition to the arguments presented by Hall and Wawrukiewicz) do not favor the pre-main sequence contraction state of evolution suggested by Field (1969) . RW Gem The spectroscopic work of Struve (1946b) was used in analyzing this star. Except for 3 questionable points near phase 0.96, the radial velocity curve is well represented by a circular orbit, with an excellent fit to the amplitude of the Rossiter effect being achieved with F = 2.1 (see Figure A-9) . The spectral type of the primary component has been given as B5 V (Struve, 1946b) and B6 V (Lucy and Sweeney, 1971). The spectral type of the secondary was given by Struve as roughly F5 subgiant and FO IV by Lucy and Sweeney (1971). The derived value of T is consistent with an FO I I I I I classification. The revised values of K 1 and y given by Lucy and Sweeney were used in the fitting procedure. No emission lines are noted by any of the above authors. The V light curve of Tremko and Vetesnik (1974) was used for the photometric analysis. No other photoelectric data were available, although a photographic light curve by Gaposchkin (1953) does exist. The published

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41 normal points were used, although a second solution was made after the normal points between phases 0.1 and 0.4 were removed. There is a definite distortion of the light curve at these phases. The difference between the two solutions is not as large as would be expected (see Tables III and IV, RW Gem 1 and 2) . The fit to the observed light curve is shown in Figure B-10. There is evidence of period changes in this system (Rafert, 1977) . TX UMa The spectroscopic observations of Hiltner (1945) were used in the present investigation. Other spectroscopic work has been carried out by Swensen and McNamara (1968). The spectral type of the primary is B8 V. According to Hiltner, the spectral class of the secondary component is gF2. However, a more recent study (UCLA Observatory Report, 19 76) gives a classification of GO III-IV. This is in agreement with the classification of F8-F7 III found from the derived value of T . The radial velocity curve appears symmetric, as the value of e = 0.029 derived by Hiltner suggests. The observations of Swensen and McNamara (1968) indicate a variable shape for the radial velocity curve, although this may reflect differences in the measuring technique used by the different authors. The magnitude of the rotational disturbance is unequal during the partial phases of primary eclipse, it being smaller during ingress and larger during egress from primary eclipse. A value of F = 2.0 gave a satisfactory "average" fit to the data. No emission lines have been reported for this system. Figure A10 shows the fit to the spectroscopic data. Of the light curves available in the literature, the blue photoelectric light curve (A = 4500 A) of Huffer and Eggen (1947) was used

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42 for this analysis. Other work has been published by Koch (1961), and Hill and Hutchings (1973) . Forty-seven normal points were used for this investigation. The fit to the light curve is shown in Figure B-ll. The derived value of q = 0.29 fortuitously agrees with the value of 0.27 found by Grenwing and Herczeg (1966) from an analysis of the slope of the radial velocity curve of the secondary component during primary eclipse. Rafert (1977) has summarized the evidence for period changes in this system. TV Cas The spectroscopic work of Sahade and Struve (1945) was used in the present investigation. The spectral type of the primary is given as B9. The secondary spectrum is not observed, although the derived value of T~ implies a spectral type of G2 III or Gl IV. A small to moderate Rossiter effect is seen during the egress phases from primary minimum. Although the data are sparse, a circular orbit is indicated, with a value of F = 2.1 giving a satisfactory fit to the rotation effect (see Figure A11) . Several authors have published light curves for this system. A recent paper by Walter (1979) gives a thorough and detailed discussion of this system, as well as presenting a new set of observations. One notes that the light curves are variable, and that there is definite evidence for period changes in this system. It was noted that the photographic light curve of Gaposchkin (1953), which is based on 2651 plates, represents a "mean" light curve when compared to the other published blue light curves. Thus, in view of the quantity and quality of the spectroscopic data, and in the interest of avoiding problems due

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45 to asymmetries, the Gaposchkin light curve was used in the present study (see Figure B-12) . The results of the present study match the previously reported results or other authors' analyses very closely and thus confirm that the photographic light curve represents a mean light curve of the system. The cause of the periodic fluctuations present in the light curves is thought by Walter (1979) to be due to a gas stream between components, and a hot spot present on the primary component. Although no emission lines were seen by Sahade and Struve (1945), their small number of observations coupled with the intermittent nature of the light curve asymmetries does not make this surprising. Evidence for period changes is summarized by Rafert (1977). AQ Peg The spectroscopic data of Struve (1946a) were used for this investigation. The spectral type of the primary component is A2 V. The spectral type of the secondary, which is seen during the total phase of primary eclipse, is given as G5. This is in fair agreement with the type KO III or Kl IV given by the derived value of T_,. The latter is in good agreement with the secondary spectral type of K2 IV found by Hall (1979) from (B-V) . The emission seen during primary eclipse is indicative of a ring around the primary component. Red-shifted emission components for the H, Mg, and Ca II lines are seen during ingress to primary eclipse. Near central eclipse the emission is composed of two unequal components, the stronger being the red-shifted, and the weaker being the violetshifted emission lines. During egress, the red-shifted emission lines disappear, while the violet-shifted components become stronger. The radial velocity curve is asymmetrical (leading to a value of e = 0.24),

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44 and large scatter near phase 0.6 is especially noticeable. Both of these effects are probably due to the effects of the gas stream and the ring structure present. A very large Rossiter effect is present, with an excellent fit to the rotational disturbance being achieved with F = 6.7 (see Figure A12) . A photographic light curve by Gaposchkin (1953) and UBV photoelectric photometry by Hall (1979) exist. The BV light curves of the latter were used for this study. Except for a slight asymmetry in primary eclipse and a disturbed region near phase 0.1 in the V_ light curve, the BV light curves are free of large distortion. At some phases, the scatter may be larger than expected by Kail (1979) and is probably due to the complicated nature of the system. Of interest here is the plot (see Figure C-l in Appendix C) of the minus C residuals in primary eclipse. As with Y Psc, no excess light near second or third contact was found. Indeed, the rounded bottom, which according to Hall is due to emission from circumstellar matter, is well fit by the model used here, which includes the effect of rotational flattening (see Figure B-13). Hall (1979) cites evidence for period changes in this system. SW Cyg The spectroscopic data of Struve (1946b) were used for this study. The skewed, distorted shape of the radial velocity curve is obvious (especially between phases 0.45 and 0.75), and is responsible for the value of e = 0.3 found by Struve. Thus, as with the other system showing similar distortions, the value of K 1 must be viewed with caution. A large rotation effect is present during egress from primary eclipse, making a value of F = 5.0 necessary in order to achieve a satisfactory

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45 fit. Figure A-15 shows the fit to the observed radial velocity curve. The spectral type of the primary is A2 V. According to Struve, the spectral type present at mid-eclipse is approximately KO. This is in good agreement with a spectral class of K2 III or K3 IV found from the derived value of T ? . Emission lines are present throughout primary eclipse. In phase order, Struve reports the presence of (1) a weak red-shifted emission feature for H 3, no violet-shifted component, (2) strong redshifted emission present in H 3 and H y, (3) slightly weaker red-shifted emission in H 3, (4) strong violet-shifted emission in H 3 and H y, and (5) weak violet-shifted emission in H 3 . This definitely indicates an emission ring structure around the primary component. No velocity measurements for the emission lines are given. The light curves used are the BV light curves of Walter (1971) (see Figure B-14) . Additional light curves are published by Wendell (1909), and most recently Hall and Garrison (1972). Walter, and Hall and Garrison give detailed analysis of the available light curves. The model of Hall and Garrison deals with a partial ring structure which intersects the primary instead of encircling it. They also state that a "protuberance" must be present on the primary in order to explain an excess of light in the V band during certain phases. Walter prefers a model with absorption in the gas stream from the secondary to the primary the absorption being strongest during the ingress phases of primary eclipse. In addition, extra light is present at some phases due to the presence of a hot spot on the primary component. All authors agree that the disturbance of the U_ light curve near second contact is due to light from either a hot spot on the primary, or a hot spot in the ring structur:

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46 where the gas stream intersects it. Figure C-2 shows a plot of the minus C residuals during primary eclipse taken from the present work. Again, while systematic trends may show the presence of absorption or extra light during ingress and egress from primary eclipse, no definite evidence of residual light at second and third contact is apparent. Thus, the "protuberance" needed by Hall and Garrison to supply extra light in V at some phases may simply be an artifact of their model, which does not include corrections for rotational flattening of the primary. A discussion of evidence for period changes is given by Rafert (1977) . Y Psc The spectroscopic data of Struve (1946b) were used to study this system. The primary component is of spectral type A3 V ("with many sharp lines present"), and the derived value of T 7 implies a spectral type of Kl III or K2 IV, in agreement with Struve' s estimate of KO. The theoretical fit to the radial velocity curve is shown in Figure A14. The value of e = 0.12 found by Struve is probably due to the obvious distortion of the radial velocity curve by a gas stream, whose presence is implied by an H 3 violet-shifted emission feature seen during egress from primary eclipse. The distortion of the radial velocity curve is especially pronounced between phases 0.5-0.7 (as in SW Cyg, U Sge and other systems thought to contain gas streams); i.e., when the observer sees the light of the primary component through the gas stream. A good fit to the amplitude of the Rossiter effect is given with F = 1.65. The photoelectric data of Walter (19~3a, 1973b) were chosen for this analysis i^see Figure B-15) . A photographic light curve by Gaposchkin (1955) also exists. This system is one of several for which Walter has

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47 hypothesized a bright hot spot on the primary component in order to explain "extra light" present at second and third contact. Figure C-3 shows a plot of the minus C residuals for primary eclipse from the present analysis. The effect seen by Walter is not evident on the plot. This is probably due to the difference in shapes assumed for the stars by the two models used. In particular, the Russell -Merrill method used by Walter does not take into account rotational flattening. The fact that the Wilson-Devinney model, which does include the effects of rotation, does not predict extra light at second and third contact, as did Walter's Russell-Merrill modeling, probably shows the necessity of modeling this effect when analysing the light curves for these systems. Possible period changes are discussed by Rafert (1977). W Del The spectroscopic data used in this study are that of Struve (1946b) The radial velocity curve is skewed and shows large scatter at some phases. This is reflected in the "classical" value of e = 0.2 found by Struve. The spectral type of the primary is AO V-B9.5 V (Struve, 1946b), and Hill et al . (1975). The derived value of T_, implies a spectral type for the secondary of GS III or KO IV, in fair agreement with Struve 's estimate of G5 subgiant. A red-shifted H 3 emission component is easily seen during ingress from primary eclipse, and faint H 3 violet-shifted emission is seen during egress from primary eclipse. The H emission seen, and evidence of period changes in this system (Rafert, 1977, Plavec, 1960) point to a gas stream and an asymmetric ring structure. The stronger red-shifted emission component may also indicate a hot spot on the trailing edge of the primary component. The pronounced Rossiter

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48 effect has a satisfactory fit with F = 1.7. Since the radial velocities given are averages of all lines, this value of F is probably an underestimate. The fit to the radial velocity curve is shown in Figure A-15. The photoelectric data used for this system are that of Walter (1970). A photographic light curve by Gaposchkin (1953) also exists. The deep primary minimum (2.6 in V, and 3l4 in B_) is definitely asymmetric as pointed out by Walter. This appears in the present solution as long runs of systematically positive or negative residuals in primary eclipse. A likely explanation is that extra light from a hot spot on the primary or ring structure is present during egress from primary eclipse. The fit to the light curves is shown in Figure B-16. RY Gem The spectroscopic work of McKellar (1949) , carried out at dispersions of 50 A/mm and 135 A/mm, supplied the data for the present analysis. Spectroscopic work has also been carried out by Gaposchkin (1946) and Wyse (1954). The spectral types given are A2 V and K2 subgiant. The latter agrees well with the value of T derived in this work, which implies a spectral type of KG III or Kl IV. Wyse (1934) noted violetshifted emission in H for plates taken during totality. McKellar notes double emission at mid-primary, and violet-shifted H B emission during egress from totality and during the latter phases of totality. The double emission is seen in H B to H i , and in K of Ca II. The emission lines yield a velocity of particles in the ring of ± 200 km/sec with respect to the system. Thus this system probably contains a gas stream and a ring structure similar to AQ Peg and RZ Set. Out of eclipse the radial velocity curve shows severe distortion and large scatter at most

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49 phases. Both of these are due to the above mentioned streamring structure. The value of K., is thus suspect, and may be in error up to 25%. Figure A16 shows the fit to the observed radial velocity curve. The only light curve available was the photographic light curve of Gaposchkin (1955) (see Figure B-17). The scatter is large between phase 0.5-0.45, and the light curve is asymmetric, with the points between phases 0.65 and 0.75 being low. The value of q is therefore fairly uncertain. Period changes have been observed for this system (cf. Rafert 1977). U Sge The spectroscopic data of both Struve (1949) and McNamara (1951a) were used in this study. McNamara' s work was done at a dispersion of 26 A/mm, and 75 A/mm at minimum light, while that of Struve was dene at 40 A/mm (with a few plates at 10 S/mm) . The spectral type of the primary component is B8.5 V, and that of the secondary component G5 III. The latter agrees perfectly with the classification of G5 III found from the derived value of L. A detailed discussion by the above mentioned authors points out the following: (1) the radial velocity curves given by the He lines and the H lines are different, as in the cases of RY Per and TZ Set, (2) the rotation effect is larger for the He and Mg lines than for the H lines (see McNamara, 1951b), (3) sporadic emission lines are present during primary eclipse, and (4) "satellite" H lines, as seen in 3 Lyrae are present. The fact that the distortions are not nearly as large as in, for instance, RY Per (as seen by the derived value for U Sge of e = 0.04) and in the presence of sporadic emission activity indicates a variable ring and gas stream structure in

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50 the system. Only the He line measurements of Struve and the mean velocity of all lines except H and Ca for McNamara's data were used for the present work. A final value of F = 4.2 gave a satisfactory fit to the Rossiter effect, as shown in Figure A17. The excellent uvby photometry of McNamara and Feltz (19 76) was used for the photometric analysis (see Figures B-18 and B-19). Recent photometry of this system has also been published by Cester and Pucillo (1972) . Approximatley 50 normal points in each color were used for the analysis. Of interest here is the value of q = 0.41 found by the present work. Recent infrared spectroscopy by Tomkin (1979) indicates a value of 0.33. Although no correlation problems were indicated by the DCP, trial runs were made in both mode 2 and 5 wherein the value of q was set to 0.55 and not adjusted. The results gave much inferior fits to the light curves. Perhaps the difference between the photometric and spectroscopic values of q lies in the fact that the large temperature difference between components can lead to severe modification of the spectral lines of the secondary, and thus to the resultant value of q. In support of the mode 5 solution for this system is the fact that in addition to the emission activity the period of this system is known to be variable (Rafert, 1977) . U Cep A great deal of work, both spectroscopic and photometric, has been done on this system. A complete summary of the spectroscopic work can be found in a recent article by Batten (1974) . The radial velocity curve is extremely distorted, as can be seen in Figure AIS. However, Hardie (1950) has published an interesting article in which the radial

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velocity measurements for the H lines (using Struve's 1943 radial velocity measurements) have been "corrected" for distortions present in the line profiles. The corrected radial velocity curve yields a value of e = 0.0, which is in accord with the value implied by the photometry. The new value of K 1 , 85 km/sec, is quite different from the older value of 120 km/sec. This difference leads to a large change in the mass function from 0.41 to 0.16. Batten (1974) gives the spectral type of the primary component as B7 V, and that of the secondary as G8 III-IV. The latter agrees well with G8 III or KO IV found from the derived value of T-. The large amplitude of the Rossiter effect necessitated a value of F = 8.0. The large amount of data on emission-line activity in this system is summarized by Batten (1974) . The theoretical fit to the radial velocity curve is shown in Figure A19. The fit during egress from primary eclipse is not good, and may be due to the reconstruction technique used by Hardie during these phases, or to problems measuring the line centers at such times. The photometric history of this system is summarized in the recent work of Markwcrth (1977) . He attempted a Wilson-Devinney solution of his UBV light curves and achieved a satisfactory fit to them. For this analysis, he assumed a value of F = 5.0. However, the theoretical radial velocity curves calculated using the parameter values found by Markworth (1977), and a value of F = 5.0, resulted in too small a Rossiter effect. Consequently, the BV light carves of Markworth were reanalyzed using a value of F S.O and using the parameter values of Markworth as the starting values for the analysis. The result is shown in Figure B-20. Of interest in the new results are the lower value of q found (0.57

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52 versus 0.64), and the higher value of g and lower value of g ? found. However, the distorted nature of the light curves makes the determination of such insensitive parameters such as g and A 1 very uncertain. The intermittent nature of the emission activity and the distortions (sometimes very large) in the light curves indicate that sporadic mass transfer events are taking place in this system. The large amount of data on the nature of the period changes seen in this system are summarized by Rafert (1977). RY Per The 62 spectroscopic observations of Hiltner (1946) were used for this analysis. Wyse (1954) gives the spectral types as B6 and FS. Hiltner gives the spectral type of the primary as B4 V, and states that the He lines are more diffuse than the H lines. The secondary's spectrum is visible on seven plates taken during primary minimum. Hiltner gives the secondary's spectral type as "F5 with giant characteristics." Another study (UCLA Observatory Report, 19 76) gives FO III as the secondary's spectral classification. These estimates correspond well with the derived value of 6600 K. The radial velocity curve is asymmetric, and displays large scatter throughout. An extremely large rotation effect is present, which leads to a final value of F = 10.0. As discussed by Hiltner, the more interesting aspects of the spectroscopic data are: (1) The amplitude of the Rcssiter effect is 2-5 times larger for the He lines as for the H lines (an effect discussed in Chapter II), (2) Both the amplitude and y velocities are different for the radial velocity curves of the two lines, and (5) There is a marked difference between the two radial velocity curves between phases 0.90 to 0.95. These effects can be explained by the modification of the normal

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55 hydrogen line profiles by emission and/or absorption in the gas stream/ ring structure thought to be present. Thus the He velocities are thought tc be more indicative of the true stellar rotation rate. Strangely, no mention is made of the presence of emission lines, although Hiltner does mention the appearance of "satellite" hydrogen lines (such as are seen in 2 Lyrae) , which are thought to be caused by absorption in a thick stream silhouetted against the B4 primary component. There is an indication of polarization (1%) of the light of this system. The fit to the radial velocity data is seen in Figure A-20. Several photographic light curves exist for this system, as well as an excellent visual light curve (e.g. Gaposchkin, 1955, and Wood, 1946). However, Dr. D. Popper (1979) kindly provided his new UBV light curves. The B_V light curves were used for the analysis, as it was suspected that the U light curve was asymmetric in primary eclipse. The fit to the photoelectric data is shown in Figure B-21. There is evidence that the light curve is variable between phases 0.08 and 0.50, as seen in Figure B-21. No period changes are suspected for this system (Wood, 1946), although the data are sparse. RZ Set The spectroscopic data of Neubauer and Struve (1945) and Hansen and McNamara (1959), the latter work being the more extensive, were used in this investigation. The radial velocity curve exhibits a distorted shape, large scatter throughout, a large disturbance present from approximately phase 0.85 to 0.90, and doubling of the hydrogen absorption lines during eclipse. Both redand blue-shifted emission components are present for the hydrogen lines during eclipse. The very large

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54 Rossiter effect present was fit with a value of F equal to 15. This system not only shows the previously discussed effect of the He lines implying higher values of V than the H lines, but there is definite evidence that the higher excitation He lines show a larger rotational disturbance than the lower excitation He lines! Thus there is clear evidence for a substantial stream/disk structure in this system. Another interesting facet of this system is the odd behavior of the hydrogen emission components during eclipse. In contrast to most other systems, the red-shifted emission component is weaker during ingress to eclipse and stronger during egress from eclipse [and vice versa for the blue-shifted component) ! All lines show pronounced asymmetric profiles during eclipse (cf . Hansen and McNamara, Figures 5 and 4) . Although Hansen and McNamara attributed this to modification of the line profiles by emission/absorption arising in the stream/disk structure, the continuous variation and the shape exhibited in the above mentioned figures are what would be expected for a normal rotation effect. However, such emission/ absorption effects are seen at many phases, although at these phases the line profile changes are usually nonsystematic, and the resultant line profiles are very complicated. Hansen and McNamara (1959) give the spectral type of the primary component as B2 II, and AO IIIII for the spectral type of the secondary component. The latter is in excellent agreement with the value of T found in this study. Due to the aforementioned distortions of the radial velocity curve, the value of K. is probably accurate to only ± 20%. Figure A-21 shows the fit to the Rossiter effect for solution one (see below) .

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55 The B_ and V light curves of Wilcken, McNamara, and Hansen (1976) were utilized in this study. Unfortunately, the large distortions present at almost all phases of the light curve rendered the solution results questionable. Two types of solutions were attempted. For solution one, the observed points between phases 0.05 and 0.45 were removed from the solution process. This was done under the assumption that the points in this phase range were high due to added light from a hot spot on either the primary component or at a possible junction of the ring or disk and the gas stream between components. Similarly for solution two, all points between phases 0.70 and 0.95 were removed from the solution process. In this case it was hypothesized that the ingress shoulder of primary eclipse was low due to absorption of light by the stream/disk structure. Tables III and IV display the unexpectedly similar results for both solutions. Because solution two gave a poorer fit to the light curve, solution one was adopted as the preferred solution, although in view of the large distortions present in the light curve, it must be considered tentative. The value of M found was low, but not unreasonably so. The situation is probably even more complicated than this simple dichotomy presented here, i.e., both large scale absorption and added light from a hot spot are probably distorting the light curves! Much more work needs to be carried out for this interesting system. Evidence for ar. increase in the period of this system has been given by Karentnikov (196 7) .

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56 Having summarized the basic information concerning the systems studied, the next chapter presents a detailed discussion of the results obtained in this investigation.

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CHAPTER IV RESULTS AND CONCLUSION'S The purpose of this final chapter is to present the results of this investigation, and discuss these results both generally and with regard to the individual systems. The general discussion is presented first. General Discussion The Hertzsprung-Russell Diagram Figure 4 shows a Hertzsprung-Russell Diagram (hereafter HRD) which displays the positions of the systems investigated in this work, the position of the Zero Age Main Sequence (hereafter ZAMS) , the position of the Terminal Age Main Sequence (hereafter TAMS) , and the areas populated by stars in luminosity classes III and IV. The values of M , the v absolute visual magnitude, for the components of the systems studied were calculated in the following way. The LCP calculates the value of the surface area of each component, using the separation of centers as the unit of length. Since the separation of centers in kilometers is known (Table V), a radius for each component, R* (which represents the radius of a sphere with the same surface area) , can be calculated. This value of R + and the known value of the stellar effective temperature, T q iti are then used in the following equation, which yields a value of log (L^/L^j (where L^ is the stellar luminosity, and L is the solar luminosity) . log(L*/L Q ) = 2 log(R*/R Q ) + 4 log(T e yT 6)Q ) (2) 5;"

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T3 S-i +-> -H , C -3 oOrT3 X =

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59 OCTO 03" I OO'g iiVti CO '9 OS'!!CD'S OS'fl C0"3 OS'i GO'S OS'OI

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60 +-> c c <-* C -H O -H U *J-n a, O -H +.1 In S ri a) (J-lii J a. .-J o o lt, to to cm <7l 00 CM tO OC -rr c> to v£i to to CM to tN CM to CM to \C> to to CM CM so t-» — i in < 5 L~, to LO CTi \o LO to LO CM f> —i o O CM — I CM rH — l tO tO i-H r-J f>"St &> n-t o o o cotOrnr^^r^t^vO' fo ci lo oi i-i rto to ! tH ^H — I O CM i-i — I ,-H [ lo lo to r-o

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61 A value for M was then calculated through the relations v s and, ^ol,* = 4 ' 72 2 5 lo 2( L */ L ) (V M . = M. , „ Bolometric Correction (4) v 3 * bol,* y J The values of the Bolometric Corrections and M. . _ were taken from *bol,0 Harris (1963). The values of L A , R^., and M + are given in Table VI for the primary components, and Table VII for the secondary components. The positions of the indivudal systems in the diagram will be discussed in a later section. Equatorial Velocities The primary aim of this dissertation was the derivation of V e for the 19 systems selected. These values are given in Table V. The major source of error in the derived value of V for systems possessing photoelectric observations lies in the value of K-. used. The error in V^ should be proportional to that in K.. . In the case of U Cep, as previously shown, this may reach a factor of 25% ! However, the low mass found for the primary component of U Cep may indicate that the significant reduction of K 1 found for this system via the "reconstruction" technique of Hardie (1950) may have been too large. In most cases, however, the derived values of V appear to be reliable, since the derived masses for many of the systems are in good agreement with the values expected for the associated spectral types. The above statement is justified because the masses depend on K ", whereas the value of V depends linearly on K, . Thus, any large error in K, will immediately appear as a large deviation in the expected value of the derived masses. It is interesting that the large distortions of the radial velocity curves nresent in some

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62 TABLE VI ABSOLUTE ELEMENTS-PRIMARY COMPONENTS Name

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63 TABLE VII ABSOLUTE ELEMENTS-SECONDARY COMPONENTS Name R 2,*t R J lo §^ R 2,*^ lo g( T e J L 2,*^ L 0^ lo S( L 2 X Tri

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64 systems (e.g. SW Cyg) do not seem to have greatly affected the associated values of K-, as shown by the values of the derived masses. The author estimates that an error of 10% is a realistic upper limit to the errors in V . This value may be 20% for those systems which possess only photographic light curves, due to the uncertain values of q found in these cases. A comparison should be made between the values of V found in e this study, and those values available in the literature found from line profile analysis. Table VIII shows such a comparison for 10 systems for which values of V sin i are available. For W UMi and U Cep the values are comparable for the two methods. For TV Cas , W Del, Y Psc, RZ Set. RZ Cas, U Sge, and TX UMa the values found in the present study are higher than the line profile values by factors of 1.6 to 2.6. Ihe value of V for TX UMa found in this study is uncertain due to the aforementioned difference in the magnitude of the rotation effect during ingress into and egress from eclipse. If a value of F = 3 is used (which would fit the amplitude of the Rossiter effect during egress from primary eclipse), then a value of V = 114 km/sec results--a value in good accord with the value found by Mallama (1978). The result found for RY Per must be viewed with caution, as will be discussed later. Thus it is seen that the results from line profile analysis yield values of V • e equal to or greater than the values given by the rotation effect. This might be explained by hypothesizing that the assumed rotational velocities of the standard stars are systematically underestimated.

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65 TABLE VIII COMPARISON OF V 's FOUND BY ROSSITER EFFECT AND LINE PROFILE .ANALYSIS e V (present V (line profile Name study) (km/sec) analysis) (km/sec) Reference 70 Van den Heuvel (19 70) 280 Van den Heuvel (1970) 75 Van den Heuvel (1970) 30 Van den Heuvel (19 70) 37 Van den Heuvel (1970) 310 Olson (1963) 82 Olson (1968) 240 258 Van den Heuvel (1970) 88 Olson (1968) 125 MaHama (1978) Only the results for solution RZ Set I are presented, as they are probably more accurate than the results for RZ Set 2. TV Cas

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66 Mass Determination Table IX gives the derived values of M , M 7 , and M . These masses were determined from the equations: !4 2 = f(m)/sin°i (1/q + l) 2 (5j and, M 1 = M 2 /q (6) For those systems with photoelectric light curves, the major source of error is in the value of K, used. The value of K., enters i 1 the above mass equations through the mass function: f(m) = 1.0385 x 10"'' P K. 3 (7) It can be seen that the error in K, is given by: A(K 1 ) = 5K 1 " AK 1 (8) Thus, the fractional error is: ACK^/K^ = 3AK 1 /K ] (9) Therefore, a 10% error in K, gives a 50% error in f (m) , and hence in the mass values. So, 50% is adopted as a reasonable upper limit to the error in the masses. There is good agreement in the derived values of M* found for the A2-A5V primary components. These values lie between 1.5 and 2.0, with an average mass of 1.75 for the seven systems with reliable masses. The values of M for the A0-B5 spectral class primaries is in good agreement with the expected values (see Underbill, 1966, pp. 140-145) with the exceptions of U Cep and RY Per. The value of !> for U Cep is lower than expected {2. 21-' vs. l.SM ), but not totally unreasonable. As noted, this is probably due to an overcorrection in the value of K found by Hardie (1950). The value of A/ found for RY Per is extremely

PAGE 75

67 cn en t-~Ot \C O tO LO (N CM r\| CN vO tO tO 0} 00 Oi to lO O o o o y> vc — i o o o o o cOLOoooLo^roomNoc^fOoo OrItI O O -3" ^1 CI tO — r-i — i c o o cs o "N r-» oi lo to r-i Ul rj O N SO O CD O O O © y r 1 * 2s 2 >< >

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68 low for a spectral classification of B5, and is probably due to the inaccurate values of q and K.. characterizing this system. The discordant masses found for RY Gem and RX Hya should be viewed with caution because they are due to values of q found from the analysis of photographic light curves. The high values of AL found for W UMi and WW Cyg, coupled with their positions in the HRD, point to evolutionary effects. All the reliable masses reported here are lower than the values quoted by Allen (1964) . One straightforward explanation for this is inappropriate weighting given to stellar masses predicted by theory, as opposed to observed "dynamical" values. The total masses for these systems are also of interest. Van den Heuvel (1970) has studied the rotation of primary components of 25 Algol systems through line profile analysis. He concludes that (a) for systems with a period < 5 days and primary spectral types of B8 or later, the deviation from synchronous rotation is small for 14 out of 15 systems studied, and (b) primaries of spectral type B8 or earlier rotate, on the average, at twice the synchronous rate regardless of the value of the period. He attempts to explain these results as due to the differences in Case A and Case B mass exchange. For Case B evolution (i.e., the Roche limit is reached after the end of core hydrogen burning, but before helium burning) one expects Algol-type systems to be produced (Kippenhahn et al . , 1967, and Refsdal and Weigert, 1969) for (original) primary masses of2.8M-.or less, and total system masses of 4.5AL or less. On the other hand, Algol systems can be produced through Case A evolution (i.e., the Roche limit is reached during core hydrogen burning)

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69 for almost any initial mass for the (original) primary component. This, plus other statistical evidence given by Van den Heuvel (1970), indicates that the Algol systems with B8 or later primary components are probably the result of Case B evolution, whereas the systems with primary components of spectral class B8 or earlier are the result of Case A evolution. (For another facet of this apparent dichotomy of systems, see Devinney, 1973.) Van den Heuvel thus explains the two conclusions given above as follows: For Case B evolution, the rapid phase of mass transfer is short lived, the amount of mass transferred is relatively small as compared to Case A, and there is no long lasting stage of slow mass transfer during which large amounts of mass and angular momentum are transferred to the "new" primary component. Thus, synchronization through tidal braking can start immediately after the phase of rapid mass transfer. For Case A evolution, not only is there relatively more mass and angular momentum transferred during the rapid phase of mass transfer, but there also exists a long phase of slow mass transfer during which significant amounts of mass and angular momentum are constantly transferred to the "new" primary component, thus keeping it in a prolonged state of asynchronous rotation. Thus, following Van den Heuvel's scenario one would expect to have a much higher probability of finding a Case A system in an asynchronous state of rotation as compared to the Case B systems . On the other hand, it should be pointed out that (a) for Case B mass exchange, helium ignition in the "original" primary component will cause this component to "break" contact and shrink within its limiting Roche surface, and (b) for either Case A or B mass exchange, the slow

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70 phase of mass transfer may not lead to the same "spinning up" of the primary component. That is, the slow phase of mass exchange may be slow enough so that, for shorter period systems, tidal braking can continually resynchronize the rotation of the primary component (once the initial asynchronism has been dealt with) . With all these points in mind, the results of this investigation are examined below. The data presented in this study are consistent with the scenario given by Van den Heuvel, with a few exceptions. An examination of Table IX shows that for systems with M <3.5M , and a period less than 5 days, the values of F range between 1 and 2 (except for the case of SW Cyg, which has a period of 4.57 days). For systems with a primary spectral type of B9 or earlier, M is usually greater than 3.5A' , and 1.5 <_ F <_ 10.0. WW Cyg and W UMi probably have rotation ratios affected by evolution off the main sequence. It is probable that AQ Peg, RY Gem, SW Cyg, and Y Psc are Case B systems "caught" at or just past the rapid phase of mass transfer. Thus we find them with low M , a spectral tvr>e tot r r of the primary component later than B9, but a high value of F, and a ring-stream structure present. Extra Light at Second and Third Contact As mentioned in Chapter III, the idea has been suggested (Walter, 1973a) that for several systems extra light is present near second and third contact. The source of this extra light has been identified with either a hot spot on the primary component (Walter, 1973a), or a "protuberance" on the trailing side of the primary component (Hall and Garrison, 1972). As an example, consider Walter's analysis of Y Psc. His Figure 5 clearly shows extra light present at both second and third contact, the amplitude of the effect being approximately equal to 0TYj2.

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71 This should be compared to Figure C-l, which displays the analogous plot for the present solution of Y Psc. One immediately sees that the current analysis does not show the effect given by Walter's analysis. The other figures in Appendix C display minus C residual plots for 6 other systems for which extra light has been hypothesized. Considering the scatter of points, there is no definite evidence of extra light at second and third contact for W Del, WW Cyg, AQ Peg, and SW Cyg. The large scatter and complicated behavior of the residuals seen in the minus C plot for U Cep (Figure C-6) is probably related to the disturbed nature of the light curve present during this particular epoch of observation (see Markworth, 1977). Figure C-7, which displays the results for U Sge, shows definite evidence of absorption of light near first and fourth contact. The cause of the discrepancies between the results presented here, and those of previous authors is probably related to the inadequate description of the stellar figures by models not taking into account asynchronous rotation. Detailed Discussion Discussion of Individual Systems X-Tri .--The position of this system in the HRD shows the primary component to be on the ZAMS, and the secondary component to be approxim mately 1.2 below the region of luminosity class IV objects. The detached nature of the final solution, the low values of F and A ? found, and the fact that the period change data is indicative of a light time effect rather than a mass transfer effect all point to a pre-main sequence evolutionary state for this system.

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72 Y Leo .--Y Leo is very similar to X Tri and RZ Cas in that the primary is very close to the ZAMS, and the secondary is approximately 1.5 below the luminosity class IV region. The evidence for erratic period changes and the derived value of F = 1.5 indicate a system in the phase of slow mass transfer. RZ Cas . --The primary component of RZ Cas lies a little below the ZAMS, and the secondary component lies about 1.4 below the luminosity class IV region. The value of F = 1.6 and the period change information indicate a system akin to Y Leo, i.e., in the phase of slow mass transfer. ST Per .--ST Per is similar to the last three systems described. An interesting point here is that even with a small value of F, the Rossiter effect was still very evident. Since the synchronous velocity is also low (37 km/sec) , it is evident that the present method of analysis should yield a much more accurate value of V than normal e spectroscopy carried out at 40 or 50 A/mm (i.e., an error of 40 to 50 km/ sec !) . RX Hya .--The position of this system in the HRD would seem to imply a system with its primary component evolved from the main sequence. However, the derived value of M. is much too high. This is probably due to the fact that a photographic light curve was used for the photometric analysis. A change in q from 0.17 to 0,22 would give a. mass in the expected range. The value of F, period change data, and spectral type of the primary hint that a more accurate value for q would lead to a solution similar to that for Y Leo and similar systems. W UMi . --This system shows evidence of being in an evolved state. The mass of the primary component and the position of the primary component in the HRD support the picture of a primary which has evolved

PAGE 81

73 away from the main sequence after the end of the phase of slow mass transfer. The lower than synchronous value of F would then be explained through the normal expansion of the primary during this evolutionary phase, and normal tidal braking (see also Devinney and Sutton, 1979). WW Cyg .--The primary component of this system is characterized by a large mass and a low value of F. The secondary component lies in the region populated by luminosity class III objects. The position of the primary component in the HRD implies that it has evolved from the main sequence. In view of the scenario for Case A evolution discussed earlier, it may seem strange that the value of F is only 1.55. This value of F probably indicates both the effect of tidal braking and the effect of the expansion of the primary during its evolution off the main sequence. RW Gem . --The position of the components of this system in the HRD reveal a primary near the ZAMS and a secondary found in the luminosity class III area of the HRD. The mass of the primary component is normal for its spectral type. Thus, this is a normal Algol system in the slow phase of mass transfer. TX UMa . --The placement of this system in the HRD is in accord with the picture of a typical Algol system in the slow phase of mass transfer. Similar to RW Gem, TX UMa has a primary on the ZAMS, and a secondary in the luminosity class III area. The mass agrees with its spectral type. More spectroscopic work is required in order to see if the asymmetry in the amplitude of the Rossiter effect is real, and if not, what the actual amplitude is.

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74 TV Cas . --While similar to TX UMa in its placement in the HRD, the mass found for the primary component of this system seems high for a spectral type of B9. In view of the sparse spectroscopic data, and the photographic light curve used, this value for AL should be viewed as tentative. AQ Peg . --The position of this system in the HRD indicates a normal main sequence primary component and a secondary component which lies in the area populated by luminosity class IV objects. The derived mass of the primary is normal for its spectral class. Along with SW Cyg, W Del, RY Gem, RY Per, Y Psc, and RZ Set, this system represents those Algoltype binaries possessing a gas stream and a ring structure around the primary component. A determination of the radius of the ring around the primary can be made by utilizing the published descriptions of the behavior of the emission features during primary eclipse. Using the parameters determined in this study, Figure D-l (see Appendix D) was constructed. This shows the system geometry at those phases for which emission lines were observed. By correlating the presence (or absence) of red or blue emission features with the position of binary components for several different phases, one can deduce the distance from the primary component at which the greater part of the emission is arising. This distance can then be identified with the radius of the ring around the primary component. In this case, a ring radius of 4 to 4.5 R_ is consistent with the emission line behavior. As a consistency check, one can assume Keplerian motion for the particles in the ring. Thus, the absolute mass of the primary component can be calculated via the equation:

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75 M. = v 2 R . /G (10) * ring where M^ is the mass of the primary, v is the velocity of the ring particles, R . is the ring radius, and G is the universal gravitation r ring to ° constant. In this case, the mass derived using equation 10 is in perfect accord with that obtained by the method outlined earlier in this chapter (a ring radius of 4.5R~ gives perfect agreement). SW Cyg . --This system is almost identical to AQ Peg as the HRD plot shows. Once again, the description of the emission lines given by Struve (1946b) allows one to deduce, using Figure D-2, the radius of the ring around the primary component. In this case, a value near 3.5R„ is indicated. This would predict a velocity for the particles in the ring of 320 km/sec. Unfortunately, velocity measurements for the emission lines were not published, thus confirmation of this ring radius must await further work. Y Psc .--This system falls in the same area of the HRD as the last two systems. No values of V .sin i are available for this system, emission and only a few plates show the emission activity. This system is particularly difficult for an analysis of the emission features, due to the grazing configuration of eclipse, as shown in Figure D-3. Nevertheless, a value of R . = 3 to 3,2Rseems to fit the available data, ring W Del . --The location of this system in the HRD is typical for an Algol system with a main sequence primary component and a luminosity class III-IV secondary component. The mass of the primary component is in accord with its spectral type. As with the previous three systems, the emission line data were analyzed in order to deduce a value of R . . Figure D-4 shows the system geometry at phases of interest. A

PAGE 84

76 emission / emission value of R r = 4 0R q is indicated, implying a value of V 540 km/sec. Once again, however, no published values for V were given by Struve (1946b) . RY Gem . --The HRD plot for this system shows a primary component approximately 1.3 above the main sequence. However, the value of M found for this system is much too high, and is probably affected by the value of q found from the photographic light curve. In this case, a better value of M^ is found by using the description of the emission line behavior to determine a value of R . , the value of V ring emission 200 km/sec given by iMcKellar (1949), and using equation 10 to determine a value of My Doing so yields a value of M = 1.7// in excellent agreement with the results for the other A2-A5V primary components studied. The apparent overluminosity of the primary is also uncertain due to the photographic light curve solution. It is probable that a reasonable value of q would lead to a small value of R^, and hence a lower value of M v . More accurate results must thus await a photoelectric light curve. In addition, the value of Kj is very uncertain, witness the large distortions present in the radial velocity curve. A change of K from 28 km/sec to 21 km/sec would also bring the mass down to a reasonable value, although the radius of the primary component would still be in doubt. U Sge . --The primary component of this system fits approximately 1.0 above the main sequence, while the secondary component lies in the luminosity class III area. The derived mass for the primary component is in good agreement with its spectral type. McNamara (1951a) has measured the value of V . . -sin i on two plates, and finds

PAGE 85

77 V emission' sin i = 280 km / sec Figure D-6 shows the eclipse geometry. Unfortunately, the red-shifted emission component was not observed. Thus, all that can be said is that a value of R . = 6.0R„ ffound from ring v the above value of v emission sin i and the previously derived value of M 1 is compatible with the behavior of the blue-shifted emission component. The sporadic nature of the emission and the position of the primary component in the HRD argue that this system is in an evolved state--probably near the end of the slow phase of mass transfer for Case A evolution. Hence the high value found for F. U Cep . --The primary component of this system lies very near the ZAMS, while the secondary is situated in the subgiant region of the HRD. Possible reasons for the low value of M have already been discussed. The high value of V found for this system might lead one to consider whether or not this star is filling or almost filling its limiting rotational lobe (see Chapter I). If so, it would mean that the primary component could not accept any further mass or angular momentum from the secondary component until tidal braking has transferred rotational angular momentum back into orbital angular momentum. In this case, the matter which could not be accepted by the primary would be forced to orbit around the primary, thus leading to a temporary ring structure. This could then be cited as the cause of the sporadic emission and light curve anomalies seen in this system (Markworth, 1977; Batten, 1974). The possibility of this type of double-contact binary (i.e., the secondary filling its normal, synchronous Roche lobe, and the primary filling its critical rotational lobe) has been discussed by Wilson and Twigg (1979). Table V presents both the percentage of the

PAGE 86

78 limiting rotational lobe filled by the primary component, and the percentage of the Roche lobe filled by the primary component. One sees from Table V that only U Cep and RZ Set are strong candidates for being doublecontact systems. However, one notes several systems that fill 40-70% of their limiting rotational lobes. Considering that, as stated in Chapter II the estimates for F given here are probably lower limits, it is possible that further study will reveal more candidate double-contact systems . RY Per . --The primary component of this system lies on the ZAMS, and the secondary is within the luminosity class III area of the HRD. The low mass is probably due to the q found from the light curve solution. This is due to the large variability of the light curve between phases 0.15 and 0.45 (very similar to RZ Set). In addition, the value of K. is very much in doubt. The value of f(m) calculated from K 1 given by the He lines is twice that of the value given by the H lines. Much more detailed spectroscopic work must be done on this system before a reliable set of absolute elements can be deduced. RZ Set . --As described earlier, the light curve solution, and hence the absolute elements are very uncertain. However, solution one (see Chapter III) does give a consistent picture of a 7 to 14/-L. primary located near the ZAMS, and a secondary component in the normal position for an AO I I I I I star. Judging from the totally asymmetric light curve and the distortions present in the radial velocity curve, this system is probably in the last states of rapid mass transfer (e.g., V356 Sgr, Wilson and Caldwell, 1978) . The odd behavior of the emission components of the H lines during eclipse indicates a retrograde ring around the

PAGE 87

79 primary component. It appears that the particles leaving the vicinity of L^, the inner Lagrangian point, possess an initial velocity toward the leading side of the primary component, the velocity being large enough to lend to the formation of the retrograde ring. This picture is consistent with the presence of "extra" light, presumably due to a hot spot where the stream intersects the ring structure, at phases just after primary eclipse. Suggestions for Further Work The method outlined in this work can yield accurate values of both V e and the absolute elements of Algol-type binaries. As stated, the fit to the amplitude of the Rossiter effect leads to values of V that are e equal to or greater than the values found by line profile analysis techniques. Whether the line profile method is underestimating V o^ 6 e the rotation effect method is overestimating V can only be answered by more work in this field. However, the consistent results for the masses, especially for the A2-A3 starts, indicates (1) that the distortions preseni in the radial velocity curves may not affect the value of K 1 as severely as previously thought, and (2) that the values of q derived from the photometric analyses are reliable. As shown by ST Per, the amplitude of the Rossiter effect can be moderately large even for low values of F. For this reason it appears that this method will find its greatest use in determining V for such cases as ST Per (i.e., systems with low equatorial rotational velocities and small departures from synchronous rotation) , since the line profile method may give errors as large as the amplitude of the radial velocity curve for these cases (see the discussion of ST Per fcr such a easel .

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80 With the modification of the LCP for asynchronous rotation, and its ability to generate theoretical line profiles, an even more accurate method for determining V is available. Instead of fitting a gross property of the radial velocity curve (such as the amplitude of the rotation effect), and thus finding a single, best fitting value for F, one could in principle generate theoretical line profiles at each phase for which a spectroscopic observation is available. Then, one could obtain densitometry tracings of the desired spectral lines, and match the theoretical and observed profiles for each phase point. In this way, several determinations of F are obtained, which can then be suitably averaged for a final value. Therefore, (1) several independent determinations of F can be made, (2) only those lines which one assumes arise in the primary component are used, and (3) the effects of gas stream/disk emission/absorption would be more obvious, and thus, hopefully, avoidable. Thus, a line fitting technique is used, but the underlying geometric cause of the asymmetric profile is retained. In summary, this work has shown that an accurate value of V q fat worst a lower bound) can be determined via a careful analysis of the Rossiter effect in eclipsing binary systems of the Algol-type. This investigation was somewhat limited in its scope by the availability of computer time. Thus, not all light curves were analysed to their full potential. However, it is hoped that the solutions and results contained herein will be of some use as a guide to further, more refined analysis (in particular, the line profile matching method outlined above.)

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APPENDICES

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APPENDIX A Appendix A contains figures showing the theoretical fits to the observed Rossiter effect for the systems studied. For each figure, the abscissa is orbital phase, and the ordinate is dimensionless velocity, V . Figure A18 shows only the "uncorrected" radial velocity observations of U Cep, for comparison with Figure A19 which shows the "corrected" (Hardie, 1950) radial velocity observations and the theoretical fit to the Rossiter effect for U Cep. s:

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APPENDIX B Appendix B shows the theoretical fits to the observed light curves for the systems investigated in this study. In each figure the abscissa is orbital phase, and the ordinate is light level (normalized so that the light level is approximately one at phase 0.25). 127

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APPENDIX C Appendix C contains the O-C residual plots near primary minimum for seven systems of interest. For each plot, the abscissa is orbital phase, and the ordinate is 0-C (light level). The outer pair of arrows indicates the phases of first and fourth contact, and the inner pair of arrows indicates the phases of second and third contact. The error bar on the right hand side of the figure indicates the range (plus and minus) of the average value of a weighted residual, as determined by the light curve solutions. 174

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APPENDIX D Appendix D contains the figures used for determining the radii of the gas rings which may be present around the primary components of six of the systems studied. Each diagram displays the system geometry for several phase values which are labeled in increasing phase order. A description of the emission activity at each of these phases is provided in the figure captions. 189

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Figure D-l. Ring radius plot for AQ Peg. i. 9 = 0.983 = Strong red-shifted emission component visible for many spectral lines. 2. 9 = 0.997 =----Weak redand blue-shifted emission components visible for many lines; the red-shifted components being stronger. 5. 9 = 0.012 = Blue-shifted emission components very strong, no red-shifted component visible.

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Figure D-2. Ring radius plot for SW Cyg. 1. 9 = 0.977 = Spectra of both stellar components visible. 2. Q = 0.985 = Weak red-shifted emission component of H 3 present . 5. 9 = 0.985 = Strong red-shifted emission components visible for H 3 and H v. 4. 9 = 0.991 = Red-shifted emission component slightly weaker than at (3) . 5. 9 = 0.994 = Same as (4). 6. 9 = 0.012 = Red-shifted emission components not present. Strong blue-shifted emission components seen for H 3 and H y. 7. 9 = 0.018 = Blue-shifted emission components for H 3 and H y are now very weak. 8. 9 = 0.222 = No emission components seen, stellar spectra predominate .

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Figure D-3. Ring radius plot for Y Psc. 1. 6 0.990 = Spectra of both stellar components visible. 2. 9 = 0.997 = No emission lines visible, spectrum of secondary component visible. 5. 6 = 0.005 = _ _ Possible weak violet-shifted emission component at H 3 . 4. S = 0.015 Spectra of both stellar components visible.

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Figure D-4. Ring radius plot for W Del. 1. 9 = 0.985 = H 3 shows a weak red-shifted emission component . 2 . 9 = . 994 = _ Same as [1) . 3. = 0.004 = Very weak blue-shifted emission component visible for H g.

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Figure D-5. Ring radius plot for RY Gem. 1. 9 = 0.001 = Strong redand blue-shifted emission components visible for K B and K y. 2. 6 = 0.005 = Only blue-shifted emission component visible for H £ and H y.

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Figure D-6. Ring radius plot for U Sge. = 0.005 = Very strong blue-shifted emission component visible for K 3. = 0.013 = _ Very strong blueshifted emission component visible for H 3 . = 0.022 = _ _ Spectra of both stellar components seen, no emission present.

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BIBLIOGRAPHY Abt, H. A. 1979. Private communication. Allen, C. W. 1964. Astrophysical Quantities (London: William Clowes and Sons, LTD), p. 203. Arp, K. C. 1961. Ap. J. 133 , 869. Batten, A. H. 1974. Pub. D.A.O. 14 (10). Bozkurt, S. , Ibanoglu, 0., GUlmen, 0., and Gudttr, N. 1976. Astron. and Astrophys. Suppl. 2_3, 439. Cester, B. and Pucillo, M. 1972. Mem. Soc. Astr. Ital. 43, 501. Chambliss, C. R. 1976. P.A.S.P. 88_, 22. Crawford, J. A. 1955. Ap . J. 121 , 71. Devinney, E. J., Jr. 1975. P.A.S.P. 85_, 550. Devinney, E. J., Jr. 1979. Private communication. Devinney, E. J., Jr., Hall, D. S., and Ward, D. H. 1970. P.A.S.P. 82_, 10 . Devinney, E. J., Jr. and Sutton, C. S. 1979. Paper in preparation. Field, J. V. 1969. M.N.R.A.S. 144 , 419. Gaposchkin, S. 1946. Ap. J. 104 , 583. Gaposchkin, S. 1953. Harvard Annals 115 , 69. Grenwing, M. and Herczeg, T. 1966. Is . fur Astrophys. 6_4, 256. Hall, D. S. 1979. Acta Astron. 29, 259. Hall, D. S. and Garrison, L. M. , Jr. 1972. P.A.S.P. 84, 552. Hall, D. S. and Wawrukiewicz . 1972. P.A.S.P. 84, 541. Hansen, K. and McNamara, D. H. 1959. Ap . J. 150 , 789. Hardie, R. H. 1950. Ap. J. 112 , 542. Harris, D. L., III. 1965. In: Basic Astronomical Data , ed. K. Aa. Strand (Chicago: Univ. of Chicago Press), p. 265. 202

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203 Hill, G., Hilditch, R. W. , Younger, F., and Fisher, W. A. 1975. Mem. R.A.S. 79_, 142. Hill, G. and Hutchings, J. 3. 1973. Astrophys. and Space Sciences, 20_, 123. Hiltner, W. A. 1945. Ap . J. 101 , 108. Hiltner, W. A. 1946. Ap. J. 104 , 396. Horak, H. G. 1952. Ap. J. 115 , 61. Buffer, C. M. and Eggen, 0. J. 1947. Ap. J. 105 , 217. Johnson, H. L. 1960. Ap. J. 131 , 127. Jordan, F. C. 1914. Publ. Allegheny Obs. 3_, 157. Karentnikov, V. G. 1967. Astr. Zu. 44, 22. Kippenhahn. R. and Weigert, A. 1967, 2s. fur Astrophys. 6_5, 251. Kippenhahn, R. , Kohl, K. and Weigert, A. 1967. Zs . fur Astrophys. 66_, 58. Koch, R. H. 1961. Astron. J. 66, 250. Koch, R. H., Olson, E. C, and Yoss, K. M. 1965. Ap . J. 141 , 955. Lee, Y. S. and Lee, Y. 6. 1977. Publ. Korean Nat. Astron. Obs. 2, 27. Levato, 0. H. 1975. Astron. and Astrophys. Suppl. 19_, 91. Lucy, L. B. and Sweeney, M. A. 1971. Astron. J. 76, 544. Mailama, A. D. 197S. Acta Astron. 28., 51. Markworth, N. L. 1977. Dissertation, University of Florida. McKellar, A. 1949, Pub. D.A.O. 8, 244. McLaughlin, D. 1924. Ap. J. 60, 22. McNamara, 0. H. 1951a. P.A.S.P. 65_, 38. McNamara, D. H. 1951b. Ap . J. 114 , 515. McNamara, D. H. and Feltz, K. A., Jr. 1976, P.A.S.P. 88, 688. Nariai, K. 1971. Publ. Astr. Soc. Japan 2_3, 529. Neubauer, D. H. and Struve, 0. 1945. Ap. J. 101 , 240. Olson, E. C. 196S. P.A.S.P. 80, 183.

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204 Parise, R. A. 1979. Dissertation, University of Florida. Plavec, M. 1960. Bull. Astr. Inst. Czech. li_, 148. Popper, D. 1979. Private communication. Rafert, J. B. 1977. Dissertation, University of Florida. Refsdal, S. and Weigert, A. 1969. Astron. and Astrophys. 1, 167. Rossiter, R. A. 1924. Ap. J. 60_, 15. Sahade, J. 1945. Ap . J. 102 , 470. Sahade, J. and Struve, 0. 1945. Ap. J. 102 , 480. Schlesinger, F. C. 1910. Publ. Allegheny Obs. 3, 173. Struve, 0. 1945. Ap . J. 102 , 74. Struve, 0. 1946a. Ap. J. 105 , 76. Struve, 0. 1946b. Ap. J. 104, 253. Struve, 0. 1949. M.N.R.A.S. 109 , 492. Struve, 0. and Elvey, C. T. 1951. M.N.R.A.S. 91, 665. Swensen, P. R. and McNamara, D. H. 1968. P.A.S.P. 80_, 192. Tomkin, J. 1979. Ap. J. 251 , 495. Tremko, J. and Vetesnik, M. 1974. Bull. Astr. Inst. Czech. 2S_, 331. UCLA Observatory Report. 1976. B.A.A.S. 8_, 57. Underbill, A. B. 1966. The Early Type Stars (Dordrecht, Holland: D. Reidel Publ. Co.), p. 140. Van den Heuvel, E. P. J. 1970. In: Stellar Rotation , ed. A. Slettebak (Dordrecht, Holland: D. Reidel Publ. Co.), p. 178. Walter, K. 1971. Astron. and Astrophys. 13, 249. Walter, K. 1975a. Astrophys. and Space Sciences 21_, 289. Walter, K. 1975b. Astrophys. and Space Sciences 24, 189. Walter, K. 1979. Astron. and Astrophys. Suppl. 3^7, 493. Weiss, E. W. and Chen, K. Y. 1976. Acta Astron. 26, 15.

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:os Wendell, 0. C. 1909. Harvard Annals 69, 1. Wilcken, S. K. , McNamara, D. H., and Hansen, H. K. 1976. P.A.S.P. 88, 262. Wilson, R. E. 1974. Ap. J. 189 , 319. Wilson, R. E. 1979. Paper submitted for publication (Ap. J.). Wilson, R. E. and Biermann, P. 1976. Astron. and Astrophys. 48_, 349. Wilson, R. E. and Caldwell, C. N. 1978. Ap. J. 22_, 917. Wilson, R. E. and Devinney, E. J., Jr. 1971. Ap. J. 1_66, 605. Wilson, R. E. and Devinney, E. J., Jr. 1973. Ap . J. 182 , 539. Wilson, R. E. and Stothers, R. 1974. M.N.R.A.S. 170 , 497. Wilson, R. E. and Twigg, L. W. 1979. Proceedings of the Toronto Meeting of Commission 42, In press. Wood, F. B. 1946. Princeton Contr., No. 21. Wyse, A. B. 1954. Lick Obs. Bull. 17, 57.

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BIOGRAPHICAL SKETCH Laurence William Twigg was born May 24, 1951, in Brockton, Massachusetts. When he was 6 years old, his family moved to Gainesville, Florida. In 1965, the family moved to Dade City for one year, and thence to Temple Terrace, where his parents still reside. In 1969, he graduated with honors from King High School, and subsequently entered the University of South Florida. In 1975, he received three BA's (with honors) in astronomy, physics, and mathematics. He started his graduate work at the University of South Florida in the fall of 1973, and completed the requirements for his MA in astronomy in April of 1976. His thesis title was; "An Investigation of the Wilson-Devinney Differential Corrections Computer Program and Applications to Five W Ursae Majoris Binary Systems." Following a research trip to Mt . John Observatory, New Zealand, in the summer of 1974, he transferred to the University of Florida, where he completed his graduate work. During the summer before graduation, he was a research assistant studying eclipsing binary systems on an NSF grant. Upon the expected granting of his Ph.D. in December of 1979, he expects to assume a postdoctoral research position at the University of Calgary, Alberta, Canada. Currently, he has eight papers published or submitted for publication. The topics covered in these publications include the analysis of W UMa eclipsing binary systems and discussions of anomalous values of certain astrophysical parameters found from analysis of several types of eclipsing binary swstems. 206

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207 He is currently a member of the American Astronomical Society, Phi Kappa Phi Honor Society, and Sigma Xi, the Scientific Research Society. Laurence's father, John, is an engineering professor at the University of South Florida, and his mother, Armandine, is a past president of the Florida Hospital Auxiliary. He has one older brother, John, Jr., who is head engineer at KCBS in San Francisco, a younger brother, Jerry, who is a LTJG in the United States Navy, and a younger sister, Janine, who is a research chemist.

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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. Robert E. Wilson, Chairman Professor of Astronomy I certify that 1 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. jo '-/>*C Frank B. Wood, Co-Chairman Professor of Astronomy I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Edward J. Devi-nney Associate Professor of Astronomy I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. r\ r\ \\ f \ \ i -r John; P . Olivel As^sc/ciate 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. // / 7% / / t/ Hu gh ^/. Campbell ~/KZZ / Associate Professor of Nuclear Engineering Sciences

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This dissertation was submitted to the Graduate Faculty of the Department of Astronomy in the College of Liberal Arts and Sciences and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree Doctor of Philosophy. December 1979 Dean, Graduate School

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UNIVERSITY OF FLORIDA 3 1262 08553 1472