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\IBVShead{4362}{5 August 1996}

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\ft{ECCENTRIC ECLIPSING BINARY STARS AS TEST}
\ft{OF GENERAL RELATIVITY: THE CASE OF V541~CYGNI}
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\begintext

V541~Cyg (BD+30\degr 3704; $V_{max} = +10.35$; B$-$V = +0.035) is a detached 
eclipsing binary consisting of a pair of B9.5\,V stars having an eccentric
orbit (e = 0.474) and an orbital period of $P_{orb} = 15.34$ days.  
Khaliullin (1983; 1985) was the first to show that this binary could be 
an important test case for General Relativity (GR) because the apsidal 
motion expected from GR is significantly larger than the classical apsidal 
motion arising from the tidal and rotational distortions of the component 
stars.  He found that the rate of apsidal motion expected from GR is 
$\dot{\omega}_{GR} = 0\fdg 82/100$yr, while the contribution to apsidal motion 
from classical effects is $\dot{\omega}_{cl} = 0\fdg 15/100$yr.  
Moreover, the relativistic apsidal motion expected for V541~Cyg is 
large --- about 70 times greater than the corresponding relativistic 
apsidal motion of Mercury-Sun of $\dot{\omega}_{GR} = 43''/100$yr.

From the data available at that time, Khaliullin (1985) found good 
agreement between the observed apsidal motion rate of V541~Cyg of 
$\dot{\omega}_{obs} = 0\fdg 90/100$yr $\pm 0\fdg 15/100$yr and the 
theoretical combined relativistic and classical apsidal motion of
$\dot{\omega}_{GR+cl} = 0\fdg 97/100$yr.  However, this determination of 
apsidal motion was based on only two epochs:  very accurate eclipse timings 
from his photoelectric photometry made in 1981--83 and less accurate 
photographic minima determinations of Karpowicz (1961), made during 1955--59.  
Since 1985, several accurate times of primary and secondary 
minima have been determined from photoelectric or CCD photometry.  
Recently Wolf (1995) re-determined the apsidal motion using Khaliullin's 
data as well as more recent eclipse timings and derived a more refined 
apsidal motion rate of 
$\dot{\omega}_{obs} = 0\fdg 53/100$yr $\pm 0\fdg 11/100$yr.  
However, this revised apsidal motion rate is significantly smaller than 
expected from theory.  Using updated values for the internal structure 
constant (see Claret and Gimenez 1992), theory predicts relativistic 
effects of 
$\dot{\omega}_{GR} = 0\fdg 77/100$yr $\pm 0\fdg 05/100$yr 
and classical effects of 
$\dot{\omega}_{cl} = 0\fdg 10/100$yr $\pm 0\fdg 02/100$yr, 
resulting in a combined apsidal motion rate of 
$\dot{\omega}_{GR+cl} = 0\fdg 87/100$yr $\pm 0\fdg 07/100$yr.
This result is particularly interesting because in V541~Cyg most of the 
apsidal motion is expected to arise from GR.

Starting in the Spring of 1995, UBVR photoelectric photometry of V541~Cyg
has been conducted on the Villanova-Fairborn 0.8m Automatic Photoelectric
Telescope (APT), at Mt. Hopkins, Arizona.  During 1995, differential 
photometry of the star was obtained on 63 photometric nights.  Nearly 
complete light curves have been obtained and new eclipse timings have 
been made from these data.  The photoelectric observations were carried 
out using the usual observing sequence of 
sky-comparison-check-variable-comparison-sky and an integration time of 
10 seconds.  Because of the relative faintness of V541~Cyg, blind-offsets 
from the position of the comparison star were used to acquire the star.  
Initially HD\,332470 (SAO\,68749; $m_v = +8.4$; K3~III) was used as the 
primary comparison star and HD\,331210 (SAO\,68756; $m_v = +9.6$; G8~III) 
served as the check star.  However, after a few months into the observing 
program, HD\,332170 began to show evidence of small systematic changes 
in brightness especially in the U and B bandpasses.
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Figure 1.  A plot of the the V-band light curve showing the secondary minimum 
in an expanded phase scale
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Figure 2.  A scale model of the system, showing the orientation of the orbit 
and the stars drawn to approximate scale
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Figure 3.  A plot of the apsidal motion rate determination showing the change 
in the displacement of the secondary eclipse (D = $(t_{1} + t_{2} - 0.5P)$) 
with time
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\noindent  Fortunately, frequent 
observations of the check star were made which enabled us to use 
HD\,331210 as the primary comparison star for the entire 1995 data set.  
The observations were reduced in the usual way in which times were 
converted to Heliocentric Julian Day Numbers and the magnitudes were 
corrected for differential atmospheric extinction.  Because of angular 
proximity of the variable, comparison, and check stars, the differential 
extinction corrections were very small.  Nightly means were formed from 
the observations outside of the eclipses; typically 3--5 observations 
comprise each normal point per filter.  The observations inside the 
eclipses were not averaged.


Figure 1 shows the V-band light curve in which the phases were computed 
from the light elements of Khaliullin (1985); the secondary minimum in an 
expanded phase scale is also shown in the figure.  The eclipses are deep 
and very narrow; secondary minimum is well defined and occurs near 0.4575 
phase, but primary minimum is poorly covered and needs further observations 
before it is satisfactorily defined.  As shown by Khaliullin's photometry, 
the primary minimum is much broader than the secondary minimum because of 
the orientation of the orbit ($\omega = 263\degr$), in which periastron and 
apastron occur near to the times of the secondary and primary eclipses, 
respectively.  A scale model of the system, showing the orientation of 
the orbit and the stars drawn to approximate scale is shown in Figure 2.

A very accurate determination of the time of secondary minimum was made 
from UBVR photometry, obtained near the lower portions of the minimum on 
the night of 7 July 1995 UT.  The time of mid-eclipse was found from least 
squares fits of the data and by the bisecting cord method.  Independent 
determinations of mid-eclipse were made from the different bandpasses.  No 
systematic differences were found so that a mean timing was calculated 
from the four data sets:
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\centerline{T (Min II) = HJD\,2449904.7145 $\pm$ 0\fd 00012}

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A new determination of apsidal motion was made using this timing along
with timings given by Khaliullin (1985) and Wolf (1995).  In addition to 
these, the photoelectric and CCD eclipse timings obtained by Lacy and Fox 
(1992) and Diethelm (1995) were also included.  The photographic timings 
of Karpowicz (1961) were also included, but assigned lower weights than the 
photoelectric or CCD observations.  The analysis of the timings yielded an 
apsidal motion rate of 
$\dot{\omega}_{obs} = 0\fdg 52/100$yr $\pm 0\fdg 14/100$yr.  
This apsidal motion rate is very nearly the same as found by Wolf (1995), 
which was based on fewer observations.  A plot of the apsidal motion rate 
determination is shown in Figure 3 in\break
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\centerline{4}

\noindent which the change in the displacement 
of the secondary eclipse with time is shown.  The older photographic timing 
estimates were not used in the least squares determination of the apsidal 
motion, but the apsidal motion found from the modern data fits the older 
data quite well.  More interestingly, this study confirms that V541~Cyg 
has an observed rate of apsidal motion that is significantly less than the 
theoretically expected apsidal motion.
This smaller than expected apsidal 
motion found for V541~Cyg is difficult to explain and the discrepancy is in 
the same sense as found for two other eclipsing binaries, DI~Her and AS~Cam, 
in which the relativistic contributions to apsidal motion are also 
significant (see Guinan and Maloney 1985; Maloney {\em et al.} 1991; 
Guinan {\em et al.} 1994).

Spectroscopic observations of V541~Cyg have been obtained several years ago 
(by EFG) which indicate approximate stellar masses for the system of about 
$M_1 = M_2 = 2.4 \pm 0.2 M_{\odot}$ and projected rotational velocities of 
the components of $v_1~sin(i) = v_2~sin(i) = 20 \pm 5$ km/s.  Ultraviolet 
spectrophotometry (1150 -- 3200\AA) has also been obtained with the IUE 
satellite and the preliminary analysis of this data indicates a mean 
temperature for the two stars of about $T_1 = T_2 = 9900 \pm 400$K. These 
temperatures correspond to spectral types of about B9.5~V -- A0~V.  These 
spectral types and temperatures are in good agreement with the B$-$V and U$-$B 
indices measured recently by Lacy (1992), after the color indices are 
corrected for interstellar reddening.
 
We plan to continue photometry of the star with the APT during 1996 to 
complete the UBVR light curves, in particular, to cover fully the primary 
eclipse.  Also, we are aware that spectroscopic radial velocity 
observations of V541~Cyg are currently being conducted at San Diego State 
University by Paul Etzel (priv. commun.).  Once the light and radial 
velocity curves are complete, a more thorough study of this important 
binary can be made and a more definitive determination of its orbital and 
physical properties can be obtained.

This study is supported by NSF grants AST-861362 and AST-9315365 which we
gratefully acknowledge.  The reduction and analysis of the IUE observations 
were supported by NASA Grant NAG 5-2160.
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\beginauthors
\authorsrightcol
Edward F. GUINAN
Jamison A. MALEY
James J. MARSHALL
Dept. of Astronomy and Astrophysics
Villanova University
Villanova, PA  19085
U.S.A.
\endauthors
\vskip -6mm
\references

Claret, A. and Gimenez, A., 1992, {\it Astron. Astrophys. Suppl. Ser.}, {\bf 96}, 255

Diethelm, R., 1995, {\it B.B.S.A.G. Bull.}, 110

Guinan, E.F. and Maloney, F.P., 1985, {\it Astron. J.}, {\bf 90}, 1519 

Guinan, E.F., Marshall, J.J., and Maloney, F.P., 1994, {\it I.B.V.S.}, No.\,4101

Karpowicz, M., 1961, {\it Acta Astr.}, {\bf 11}, 51

Khaliullin, Kh.F., 1983, {\it Astr. Circ. USSR}, {\bf 1270}, 1

Khaliullin, Kh.F., 1985, {\it Ap.J.}, {\bf 299}, 688

Lacy, C.H., 1992, {\it Astron. J.}, {\bf 104}, 801

Lacy, C.H.S. and Fox, G.W., 1992, {\it I.B.V.S.}, No.\,4009 

Maloney, F.P., Guinan, E.F., and Mukherjee, J., 1991, {\it Astron. J.}, {\bf 102}, 256

Wolf, M., 1995, {\it I.B.V.S.}, No.\,4217


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