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\IBVShead{4690}{1 April 1999}

\IBVStitletl{The Third Body in the Eclipsing Binary}{ AS Camelopardalis}

\IBVSauth{V.S. Kozyreva, A.I. Zakharov, Kh.F. Khaliullin}

\IBVSinsto{Sternberg Astronomical Institute, Moscow University,
13, Universitetsky Ave., Moscow 119899, Russia\\ 
{[valq@sai.msu.su, zakh@sai.msu.su, hfh@sai.msu.su]}} %email


\IBVSabs{The eclipsing variable AS Cam is a binary system with}
\IBVSabs{anomalously slow apsidal motion.}
\IBVSabs{We determined the times of minima from 1993 to 1996 and analyzed them}
\IBVSabs{to reveal a "light time" effect with an amplitude of 3 minutes}
\IBVSabs{and a period of 2.2 years thereby providing evidence for a third}
\IBVSabs{body in the system.}
\IBVSkey{eclipsing binary stars, apsidal motion}
\SIMBADobj{AS Cam}

\begintext

The eclipsing binary AS Cam (HD 35111 = BD+69\deg325 = SAO 1357 =
BV 268, $V_{\rm max} = 8\fmm6$; Sp.: B8 + B9.5\,V) is a well-known
system having an eccentric orbit ($e=0.17$) and an orbital period of
$P_{\rm orb}= 3.43$ days.  The AS Cam system was discovered
photographically by Strohmeier\,(1963). Hilditch\, (1969) obtained
spectra and reanalyzed the photographic data, supplemented by
photoelectrically determined times of minima, to show that AS Cam
consists of a pair of B9 V stars.  Hilditch\, (1972a) estimated the
masses of the components to be $M_1=3.3\,M_\odot$ and
$M_2=2.5\,M_\odot$. He obtained a two-year long photometric dataset
extending from 1968 to 1970.

In 1981 we began the photoelectric observations of the star with a
50-cm Cassegrain reflector of the Tien-Shan observatory of the
Sternberg Astronomical Institute.  Observations of the primary and
secondary minima were carried out on November 28 and 30, 1981,
respectively, and the corresponding light curves can be found in the paper by Khaliullin and Kozyreva (1983).  Our observations provide complete and
accurate coverage of all parts of the light curve minima except for a
small interval at the beginning of the descending branch of the primary
minimum. On the average, the standard error of individual observation
is $\sim 0\fmm004$ in $V$. We also determined the orbital elements
and physical parameters of the components (Khaliullin and
Kozyreva,~1983).

On the base of comparison with the observations of Hilditch we
discovered AS Cam to be the system with a large disagreement between
the observed apsidal motion rate (Khaliullin and Kozyreva,~1983)
($\dot{\omega}_{\rm obs}=16\deg/100$~years) and its theoretical
value ($\dot{\omega}_{\rm obs}=44\deg/100$~years) This discrepancy
was confirmed by others (Maloney {\it et~al}., 1989).  A similar
surprising result concerning another close binary with relativistic
apsidal motion was obtained by Martynov and Khaliullin (1980):  for
DI\,Her, the theoretically expected apsidal motion caused by
relativistic contribution is larger than the classical component  by
a factor of two. The observed apsidal motion in this system is smaller
than that theoretically expected by a factor of three and, moreover,
$\dot{\omega}_{\rm obs}$ is even smaller than $\dot{\omega}_{\rm cl}$.  Both these results require adequate theoretical explanation.

Such disagreements were investigated by Maloney {\it et~al.}\ (1989)
but they did not find acceptable explanations for the conflict between theory and observations in the framework of the classical theory of gravitation.

A successful explanation has been suggested for the discrepancy between
theory and observations for DI\,Her by Khaliullin, Khodykin and
Zakharov (1991).  They developed a model of a hierarchical
triple system with non-coplanar orbits and found no conflict between
theoretically calculated and observed apsidal motion parameters for the
given longitude of periastron.  The above authors give a detailed
description of the domain of acceptable positions of the third body and
its mass. The computations are based on observational data.  This model
assumes that the orbital plane of the third body is almost perpendicular to the line of sight.



Khodykin and Vedeneev (1996) showed that a third body in AS Cam can
resolve the discrepancy between the theoretical and observed apsidal
motion rates provided that its mass is at least 1.1--1.45\,$M_\odot$.
To reveal the effects due to the third body required accumulation of
extensive and homogeneous observational datasets.



We performed our photoelectric observations in 1991--1996 at the
Tien-Shan observatory. Most of the observations  were obtained with the
same telescope as the one used for 1981 photometry.  As a light
receiver we used a four-channel {\it WBVR} photometer with dichroic
filters (Kornilov and Krylov, 1993).  We have obtained light curves  of
7 primary and 12 secondary minima.  The most accurate light curves are
those in the $V$-band because atmospheric extinction in this filter is
the lowest. The standard error of photometry for the minima of
1991--1996 was equal to 0\fmm01 and the error was as small as $\sim
0\fmm006$ on the best nights. We performed the observations using
differential method with HD 34463 as a comparison star and HD 34886, as
a check star. We found the rms scatter in the $V$-magnitude difference
between AS Cam and HD 34463 outside  the minima to be 0\fmm025, whereas
the corresponding scatter for the magnitude difference between the
comparison and check stars  did not exceed 0\fmm005.  G\"ulmen\,{\it et
al.}\ (1976), who earlier observed this star, also pointed out a
possible $\sim 0\fmm03$ variability in the $V$-band outside of the
eclipses. Physical variability of AS Cam really exists and contributes
to the errors in the elements inferred from light curve analysis. It is
therefore very desirable to understand the nature of this variability.
To do this we have to secure and analyze sufficiently long datasets
obtained outside eclipse.



Various methods are used to determine the times of minima for eclipsing
variables. They usually involve finding the symmetry axis of the light
curve. One of the most widely used method consists in fitting a
parabola to a light curve minimum.  However, the shape of the light
curve differs from a parabola and therefore the times of minima thus
obtained depend on the configuration of the binary and on the time
interval during which the light curve is observed, resulting in a
systematic error of the method.

We determined the times corresponding to the minimum projected
distances between stars. To this end, we used a model consisting of two
spherical stars with a linear limb darkening, moving in an elliptical
orbit. Adopting a particular model allows homogeneous determination of
the times of minima during eclipses.  The timings of minima were
calculated simultaneously with the photometric elements.  Note that
some of the latter could be fixed corresponding to the solution of a
best light curve (Khaliullin and Kozyreva,~1983).

Table 1 gives the times of minima for AS Cam derived using the adopted
model. Besides our minima, the timings of minima were used that we
inferred from the published light curves of Hilditch (1972b) (JD
2440132, 2440147, 2440185, 2440204, 2440545, 2440590) and Lines {\it
et~al.}\ (1989) (JD 2447443 and 2447465) and from those kindly provided
by E.F. Guinan and M. Wolf, in the framework of our model. Besides, we
used some timings of minima taken from the original papers.

\newpage

\begin{table}
\caption{Photoelectric timings of minima of AS Cam obtained at Tien-Shan observatory.}
\begin{center}
\begin{tabular}{rrc|lrc}
\hline
JD$_\odot$ 2400000+  & O$-$C & Min &JD$_\odot$ 2400000+& O$-$C & Min \\
\hline
44939.2457 & 0\fday0005 &  I &  48869.2220 & 0\fday0032 & II \\
48538.3247 &  $-$0.0016 &  I &  48982.4411 &     0.0003 & II \\
48881.4241 &     0.0014 &  I &  49003.0268 &     0.0001 & II \\
48998.0740 &  $-$0.0014 &  I &  49236.3317 &  $-$0.0010 & II \\
49238.2405 &  $-$0.0024 &  I &  49332.3975 &  $-$0.0024 & II \\
49341.1695 &  $-$0.0023 &  I &  49339.2600 &  $-$0.0018 & II \\
49557.3235 &     0.0010 &  I &  49610.3109 &     0.0023 & II \\
49622.5124 &     0.0016 &  I &  49634.3272 &     0.0018 & II \\
49773.4737 &     0.0005 &  I &  49778.4265 &     0.0003 & II \\
50418.4975 &     0.0031 &  I &  50056.3322 &  $-$0.0027 & II \\
50425.3566 &     0.0002 &  I &  50063.1937 &  $-$0.0031 & II \\
44937.3262 &     0.0005 & II &  50423.4506 &     0.0018 & II \\
48536.4094 &  $-$0.0052 & II & \\
\hline
\end{tabular}
\end{center}
\end{table}

The period of the apsidal motion is much larger than the whole
interval covered with observations, therefore the O$-$C for Min I as
well as for Min II could be reproduced with linear function of time.
$$
\begin{array}{r@{}r@{}l}
{\rm C_I} = {\rm JD_\odot\ }2444939.24524&{}+3\fday4309638&{}\times E, \\
                                   \pm 54&           \pm 4& \\[2mm]
{\rm C_{II}}={\rm JD_\odot\ }2444937.32567&{}+3\fday4309713&{}\times E. \\
                                    \pm 63&           \pm 5& \\
\end{array}
$$

The O$-$C residuals for Min I and Min II, after subtraction of linear
trend due to apsidal motion, are shown in Fig.~1.  Zero point
corresponds to year 1981.

\IBVSfig{7cm}{4690-f1.eps}{O$-$C diagram for photoelectric minima with
linear trend subtracted.  Individual  primary  ($\bullet$)   and
secondary ($\circ$) minima are shown.  Zero O$-$C corresponds to JD
~2444939 (year of 1981). The O$-$C residuals can be fitted by a
theoretical calculated curve (solid line).}

We see that the O$-$C residuals are subject to variations with a period
of $\approx 2.2$ years for both eclipses. This can be considered as
evidence for a third body in the system. The amplitude of variations,
period and eccentricity are calculated by the least square method. They
are equal to
$$
\frac{a'\sin i'}{c} = 4.18{\rm\ min}, \qquad e' = 0.5, \qquad P' = 805\day.
$$

Our investigations concerning the mass of the third body will be
described elsewhere. Here we only publish that the mass of the third component is approximately 1.1--1.7\,$M_\odot$.

{\it Acknowledgements.} We are thankful to A.B. Kusakin, E.F  Guinan and
M. Wolf for their  observations of AS Cam kindly presented to us.


\references

G\"ulmen \"O., Ibanoglu C., Bozkurt S., G\"ud\"ur N., 1976, Inf.\ Bull.\ Var.\ 
Stars, No.\,1090

Hilditch R. W., 1969, Observatory, 89, 143

Hilditch R. W., 1972a, Publ.\ Astron.\ Soc.\ Pac., 84, 519

Hilditch R. W., 1972b, Mem.\ R. Astron.\ Soc., 76, 141

Khaliullin Kh. F., Kozyreva V. S., 1983, Astrophys.\ Space Sci., 94, 115

Khaliullin Kh. F., Khodykin S. A., Zakharov A. I., 1991, Astrophys.\ J., 
375, 314

Khodykin S. A., Vedeneev V. G., 1996, Astrophys.\ J., 475, 798

Kornilov V. G., Krylov A. V., 1993, Nuclear physics, Cosmic ray physics, Astronomy (eds.\ Tikhonov A. N., {\it et al.}), Moscow: Moscow University 
press, 209

Lines H. C., Lines R. D., Glownia Z., Guinan E. F., 1989, Publ.\ Astron.\ Soc.\ Pac., 101, 925

Maloney F. P., Guinan E. F., Boyd P. T., 1989, Astron.\ J., 98, No.\,5, 1800

Martynov D. Ya., Khaliullin Kh. F., 1980, Astrophys.\ Space Sci., 71, 147

Strohmeier W., 1963, Sky and Telescope, 26, 264

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