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\IBVShead{4217}{6 July 1995}
\title{Slow apsidal motion in V541 Cygni}
\vskip -2mm
\begintext
The detached eclipsing binary V541 Cyg (BD+30\degr 3704 = GSC 2656.3703)
is a less-known binary with high orbital eccentricity $(e = 0.47)$ and a long
period of 15.34 days. It is an important system for the study of
the general-relativistic theory of the apsidal motion (Khaliullin, 1985).
The theoretically expected rotational velocity of the line of apsides could
be 0\fdg 0097 yr$^{-1}$, caused by dominant relativistic contribution
as well as by tidal distortion and rotational flattening of the component
stars.
Our new CCD photometry of V541 Cyg was carried out on 20 June 1995
at the Ond\v{r}ejov Observatory using a 65cm reflecting telescope
with a CCD-camera (SBIG ST-6) at the primary focus.
The measurements were done using the standard Johnson $B$ filter with 60 s
exposure time. The stars GSC\,2656.1627 -- listed also as star 3 by
Karpowicz (1961) - on the same frame as V541 Cyg served as a comparison star.
The CCD data were reduced using software developed at Ond\v{r}ejov
Observatory by P. Pravec and M. Velen. No correction was allowed
for differential extinction, due to the proximity of the comparison star
to the variable (2.8 arcmin) and the resulting small differences in the
air mass. The secondary minimum and their error
were determined using the Kwee-van Woerden (1956) method. The result
for the moment of eclipse is:
\begin{center}
Sec. Min. = HJD 24 49889.377 $\pm$ 0.001
\end{center}
The apsidal motion of V541 Cyg was studied by means of an O$-$C diagram
analysis. We took into consideration all photoelectric times collected
in Table 1, the photographic measurements obtained by Karpowicz (1961),
as well as the times of secondary minimum obtained by Kulikowski (1953).
The original times of primary minimum were not used due to large
scatter of the data. The epochs were calculated using the linear light
elements given by Khaliullin (1985):
\begin{center}
\medskip
\noindent Pri. Min. = HJD 24 44882.2127 + 15.337873 $\times$ E
\medskip
\end{center}
\centerline{Table 1. Photoelectric times of minimum of V541 Cyg.}
\begin{center}
\begin{tabular}{lrl}
\hline
JD Hel.$-$ & Epoch & Reference \\
2\,400\,000 & & \\ \hline
44882.2127 & 0.0 & Khaliullin (1985) \\
44889.2192 & 0.5 & Khaliullin (1985) \\
46998.8424 & 138.0 & Lines et al. (1989) \\
48839.387 & 258.0 & Diethelm (1992) \\
49168.4951 & 279.5 & Agerer (1994) $\star$ \\
49889.377 & 326.5 & this paper \\ \hline
\end{tabular}
\end{center}
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\centerline{$\star$ \it mean value of V and B measurements}
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\centerline{2}
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\centerline{Table 2. Apsidal motion parameters.}
%\begin{eqnarray}
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\begin{center}
\begin{tabular}{lcl}
& & \\
\hline
\\
T$_0$ & = & 2\,444\,881.7920 $\pm$ 0.0006 \\
P$_s$ & = & 15\fd 3379020 $\pm$ 0\fd 0000005\\
P$_a$ & = & 15\fd 3379111 $\pm$ 0\fd 0000005\\
e & = & 0.4735 $\pm$ 0.0021 \\
$\omega$ & = & (0\fdg 000\,223 $\pm$ 0\fdg 000\,045)\, \rm{cycle$^{-1}$} =\\
& = & (0\fdg 0053 $\pm$ 0\fdg 0011)\, \rm{yr$^{-1}$} \nonumber \\
$\omega$$_0$ & = & 262\fdg 7 $\pm$ 0\fdg 1 \nonumber \\
U & = & 1.614 $\times$ 10$^{6}$ P$_a$ = 68\,000 $\pm$ 13\,000 \rm{yr}\\
\hline
%\end{eqnarray}
\end{tabular}
\end{center}
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\centerline{\epsffile{4217-f1.ps}}
\begin{center}
Figure 1. Residuals for the times of minimum of V541 Cyg with respect to the
linear light elements. The continuous and
dashed curves represent predictions for primary and secondary
eclipses, respectively. The individual primary and secondary
minima are denoted by circles and triangles, respectively.
Larger symbols correspond to the photographic and photoelectric
measurements with higher weight.
\end{center}
\vskip 2mm
All photoelectric times of minimum were used in our computation,
with a weight of 10, the photographic times obtained by Karpowicz (1961)
were weighted with a weight of 5,
the older photographic measurements with a weight of 1.
A total 21 times of minimum light were incorporated in our analysis,
with 6 primary eclipses among them.
For the apsidal motion analysis we used the method
by Gim\'{e}nez \& Garc\'{\i}a-Pelayo (1983). This weighted
least squares iterative procedure includes terms in the eccentricity
up to the fifth order. Due to the high value of eccentricity of V541 Cyg,
we used all terms in our calculation.
\vfill \eject
\centerline{3}
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Adopting the orbital inclination, derived from the light curve
solution, of i = 89\fdg 86 (Khaliullin, 1985),
the mean apsidal motion elements given in Table 2 can be determined.
In this table $P_s$ denotes the sidereal period, $P_a$ anomalistic
period, $e$ represents the eccentricity, $\dot{\omega}$ the rate
of apsidal motion. The zero epoch is given by $T_0$ and the
corresponding position of the periastron is $\omega_0$. Finally,
$U$ is the period of apsidal line rotation.
The O$-$C residuals for all times of minimum with respect to the
linear part of the apsidal motion equation are shown in Figure 1.
The original primary and secondary times of minimum obtained by
Kulikowski (1953) are also plotted.
The non-linear predictions, corresponding to the fitted parameters,
are plotted as continuous and dashed curves for primary and secondary
eclipses, respectively.
We derived the apsidal motion elements using the current data set.
Our results indicate that the observed apsidal motion rate is less than
expected from theory, in contradiction with previous good agreement
announced by Khaliullin (1985) and Lines et al. (1989).
This system could be the next member of a small group of binaries,
which exhibit the discrepancy between observed and predicted rate
of the apsidal motion. These anomalous cases, like DI Her (Guinan \&
Maloney, 1985) or AS Cam (Maloney et al., 1991) were not yet explained
satisfactorily. More high-accuracy timings of this
eclipsing system are necessary in the future to enlarge the time
span for better analysis of the apsidal motion. Also the spectroscopic
orbit of this system should be determined.
\noindent {\it Acknowledgement.} This work has been supported in part
by the Grant Agency of the Czech Republic, grant No. 205-95-1498 and
by the ESO C\&EE Programme, grant No. A-02-069. I am grateful to
Ms. Lenka \v{S}arounov\'a, who took part in our observations.
\vskip 1cm
\beginauthors
\authorsrightcol
Marek WOLF
Astronomical Institute
Charles University Prague
\v{S}v\'edsk\'a 8
CZ - 150 00 Praha 5
Czech Republic
Internet : {\tt wolf@earn.cvut.cz}
\endauthors
\references
Agerer F., 1994, {\it BAV Mitteilungen}, No.\,68, 5
Diethelm R., 1992, {\it BBSAG Bulletin}, No.\,102, 4
Gim\' enez A., Garc\'{\i}a-Pelayo, 1983, {\it Astrophys. Space Sci.},
{\bf 92}, 203
Guinan E.F., Maloney F.P., 1985, {\it Astron. J.}, {\bf 90}, 1519
Karpowicz M., 1961, {\it Acta Astronomica}, {\bf 11}, 51
Khaliullin Kh.F., 1985, {\it Astrophys. J.}, {\bf 299}, 668
Kulikowski, P.G., 1953, {\it Perem. Zvezdy}, {\bf 9}, 169
Kwee K.K., Van Woerden H., 1956, {\it Bull. Astron. Inst. Neth.},
{\bf 12}, 327
Lines R.D., Lines H., Guinan E.F., Carroll S., 1989, {\it Inf. Bull. Var.
Stars}, No.\,3286
Maloney F.P., Guinan E.F., Mukherjee J., 1991, {\it Astron. J.},
{\bf 102}, 256
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