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\begin{document}

\IBVShead{6020}{10 April 2012}

\IBVStitletl{Apsidal motion of the eccentric eclipsing binary}{ GSC\,4487-0347}


\IBVSauth{Kozyreva, V.S.$^1$; Kusakin, A.V.$^2$; Menke, J.$^3$}

 \IBVSinsto{$^1$ Sternberg Astronomical Institute, Moscow
University, 13, Universitetsky Ave., Moscow 119899, Russia
{\tt valq@sai.msu.ru}} %email

 \IBVSinsto{$^2$ National Space Agency, Republic of Kazakhstan
 JSCNCSRT Department, Fesenkov Astrophysical Institute,
  Almaty 050068, Kazakhstan
 {\tt un7gbd@gmail.com}} %email

 \IBVSinsto{$^3$ Starlight Farm Observatory, 22500 Old Hundred Rd, Barnesville, Washington, MD 20838, USA\\ 
  {\tt john@menkescientific.com}} %email

\SIMBADobj{GSC 4487-0347}

\IBVSkey{CCD-photometry, spectrophotometry,  Binaries:eclipsing}
\IBVSkey{eclipsing binary stars, apsidal motion}

\IBVSabs{The eclipsing variable star GSC 4487-0347 is a recently}
\IBVSabs{discovered binary system.}
\IBVSabs{We carried out observations of the eclipsing binary using a CCD-array}
\IBVSabs{in 2009, 2011 at the Tien Shan Observatory.}
\IBVSabs{The B,V,R magnitudes were measured and the spectral range of}
\IBVSabs{components were estimated. The photometric elements were derived}
\IBVSabs{from the light curve. We found the apsidal period is U=160+-6 years.}

\begintext

The  recently discovered binary  system (GSC 4487-0347,
$\alpha_{2000}$= 23\hr46\mm10\fsec45, $\delta_{2000}$=
+71\deg29\arcm55\farcs3, $P$ = 1\fday98873) belongs to the list of ``50
new eccentric eclipsing binaries found in the ASAS, Hipparcos and
NSVS databases'' published by Otero et al. (2006).

We performed measurements in the $B$, $V$ and $R$ bands  at the Tien Shan
Astronomical Observatory using a Ritchey-Chr\'etien-350 telescope and an ST-402
CCD array in September-December  2009 and August-September 2011. We have only $V$ light curve during minima.

The spectrophotometric observations were made in Barnesville near Washington
using Newton-18-inch DSS-7 and ST-402 spectrophotometer.

At a distance of  3\farcs5 to the south of the binary star there is a neighbor fainter than the binary by 2\fmm5 $\pm$ 0.2.
The image   and the difference between  stars were obtained by Menke on a clear January night. 
On the images obtain at the Tien Shan Observatory  both stars appear as one.


 The photometric elements of the system
have been derived  by minimizing  functional depending on the
measured and theoretical magnitude differences (Kozyreva \& Zakharov, 2001).
The model of spherical stars with linear laws of limb-darkening in eccentric orbits can be used for the analysis of the light curve.


 The elements of the system are presented in Table 1.
 The luminosity of the nearby star is L$_3$. Since we did not have a sufficient phase coverage near quadratures, nor color indices throughout the whole 
   orbit, a preliminary light curve analysis was made.
 We shall have more real system parameters only after measuring a better covered multicolour light curve and after more precise knowledge of the spectra of the system's stars. 

 Column 2 shows the solution for the 2009 light curve. All parameters except the coefficients of limb-darkening, $u_1$ and $u_2$, of the stars were free in the search.
Column 3 corresponds to solution for the 2011 light curve. No reason to consider a significant change in the geometry of the binary system 
during the time between the two epochs of observations, the values of the parameter except $\omega$ were adopted in accordance with
the results of our analysis of the most accurate 2009 light curve.


  The light curve during minima  is shown in Fig.~1 (2009) and in Fig.~2 (2011). The data of
individual measurements are accessible on request 
(valq@sai.msu.ru). %email
Given at the bottom are deviations $O-C$
of the individual measurements from the theoretical light curve as computed using the theoretical elements given in Table 1.
They are shown shifted by 0\fmm6.


\begin{center}
\par\bigskip
\hangindent=2.3 cm Table 1: The photometric elements of the star
GSC~4487-0347, obtained from $V$ light curve.
\bigskip

\begin{tabular}{|c|c|c|}
\hline
\rule{0pt}{1pt}&{}&{}\\
Element&2009-value&2011-value\\
\rule{0pt}{1pt}&{}&{}\\
\hline
\rule{0pt}{1pt}&{}&{}\\
 r$_1$&$0.199{}\pm 0.005$ & $0.199{}\pm 0.005$\\
 r$_2$&$0.151{}\pm 0.005$ & $0.151{}\pm 0.005$\\
 i&86\fdeg1 $\pm$ 0\fdeg4 & 86\fdeg1 $\pm$ 0\fdeg4\\
 e&$0.131{}\pm 0.002$ & $0.131{}\pm 0.002$\\
 ${\omega}$&336\fdeg0 $\pm$ 0\fdeg3 & 340\fdeg5 $\pm$ 0\fdeg5 \\
 L$_1$&0.615${}\pm 0.020$ & 0.615${}\pm 0.020$\\
 L$_2$&0.293${}\pm 0.020$ & 0.293${}\pm 0.020$\\
 L$_3$&0.09${}\pm 0.020$ & 0.09${}\pm 0.020$\\
 u$_1$&0.38 $\div$ 0.45 & 0.38 $\div$ 0.45\\
 u$_2$&0.38 $\div$ 0.45 & 0.38 $\div$ 0.45\\
 ${\phi_{II}}$&0\fper5762 $\pm$0.0005 & 0\fper5786 $\pm$ 0.0006\\
$J_2/J_1$ & 0.827 & 0.827\\
 $L_2/L_1$ & 0.476 & 0.476\\
 $\sigma_{O-C}$ & 0.0082 & 0.0120\\
 \rule{0pt}{1pt}&{}&{}\\
\hline
\end{tabular}
 \end{center}

\IBVSfig{10.3cm}{6020-f1.eps}{$V$ light curve  of GSC 4487-0347 
obtained at the Tien Shan Observatory
in  2009. The deviations $O-C$ are shifted by 0\fmm6.}
\IBVSfigKey{6020-f1.eps}{GSC 4487-0347}{light curve}

\IBVSfig{10.3cm}{6020-f2.eps}{$V$ light curve  of GSC 4487-0347 obtained at the Tien Shan Observatory in  2011.}
\IBVSfigKey{6020-f2.eps}{GSC 4487-0347}{light curve}


The $B$, $V$ and $R$ magnitudes of GSC~4487-0347 (including the optical component) with respect to the {\it WBVR} standard
HD~222958 are given in Table 2. $V$ magnitudes of each star are calculated  using data of the luminosities (Table 1).

\begin{center}
\par\bigskip
\hangindent=2.3 cm Table 2: The $B$, $V$ and $R$ magnitudes  of GSC~4487-0347.
\bigskip

\begin{tabular}{|c|c|c|c|}
\hline
\rule{0pt}{1pt}&{}&{}&{}\\
 Stars & $B$ & $V$ & $R$\\
\rule{0pt}{1pt}&{}&{}&{}\\
\hline
\rule{0pt}{1pt}&{}&{}&{}\\
 GSC~4487-0347&11\fmm50 $\pm$ 0.02 & 11\fmm19 $\pm$ 0.01 & 11\fmm01 $\pm$ 0.02\\
primary component & -  & 11\fmm72 $\pm$ 0.02 & -\\
secondary component & - & 12\fmm52 $\pm$ 0.02 & -\\
optical component &-& 13\fmm80 $\pm$ 0.02 & -\\
\rule{0pt}{1pt}&{}&{}&\\
 \hline
 \end{tabular}
 \end{center}


In December 2010, Menke obtained spectra of GSC 4487-0347 including the optical component. SAO 10815 (A$0$V) was used as a comparison star. Unfortunately, the spectra have a low resolution ($\geq$ 7\AA /pix) but we were able to estimate the spectral type for the components of the binary system. They are stars of  B7$\div$A3.
The coefficients of limb-darkening, $u_1$ and $u_2$, of the stars
 were chosen according to Van Hamme (1993) and remained constant during the calculation.
 We found a very weak dependence of the derived photometric elements on the coefficients of a selected range ($u_1$ and $u_2$).

 The comparison of the longitude of periastron for two epochs  of observation from Table 1 gives the apsidal motion:

    $$
            \dot{\omega}_{obs}=2.26{}\pm 0.08 {}^{\circ}
                 \mbox{/year} ;\quad{}U_{apsid}^{obs} = 160\pm 6 \quad
                 \mbox{years.}
    $$

  The value of apsidal motion obtained using  the data  given by Otero et al. (2006) (the moment of primary minimum and the phase of the secondary minimum)  does not contradict this value:  $\dot{\omega}_{obs}=2.0\pm 0.3 {}^{\circ} \mbox{/year}$. The same applies to the moments of minima obtained in  2008 by Ku\u{c}\'akova
 and Koci\'an  (Br\'at et al., 2008): $\dot{\omega}_{obs}=2.8\pm 1.5{}^{\circ} \mbox{/year}$.
  The moments of minima obtained in 2009 and 2011 are given in Table~3.

\begin{center}
\par\bigskip
\hangindent=2.3 cm Table 3: The moments of minima of GSC~4487-0347.
\bigskip

\begin{tabular}{|c|c|c|c|}
\hline
$ JD_\odot$ & & &   \\
 2400000+&  Min& 2400000+& Min \\
\hline
55122.1578 $\pm$ 0.0005&I&55121.3150 $\pm$ 0.0005&II\\
55806.2827 $\pm$ 0.0005&I&55819.3656 $\pm$ 0.0008&II\\
\hline
\end {tabular}
\end {center}


The calculated ephemerides are:\\
\begin{center}
\rm Min\, I = {\rm JD$_\odot$\,}24 55122.1578(3) + 1\fday988731(1)E

\rm Min\, II = {\rm JD$_\odot$\,}24 55121.3150(4) +  1\fday988751(1)E\\

$\Delta{P}={P}_{\mathrm II}-{P}_{\mathrm I}=$0\fday000020(2)  = 1\fsec73 $\pm$ 0\fsec20
\end{center}

The stars of the obtained spectral classes and parameters have such fast apsidal motion $(2.26{}^{\circ}/{\mathrm year})$ only on  the stage of compression (Claret and Gimenez, 1993) and  the theoretical apsidal motion in average is 1.5 times smaller on the later stage.
We hope that the mass and accurate spectra of components will be derived, in the near future allowing us to compare the observational and theoretical values of apsidal motion.

{\bf Acknowledgements:}\\
  We wish to thank A.I.~Zakharov, S.E.~Leont'ev for the help on development of
  computer programs, V.B.~Sekirov for the excellent  Ritchey-Chr\'etien telescope,
 which he made with his own hands,
M.A.~Krugova for providing technical equipment and  R.I.~Kokumbaeva for the
 assistance in data processing.


\references

Br\'at, L., \u{S}mel\'cer, L., Ku\u{c}\'akova, H., Ehrenberger, R., Koci\'an, R., Lomoz, F., Urban\v{c}ok, L., Svoboda, P., Trnka, J., Marek, P. and 5 coauthors, 2008, {\it OEJV}, {\bf 94}, 1

Claret, A., Gimenez, A., 1993, { \it Astron. \& Astrophys.}, {\bf 277}, 487

Van Hamme, W., 1993, { \it Astron. J.},  {\bf 106}, 2096

Kozyreva, V.S., Zakharov, A.I., 2001, {\it Ast. Letters}, {\bf 27}, 712

Otero, S.A., Wils, R., Hoogeveen, G., Dubovsky, P.A., 2006, {\it IBVS}, {\bf 5681}

\endreferences

\IBVSedata{6020-t4.txt}
\IBVSdataKey{6020-t4.txt}{GSC 4487-0347}{photometry}
\IBVSedata{6020-t5.txt}
\IBVSdataKey{6020-t5.txt}{GSC 4487-0347}{photometry}

\end{document}

