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\input ibvs2.sty

\begin{document}

\IBVShead{6036}{17 September 2012} 

\IBVStitletl{First solution of the light curve}{ of the new variable star 3UC~281-203711}

\IBVSauth{Gorda, S.Yu.; Sobolev, A.M.}

\IBVSinsto{Astronomical Observatory, Ural Federal University, 19
Mira st., Ekaterinburg, 620002, Russia  \\
E-mail: {\tt stanislav.gorda@usu.ru}}

\IBVStyp{ E } 
\IBVSkey{eclipsing binary system, solution of the light curve}
\SIMBADobj{3UC 281-203711}

\begintext

A new variable star 3UC~281-203711 $V=12\fmm4$  was discovered
during monitoring of the young irregular variable V645 Cyg at the
Astronomical Observatory of the Ural Federal University (Gorda \&
Sobolev, 2011: GS2011). The first brightness decrease of 3UC~281-203711 by
$0\fmm08$ was registered on JD~2454966.30. The finding chart and the
data table are presented in GS2011.
Coordinates of the target, comparison and check stars are given in Table 1 
of the current paper.

The AZT-3 reflector ($D = 0.45$m, $F_{Newton} = 2.0$ m) with an
Alta-U6 CCD camera (Kodak KAF-1001E, 1048x1048, 24-micron chip)
was used. The photometry was carried out using the $V$ and $R$
Cousins/Bessell filters. The uncertainty of our brightness
measurements during individual nights was within $\pm0\fmm003$ --
$\pm0\fmm007$, as estimated by the brightness difference between the
comparison star 3UC~281-203713 and the check star 3UC~281-203646.
The reduction of the CCD frames was carried out using $Muniwin$
software.

Time of minimum $HJD I_{min} = 2455543.1338$ was calculated from
observations of one completely covered primary minimum, namely part of
the light curve prior to the eclipse, descending branch, whole bottom
plateau and a considerable part of the ascending branch. Preliminary
estimate of the period given in GS2011 was based on
the observational data covering parts of the primary minimum:  four
descending branches complemented with small parts of the bottom plateau
(brightness decrease by 0\fmm08) and two parts of the bottom plateau
complemented with ascending branches (brightness increase by the same
amount).

3UC~281-203711 is an eclipsing system. The light curve is of Algol
type and manifests pronounced ellipsoidal effects. The primary
minimum is not so deep but is much deeper than the secondary
minimum. The mean depths of the minima are about the same in both
colours and equal to $0\fmm103$ and $0\fmm030$ for the primary and
secondary minima, respectively. A plateau is observed in the
bottom of the primary minimum, indicating that one of the eclipses
is total GS2011, Fig.~1, bottom panel).

Photometric reduction of CCD frames using $Muniwin$ package was carried out 
prior to the solution of the lights curves. The results differ 
within observational uncertainties from the ones given in 
GS2011, which were obtained using the $MaxIM~DL$ package. 
For the majority of observational points the difference between the values 
computed using the two packages did not exceed $0\fmm003$. But for the data 
obtained in filter $V$ during the nights JD 2454965 and JD 2455127 these 
differences were systematic and reached the values about $0\fmm01-0\fmm02$. 
For solutions of the light curves we used almost the same data as provided in 
GS2011. Data on the two nights mentioned above were an 
exception because they have shown better correspondence with the data for the 
same photometric phases obtained during other nights. Altered data points 
are provided in (electronic) Tables 4 and 5.

A solution of the light curve was carried out with the $PHOEBE$
package with a graphic interface for Windows. Realizations of the
Wilson-Devinney light curve analysis method and of the Nelder-Mead
simplex method for search of the optimum solution from this
package were used.

Nothing was known about the physical nature of components of this
eclipsing binary system. Hence, the initial values of physical
parameters were chosen on the basis of values of the
period, surface brightness ratio, ratio of the radii of components
and their relative sizes. These values were defined from the form,
depth and duration of the primary minimum under the hypothesis of a
total eclipse. Initial values of the temperatures corresponding to
spectral class ${\rm F}0$ were chosen. Estimate of the spectral class is
based on the values of 3UC~281-203711 brightness in the optical
and infrared ranges taken from the $NOMAD$ catalog. Initial values of
the mass ratio of the components and the semi-major axis of the
orbit were chosen by assuming that both components belong to
the main sequence.

Determination of the orbital elements and the physical parameters of
the components were carried out with simultaneous use of the data in
both $V$ and $R$ filters. As a result of the preliminary solution
it was established that the total eclipse occurs in the secondary
minimum which is not deep. During the primary minimum the smaller 
and cooler star passes in front of the bigger and hotter component,
being completely projected on its surface at the moments of time
close to the middle of the eclipse.

Calculation of the physical parameters of the system with the
$PHOEBE$ package requires knowledge of the value of semi-major
axis of the mutual orbit, $a$. This value does not influence the
light curve and, hence, cannot be estimated from our data. For the
current analysis we adopted the value $a = 9R_\odot$ (see
consideration of the physical meaning of this value below).

Further, the calculation of the physical parameters of the system requires the 
knowledge of the value of another parameter - the mass ratio of the components, $q$.
This parameter only weakly influences the form of the light curve and requires
special efforts for its determination. A number of solutions were obtained for
a set of given values of $q = 0.2, 0.3, ... , 0.8$. The other parameters remained free.
It was found that the theoretical light curves do not show considerable
(i.e. exceeding observational uncertainties) systematic deviations from
the observational points by changing only the values of $q$ within the interval $0.3 - 0.6$.
Calculations with released parameter of $q$ showed that the values $q\sim 0.5$
provide the best fit.


A criterion of proximity of the
values of effective temperatures, masses and radii of components
to the values of corresponding parameters of the main sequence
stars was applied in order to choose the admissible values for
the semi-major axis of the eclipsing system, $a$.

It was found that the values of $a$ in the range $8R_\odot -
10R_\odot$ bring the parameters of the secondary component (mass,
radius, effective temperature) into close agreement with a main
sequence star of spectral class ${\rm K}0 - {\rm K}3$. Therefore we assume
that the value of the semi-major axis for the 3UC~281-203711
eclipsing binary is $a \sim 9R_\odot$.

At the same time, there are no values of  $a$ leading to overall
agreement between the physical parameters of the primary
component. Estimates of the spectral class vary in the range ${\rm A}0 -
{\rm F}0$, depending on the physical parameter (mass or temperature)
used for the estimate. The values of the radius for the given mass
and temperature are too high in all cases. Most likely, this
reflects that the star does not belong to the main sequence: it is
possibly a subgiant or starts its transformation to become a
subgiant.


Values of the photometric parameters and absolute values of the parameters
for 3UC~281-203646 components with adopted value of $a = 9R_\odot$
are given in Tables 2 and 3, respectively. Accuracy of the
parameter estimates for light curve solutions reflects scatter for $a$ and 
$q$ in the ranges $8-10$ and $0.4-0.6$, respectively.

More accurate value of the period for this eclipsing system was
obtained in the course of solution of the light curve.
The new ephemeris is the following:

\begin{center}
$
\begin{array}{ccrcrl}
HJD I_{min}  &=&  2454966.4565&+&1\fday948234&\!\!\!\cdot\, E.\\
&&\pm8&&\pm11&\\
\end{array}
$
\end{center}

In Figure~1 light curves (observational points and theoretical
curves)  are shown for $V$ and $R$ filters, respectively. In
Figure~2 residual values versus photometric phases are shown.

Observational light curves are fitted by the theoretical curves
quite well. This is seen in the residual plots which do not show
significant systematic deviations in either passbands. The brighter
and more massive component has a considerable tidal
deformation. This follows from the well pronounced maxima of
brightness in phases $0.25$ and $0.75$. It can be caused
by rather high values of the radius and of the component mass
ratio, $q \sim 0.5$.

Figure~2 (the bottom curve) shows that the color index of the
system does not vary with phase within observational accuracy. It
finds natural explanation in the fact that both ratios of the
sizes and the surface brightness of the primary and the secondary
components are high ($r_1/r_2 \sim 4$ and $j_1/j_2 \sim 16$, see
Table~1) and the luminosity of the primary component exceeds that
of the secondary component more than 200 times.


Quality of the observational data and existence of
the total eclipse in the system allowed obtaining estimates of
the relative photometric elements with small uncertainties. At the
same time absolute parameters were found with relatively high
uncertainties. This comes from the low accuracy of the value of
semi-major axis of the orbit which can be improved only by spectroscopic 
observations.

Figure~3 shows the configuration of the system corresponding to
our solution. It is seen that neither components of the 3UC~281-203711 
fills its Roche lobe. Hence, this system is a completely detached 
eclipsing binary. The primary component is probably a subgiant, hence, 
it is likely to fill in its Roche lobe in the future. In this case, after 
the start of the mass exchange phase the value of $q$ will increase and
the system can become a reverse Algol.

Authors would like to thank the referee Dr. T. Borkovits for useful
suggestions and comments which improved this paper.
The study was partly supported by the Russian federal
task program ``Research and operations on priority directions
of development of the science and technology complex of
Russia for 2007-2012" (state contract No.~16.518.11.7074).

\begin{table}[h]
\centerline{{\bf Table 1.} Designations and coordinates of the
stars }
\begin{center}
\begin{tabular}{lccc}
\hline
Name  &  $ \alpha(2000)$ & $ \delta(2000)$ &   $m_V$ \\
\hline\\[-5pt]
 3UC~281-203711 (variable)  &       21\hr39\mm52\fsec4 & +50\deg18\arcm27\arcs & 12\fmm40 \\
 3UC~281-203713 (comparison) &       21\hr39\mm52\fsec4 & +50\deg15\arcm55\arcs & 12\fmm60 \\
 3UC~281-203646 (check) &       21\hr39\mm47\fsec6 & +50\deg17\arcm03\arcs & 12\fmm22 \\[5pt]
 \hline
 \end{tabular}
\end{center}
\end{table}

\begin{table}
\centerline{{\bf Table 2.} Photometric parameters of the
eclipsing variable star 3UC~281-203711. }
\begin{center}
\begin{tabular}{ll||ll}
\hline
$k$ & $0.257\pm0.010$ & $i$ &  $81\fdeg2\pm0\fdeg5$\\
$r_1$ &  $0.294\pm0.008$ & $q$ &  $0.49\pm0.11$\\
$r_{1(pole)}$ &  $0.289$ & $j_1/j_2$ &  $15.8\pm1.4$\\
$r_{1(point)}$ &  $0.302$ & $L_1$ &  $0.996\pm0.001$\\
$r_{1(side)}$ &  $0.294$ & $L_2$ &  $0.004\pm0.001$\\
$r_{1(back)}$ &  $0.299$ & &  \\
$r_2$ &  $0.076\pm0.002$ & &  \\
 \hline
 \end{tabular}
\end{center}
\end{table}

\begin{table}
\centerline{{\bf Table 3.} Estimates of absolute parameters of the
eclipsing variable star 3UC~281-203711}
\begin{center}
\begin{tabular}{ll||ll}
\hline
$a\,(R_\odot)$ &  $9.0\pm1.0$ & $R_1\,(R_\odot)$ &  $2.65\pm0.30$\\
$T_{eff1}\,(K)$ &  $9800\pm100$ & $R_2\,(R_\odot)$ &  $0.68\pm0.08$\\
$T_{eff2}\,(K)$ &  $4900\pm80$ & $L_1\,(L_\odot)$ &  $21.85\pm0.08$\\
$M_1\,(M_\odot)$ &  $1.74\pm0.57$ & $L_2\,(L_\odot)$ &  $0.09\pm0.02$\\
$M_2\,(M_\odot)$ &  $0.85\pm0.28$ & &  \\
 \hline
 \end{tabular}
\end{center}
\end{table}

\IBVSfig{10cm}{6036-f1.eps}{Theoretical (solid line) and
observational (open circles) light curves of 3UC~281-203711}
\IBVSfigKey{6036-f1.eps}{3UC~281-203711}{light curve}

\IBVSfig{10cm}{6036-f2.eps}{Model fitting residuals for the light curves and 
color index curve
of 3UC~281-203711. The residuals for filter $V$ are shifted up by 0\fmm05. }
\IBVSfigKey{6036-f2.eps}{3UC~281-203711}{O-C and color index curve}

\IBVSfig{9cm}{6036-f3.eps}{Configuration of the system
3UC~281-203711 in the polar plane corresponding to the light curve
solution. Plus signs mark centers of mass of the stars; solid
lines show surfaces of the stars; dashed line shows Roche lobes;
dot shows $L_1$ point; filled diamond shows center of mass of the
system} 
\IBVSfigKey{6036-f3.eps}{3UC~281-203711}{Roche lobes}

\reference

Gorda, S.Yu., Sobolev, A.M., 2011, {\it Peremennye Zvezdy
Prilozhenie}, {\bf 11}, 19 (GS2011) 

\endreferences

\IBVSedata{6036-t4.txt}
\IBVSdataKey{6036-t4.txt}{3UC 281-203711}{photometry}
\IBVSedata{6036-t5.txt}
\IBVSdataKey{6036-t5.txt}{3UC 281-203711}{photometry}

\end{document}
