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\IBVShead{5591}{7 January 2005}

\IBVStitletl{A Photometric Investigation of a Close Binary System:}{ YY C\lowercase{nc}}


\IBVSauth{ZOLA, S.$^{1,2}$; CHUDY, M.$^2$; DROZDZ, M.$^2$}

\IBVSinst{Astronomical Observatory, Jagiellonian University, ul. Orla 171, 30-244 Cracow,
Poland, \\ 
 e-mail: sfzola@cyf-kr.edu.pl }
\IBVSinst{Mt. Suhora Observatory, Pedagogical University, ul. Podchorazych 2, 
30-084 Cracow, Poland, \\ e-mail: (monika,marek)@astro.as.wsp.krakow.pl}

\SIMBADobjAlias{YY Cnc}{BD +31 1838}
\IBVStyp{ CWA }
\IBVSkey{photometry}
\IBVSabs{We present new photometric light curves (BVR filters) taken with a three-channel }
\IBVSabs{PMT photometer. A new linear ephemeris for this close, eclipsing system was derived}
\IBVSabs{A preliminary solution of the light curves using the Wilson-Devinney code is also presented.}

\begintext

YY Cnc (BD+31 1838, V$_{max}$=11.3 mag) was discovered by Hoffmeister (1949). 
Coordinates and  identification for this and other Sonneberg variables in 
the MVS 308-316 were given by Kinnunen and Skiff (2000).  The third edition of
the General Catalogue of Variable Stars gives only the epoch of the primary
minimum and the period of 0.55 days. The spectral type is listed as F2 
both in the GCVS and the ADS database.\\

We present first ever obtained photometric light curves taken at the Mt. Suhora 
Observatory with the 60~cm telescope and a three channel photometer equipped with 
the wide-band UBVR filters. The observations were gathered from 11/12 to 24/25 Feb 2003. 
GSC 2483 1211 was used as the comparison star.
Additionally, to enlarge the time span, the primary minimum was observed with the 
same telescope and a SBIG ST10/XME CCD camera 
about a year later on January 27/28, 2004, and again with the three channel photometer 
on February 25/26, 2004.  
All measurements have been corrected for differential extinction and left in the 
instrumental, close to the Johnson-Morgan, system. We observed 5 primary and 
1 secondary eclipses and determined their times using the Kwee-van Woerden method.
These times are shown in Table 1. We found the period significantly longer than 
that listed in the GCVS. Using the new times of minima we determined a new linear 
ephemeris for YY Cnc:

\begin{center}
  HJD$_{\rm prim. min.}$=2452695.5815(3) + 0.698448(2) * E
\end{center}

\vskip 1cm
\centerline{Table 1. New times of minima for YY Cnc }
\vskip 3mm
\begin{center}
\begin{tabular}{cccll}
\hline
No. &     Date         &  type & Time of minimum       & Instrument   \\
\hline
1 & 12/13-02-2003      & sec   & 2452683.3464(3)       & p3ch    \\
2 & 13/14-02-2003      & prim  & 2452684.4056(3)       & p3ch    \\
3 & 24/25-02-2003      & prim  & 2452695.5811(3)       & p3ch    \\
4 & 27/28-03-2003      & prim  & 2452726.3150(4)       & p3ch    \\
5 & 26/27-01-2004      & prim  & 2453031.5443(9)       & CCD     \\
6 & 25/26-02-2004      & prim  & 2453061.5680(4)       & p3ch    \\
\hline
\end{tabular}
\end{center}
\vskip 1cm

The observations were phased with the new ephemeris and we attempted to obtain a
preliminary model for this star using the Wilson-Devinney code (Wilson 1979, 1993). 
In the first
step we assumed the primary temperature to be 6700~K as  corresponding to the 
F2 spectral type (6700~K, Harmanec 1988) and made a search for the best fit with 
the Monte  Carlo algorithm. 
Theoretical values for the albedo and gravity darkening coefficients, appropriate for
a convective envelope  were assumed. The coefficients for the limb darkening were 
taken as   functions of 
the temperature and wavelength from D\'{\i}az-Cordov\'es et al. (1995) and 
Claret et al. (1995) tables. We assumed that there is no third light in this system. 
Computations were done simultaneously for the BVR filters.
Observations in the U filter were discarded due to their bigger scatter.
With such assumptions the convergence was  very slow and we performed more computations 
for a grid of the primary temperature between 6500~K and 10000~K with a 500~K step. It 
soon turned out that for higher temperatures the solutions converged very fast and
we were able to obtain a better fit to observations, with the best solution for the
primary temperature being 7500~K.   
The fits for both models (that for the primary temperature corresponding to the F2 
spectral type (T$_{1}$=6700~K) is denoted by the dashed line and that for 7500~K by the  
solid line) are shown in Fig. 1, while the resulting parameters are presented in 
Table 2. Asterisks denote assumed parameters, while double asterisks mark
those which were not adjusted but computed by the Wilson-Devinney code.

\vspace*{2cm}

\IBVSfig{8.0cm}{5591-f1.eps}{Comparison between observed (points) and theoretical (lines) light curves.}  
\IBVSfigKey{5591-f1.eps}{YY Cnc}{light curve}

A significantly better fit (as measured by the $\chi^{2}$) was obtained for somewhat
higher temperature of the primary component than that corresponding to the F2 spectral
type listed for YY Cnc in the GCVS. 
\eject
Both solutions indicate YY Cnc to be a close system with the
hotter component almost filling its Roche lobe. The secondary component is well inside 
its Roche lobe. The system inclination is close to 90 degrees.
The mass ratio is low, about 0.2 for both solutions, regardless of the assumed 
temperature of the hotter component, as may be indicated by the flat bottom shape of the 
secondary minimum.  However, only spectroscopic observations  could confirm our results 
derived on the basis of photometric measurements only. 

\vskip 5mm
\centerline{Table 2. Results derived from the light curve modelling }
\vskip 3mm
\begin{center}
\begin{tabular}{lrrrr}
\hline
parameter            & model 1 (T$_{\rm 1}$=6700~K)  & model 2 (T$_{\rm 1}$=7500~K) \\
\hline
 configuration                      &  semi-detached     & detached    \\
 phase shift                    &  $-$0.0006$\pm$0.0002    & $-$0.0003$\pm$0.0002\\
 i (degrees)                        &  87.71$\pm$0.10    & 89.45$\pm$1.03    \\
T$_{\rm 1}({\rm K})$                &  * 6700            & * 7500            \\
T$_{\rm 2}({\rm K})$                &  4510$\pm$30       &  4010$\pm$40      \\
$\Omega_{\rm 1} $                   &  2.237$\pm$0.012   & 2.182$\pm$0.014   \\
$\Omega_{\rm 2} $                   &  2.395$\pm$0.030   & 2.256$\pm$0.029 \\
q$_{\rm phot}($m$_{\rm 2}$/m$_{\rm 1})$  & *0.20$\pm$0.01& 0.18$\pm$0.01    \\
\hline
L$_{1}~(B)  $                   & 12.243$ \pm$0.009  &12.864$\pm$0.016  \\
L$_{1}~(V)  $                   & 12.209$ \pm$0.009  &12.819$\pm$0.013  \\
L$_{1}~(R)  $                   & 12.164$ \pm$0.009  &12.715$\pm$0.012  \\
L$_{2}~(B)  $                   &  ** 0.222          & ** 0.051         \\
L$_{2}~(V)  $                   &  ** 0.292          & ** 0.093         \\
L$_{2}~(R)  $                   &  ** 0.362          & ** 0.140         \\
%l$_{\rm 3}$~(B)                     &  * 0.0            & * 0.0           \\
%l$_{\rm 3}$~(V)                     &  * 0.0            & * 0.0           \\
%l$_{\rm 3}$~(R)                     &  * 0.0            & * 0.0           \\
\hline  
$\chi^{2}$                     &  781.5       & 271.6      \\
\hline  
\end{tabular}
\end{center}
\vskip 0.5cm

\noindent
Acknowledgments
\vskip 2mm
\noindent
This work was supported by the Polish National Committee grant No.2 P03D 006 22. 
We would like to thank A. Baran and W. Ogloza for doing the CCD observations on 
January 27/28, 2004.


\vskip 2mm

\references
Claret A., D\'{\i}az-Cordov\'es  J., and Gimenez, A., 1995, {\it A\&AS}, {\bf 114}, 247

D\'{\i}az-Cordov\'es  J., Claret A., and Gimenez A., 1995,  {\it A\&AS}, {\bf 110}, 329

Harmanec P., 1988, {\it BAC}, {\bf 39}, 329

Hoffmeister, C., 1949, {\it Astron. Abh. Erg\"anzungshefte z.d. Astron. Nach.}, {\bf 12}, No. 1, A3

Kinnunen, T., Skiff, B., 2000, {\it IBVS}, No. 4906 

Wilson R.E. 1979, {\it ApJ}, {\bf 234}, 1054

Wilson R.E. 1993, {\it Documentation of Eclipsing Binary Computer Model}

\endreferences


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