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\IBVShead{5812}{8 January 2008}

\IBVStitletl{The First Light Curve Analysis of Two Overcontact}{ Binaries: EY C\lowercase{as} and NO V\lowercase{ul}}

\IBVSauth{Zasche, P.$^1$; Wolf, M.$^1$; Kotkov\'a, L.$^2$}

\IBVSinst{Astronomical Institute, Faculty of Mathematics and Physics, 
Charles University Prague, CZ-180 00 Praha~8, V~Hole\v{s}ovi\v{c}k\'ach~2, 
Czech Republic, e-mail: zasche@sirrah.troja.mff.cuni.cz} 
\IBVSinst{Astronomical Institute,
Academy of Sciences, CZ-251 65 Ond\v{r}ejov, Czech Republic}

\SIMBADobj{EY Cas}
\SIMBADobj{NO Vul}

\begintext

\vspace*{-0.8cm}

Precise photometric observations of the two neglected and
faint eclipsing binaries were carried out. All CCD measurements
were obtained by the 65-cm telescope at the Ond\v{r}ejov
observatory, using Apogee AP-7 and Moravian
Instruments\IBVSfm\ G-2 3200 ME CCD camera, only R filter was used. The 
observations were carried out from 2003 to 2007. New times of minima were also
derived using the Kwee-van Woerden (1956) method, 4 and 3 for
EY~Cas and NO~Vul, respectively (see Table 1.). \vskip 1mm

\IBVSfoot{see {\tt http://ccd.mii.cz/}}

\begin{table}[!hr]
\centerline{{\bf Table 1.} New times of minima. Epochs and $O-C$ values
correspond to the linear} \centerline{ephemeris. N denotes the
number of points, from which the minimum was computed.}
\begin{center}
\begin{tabular}{cclrrc}
 \hline
  Star  &  HJD        & Error (d) & Epoch & $O-C$ (d) & N \\
\hline
EY~Cas & 2453394.2190 &  0.0003 &$-$0.5   & 0.0022 & 48 \\
EY~Cas & 2453579.5457 &  0.0004 &  384.0  & 0.0030 & 46 \\
EY~Cas & 2454000.3222 &  0.0001 &  1257.0 & 0.0006 & 77 \\
EY~Cas & 2454027.5536 &  0.0001 &  1313.5 &$-$0.0005 & 85 \\ \hline
NO~Vul & 2453657.2381 &  0.0003 & 19718.5 & 0.0003 & 29 \\
NO~Vul & 2453934.3847 &  0.0003 & 20466.0 &$-$0.0001 & 41 \\
NO~Vul & 2454364.2876 &  0.0002 & 21625.5 & 0.0007 & 106 \\
\hline
\end{tabular}
\end{center}
\end{table}

{\bf EY~Cas} (= GSC 03660-00401,
R.A.=00\hr03\mm23\sec, Decl.=+57\deg44\arcm54\arcs, J2000.0, \linebreak$V_{max}
= 13.9$~mag) is a W~UMa-type eclipsing binary system, with
orbital period of about 0.48~days. The photometric variability of
the star was discovered by C. Hoffmeister in 1936. Distance,
spectral type as well as physical parameters of the components
are known only with a low confidence level.

The {\sc Phoebe} programme (see e.g. Pr\v{s}a \& Zwitter, 2005),
based on the Wilson-Devinney algorithm (Wilson \& Devinney, 1971),
was used. The temperature of the secondary component was fixed at
the value $T_2 = 6700$~K, according to the spectral type of 
F2 + F1.5 assumed by Svechnikov \& Kuznetsova (1990). The results
of the fit are presented in Table~2 and the light-curve with the
theoretical fit is plotted in Fig.~1. The 3-D model of the system
is in Fig.~2. Nevertheless, further observations are needed,
spectroscopy in particular, to reveal the spectral types of
the components and their respective masses.

\vspace*{-0.1cm}

\IBVSfig{55mm}{5812-f1.eps}{The R light curve of EY Cas, the solid
curve stands for the model fit (with the parameters from Table 2),
while the points represent the observed data.}
\IBVSfigKey{5812-f1.eps}{EY Cas}{light curve}

\vspace*{-0.1cm}

 One can see some distortion of the light curve near phase
$-$0.15 and larger scatter near its maxima, which could be caused by
the presence of spots, or by possible O'Connell effect. But these
hypotheses could be confirmed only by another, more detailed
analysis.

\IBVSedata{5812-t1.txt} 
\IBVSdataKey{5812-t1.txt}{EY Cas}{minima/maxima times}

The period analysis of EY~Cas was performed using 31 times of
minima (listed in {\tt 5812-t1.txt}, available through the IBVS website), 
the first one is from 1935. Four
new minima were observed, see Table~1. The linear light elements
suitable for the observations are the following
\begin{eqnarray}
 \mathrm{HJD \,\, Min{\,}I} = 24\;53394.4578 \!\! &+& \!\! 0.\!\!^{\rm d}48199184 \cdot {\rm E}.\\[-0.5mm]
 \pm \, 0.\!0009 \!\! &\pm& \!\! 0.\!\!^{\rm d}00000023
\nonumber
\end{eqnarray}

From a numerical point of view, there is a problem with fitting
the temperature. The final fit remains nearly the same for a very
wide range of values (6200~K $ < T_1 <$ 8300~K). In principle, the
temperature could not be derived only on the basis of observations
in one filter. The mass ratio $q$ is also hardly derivable only
from the photometry.

\begin{table}[!hr]
\centerline{{\bf Table 2.} The physical parameters of EY Cas and NO
Vul.\IBVSfm}
\begin{center}
 \begin{tabular}{ccc} \hline
               &  EY Cas            &     NO Vul \\
 Parameter     & \multicolumn{2}{c}{Value} \\
 \hline
 $i$ [deg]     & 77.61 $\pm$ 0.35   & 80.90 $\pm$ 0.32 \\
 $q_{ph} = M_2/M_1$ & 0.79 $\pm$ 0.10 & 0.71 $\pm$ 0.10 \\
 $r_1 / r_2 $  & 1.09               & 1.15 \\
 $T_1/T_2$     & 1.05               & 1.13  \\
 $L_1 / L_2$   &  1.17 $\pm$ 0.11   & 1.78 $\pm$ 0.16 \\
 $\Omega$      &  3.11 $\pm$ 0.20   & 3.08 $\pm$ 0.18 \\
 $f$           &  0.655             & 0.429 \\ \hline
 \end{tabular}
\end{center}
\end{table}

\vspace*{-0.2cm}

\IBVSfoot{$T_i$, $r_i$, and $L_i$ denote the temperature,
relative radius and luminosity for primary and secondary,
respectively. $f$ stands for the fill-out factor and $\Omega$ for
the modified Kopal potential. %Total luminosity is $L_{12} = L_1 + L_2$.
The temperatures $T_2$ were fixed, see the text. The ``Overcontact
binary'' mode was used for computing and the eccentricity was set
to 0 (circular orbit). The limb-darkening coefficients were
interpolated from van~Hamme's tables (see van~Hamme, 1993). The
values of gravity brightening and bolometric albedo coefficients
were set at their suggested values for convective atmospheres (see
Lucy, 1968), i.e. $G_1 = G_2 = 0.32$, $A_1 = A_2 = 0.5$. Also the
synchronous rotation was assumed for each star ($F_1 = F_2 =
1.0$). No third light was assumed: $l_3 = 0$.}

The basic physical parameters (e.g. the individual masses) of the
stars could not be derived only from the photometry. Therefore,
detailed spectroscopic analysis is needed. Nevertheless, the
results from the light-curve fit are in agreement with other
analyses of similar overcontact systems. The high degree of the
overcontactness $f = 0.66$ is comparable with other similar
systems, such as GR~Vir ($f = 0.78$, see Qian \& Yang, 2004), or
IK~Per ($f = 0.60$, see Zhu et al., 2005).

 \vspace{4mm}
 \IBVSfig{34mm}{5812-f2.eps}{The 3-D plots of EY\,Cas\,(left) and NO\,Vul\,(right) at the phase 0.25, primary is on the left.}
\IBVSfigKey{5812-f2.eps}{EY Cas ; NO Vul}{}

\vspace*{-0.2cm}

{\bf NO Vul} (R.A. = 19\hr34\mm38\sec, Decl.=+20\deg37\arcm14\arcs,
$V_{max} = 12.83~$mag) is an eclipsing binary of W~UMa type. 
The orbital period of NO~Vul is about 0.37~days and the depth of
the primary minimum is about 0.7~mag in R filter. Its photometric
variability was discovered by Kalv \& Leis (1973). However, the
basic physical parameters of the system have not been derived so
far. There is only one analysis of the period variations by Qian
\& Ma (2001).

The light curve was also analyzed by the {\sc Phoebe} code, the
same fixed values were adopted as in the case of EY~Cas. 
The light curve with its solution
is plotted in Fig.~3 and the parameters are given in Table~1. From the
spectral types F8 + F8.5 derived by Svechnikov \& Kuznetsova
(1990), we assumed the temperature $T_2 = 6100$~K (see e.g.
Harmanec, 1988).

 \vspace{-5mm} 
\IBVSfig{55mm}{5812-f3.eps}{The R light curve of NO Vul, parameters of the fit are in Table 1.} 
\IBVSfigKey{5812-f3.eps}{NO Vul}{light curve}
\vspace{-9mm}

\IBVSedata{5812-t2.txt}
\IBVSdataKey{5812-t2.txt}{NO Vul}{minima/maxima times}

Period analysis was done, using 108 times of minima,
listed in {\tt 5812-t2.txt} (available through the IBVS website). 
A few new times of minima were observed given in Table~1. 
The $O-C$ diagram is plotted in Fig.~4, where the solid
line represents the linear ephemeris, suitable for future
observations,
\begin{eqnarray}
 \mathrm{HJD \,\, Min{\,}I} = 24\;46346.3049 \!\! &+& \!\! 0.\!\!^{\rm d}37076516 \cdot {\rm E}.\\[-0.5mm]
 \pm \, 0.\!0015 \!\! &\pm& \!\! 0.\!\!^{\rm d}00000018
\nonumber
\end{eqnarray}

The previous period analysis (Qian \& Ma, 2001), indicated
quadratic term in the ephemeris, which describes the times of minima
since 2001 (see the dash-dotted line in Fig.~4). Nevertheless, the
recent times of minima deviate from this fit. Much better
explanation of the period variation could be done using a
light-time effect (see e.g. Mayer, 1990), this fit is
plotted as a dashed line in Fig.~4. The period of such variation is
about 64~years, with the semiamplitude of about 0.016~days and
an eccentricity of 0.41. A predicted third body could have a minimum
mass of about 0.36~M$_\odot$, corresponding to spectral type about M2
(according to Harmanec, 1988), and the contribution of the third
light is only about 1\%, which is undetectable in the present
analysis. Further minimum observations in the upcoming years could
prove or reject this hypothesis.

\IBVSfig{58mm}{5812-f4.eps}{The $O-C$ diagram of NO Vul, the dots
denote the primaries, the circles the secondaries, small ones for
visual and bigger ones for the CCD and photoelectric
measurements, respectively. For the explanation of the lines, see
the text.}
\IBVSfigKey{5812-f4.eps}{NO Vul}{O-C diagram}

\vspace*{-0.9cm}

\noindent \small  {\bf Acknowledgements:} This investigation was
supported by the Grant Agency of the Czech Republic, grants No.
205/04/2063 and No. 205/06/0217. We also acknowledge the support
from the Research Program MSMT 0021620860 of the Ministry of
Education. This research has made use of the SIMBAD database,
operated at CDS, Strasbourg, France, and of NASA's Astrophysics
Data System Bibliographic Services.

\large

\vspace*{-0.7cm}

\references

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

Hoffmeister, C., 1936, {\it AN}, {\bf 259}, 37

Kalv, P. \& Leis, L., 1973, {\it Astron.Tsirk}, {\bf 793}, 8

Kwee, K.K. \& van Woerden, H., 1956, {\it BAN}, {\bf 12}, 327

Lucy, L.B., 1968, {\it ApJ}, {\bf 151}, 1123

Mayer, P., 1990, {\it BAICz}, {\bf 41}, 231

Pr\v{s}a, A., \& Zwitter, T. 2005, {\it ApJ}, {\bf 628}, 426

Qian, S. \& Ma, Y., 2001, {\it PASP}, {\bf 113}, 754

Qian, S.-B. \& Yang, Y.-G., 2004, {\it AJ}, {\bf 128}, 2430

Svechnikov, M.A. \& Kuznetsova, E.F., 1990, {\it Approximate elements of eclipsing binaries}, Izd-vo Ural'skogo universiteta, Sverdlovsk
\ADSBIBCODE{1990kpfa.book.....S}

van Hamme, W., 1993, {\it AJ}, {\bf 106}, 2096

Wilson, R. E. \& Devinney, E. J., 1971, {\it ApJ}, {\bf 166}, 605

Zhu, L.-Y.; Qian, S.-B.; Soonthornthum, B. \& Yang, Y.-G., 2005, {\it AJ}, {\bf 129}, 2806

\endreferences

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