\documentstyle[twoside,ibvs2,ibvst,epsf]{article} 
\begin{document}

\IBVShead{5207}{28 November 2001}

\IBVStitle{NSV\,12223: a New W UM\lowercase{a} Eclipsing Binary}

\IBVSauth{Vandenbroere, J.$^1$; Pigulski, A.$^2$; Van Cauteren, P.$^{1,3}$}

\IBVSinst{GEOS (Groupe Europ\'e‚en d'Observations Stellaires), Parc de Levesville,
     23, F--28300 Bailleau l'Ev‰\"eque, France, e-mail: j.vandenbroere@skynet.be}
\IBVSinst{Wroc\l aw University Observatory, Kopernika 11, 
     51-622 Wroc\l aw, Poland, e-mail: pigulski@astro.uni.wroc.pl}
\IBVSinst{Beersel Hills Observatory, Laarheidestraat 166, B--1650 Beersel, Belgium,
     e-mail: Paul.VanCauteren@pi.be}

\SIMBADobjAlias{NSV 12223}{GSC 4456-1244}
\IBVStyp{  EW  }
\IBVSkey{photometry}
\IBVSabs{New B and V band photometry of NSV 12223 reveals that it is an}
\IBVSabs{eclipsing binary of the W UMa-type.  We give the ephemeris for the}
\IBVSabs{primary minimum and analyze the light curve by means of the} 
\IBVSabs{Wilson-Devinney code.}

\begintext

Strohmeier (1958) discovered the variability of NSV\,12223 (= BV\,238 = 
GSC\,4456\,1244) on photographic plates taken from 1932 to 1939.  He mentioned 
variations going from magnitude 12.0 to 12.5 (photographic) and a probable 
eclipsing type. The star is situated in Draco at 19$^{\rm h}$34$^{\rm m}$31$^{\rm s}$; 
+74$^{\rm o}$03$^\prime$ (J2000).

Vandenbroere (2000) published the results of period searches made on her 151 
first visual estimates of the star in a Note Circulaire of GEOS.  She was not 
yet able to discriminate in favour of the actual period between the peaks of 
the periodogram and she called upon CCD measurements.

P.~Van Cauteren obtained 195 $V$ and 26 B CCD measurements of the star at his private 
observatory using a 0.40-m telescope.  He used an ST7E camera and the MIRA 
Aperture Photometry software (produced by Axiom Research Inc.).  
GSC\,4456\,1751 was used as comparison star and GSC\,4457\,16 was the check star. The observations were left in the instrumental system. 
A PDM search on the $V$ measurements showed that the orbital period of NSV 12223 
is around 0.350376~d and that the star is an EW-type eclipsing binary with minima 
slightly different in depth (see Fig.~1).  The amplitudes of the light 
variations in $V$ are of 0.51~mag between the deeper minimum and its preceding 
maximum, and of 0.43~mag between the two other extrema.  The EW type is in perfect 
agreement with the differential $B-V$ indices which are nearly constant except 
for a very slight reddening during the two minima. 

A.~Pigulski analyzed the light curve of NSV\,12223 obtained from the CCD 
observations made by P.~Van Cauteren. The $V$ data were phased with a rough 
value of the period and used with the Wilson-Devinney (WD) 
code (Wilson \& Devinney 1971) to get a synthetic light curve which reproduces 
well the observations.  In the next step, this synthetic light curve was 
fitted separately to the data carried out on each of the three nights of 
observations.  During the fit, the time of minimum was derived as the 
only parameter.  The results of the fit are shown in Fig.~1.  This procedure, 
taking into account all the points in the light curve, allows to derive the 
time of minimum light even when there are no observations at minimum at all.  
So, three times of primary minima could be derived.

To these three times of primary minima, we could add ten instants determined 
from the visual estimates of J.~Vandenbroere (see Table 1). The relative
weights for the three CCD times of minimum were calculated according to the
inverse square of their r.m.s.~errors and were rescaled to be a few times 
larger than those derived from visual data.   A linear 
regression of all times of minimum gives the following ephemeris (the number
in parentheses denotes the r.m.s.~error of the last digit):
\begin{equation}
\hbox{T$_{\rm min}$ I = HJD}\,2451470.159(2) + 0.350374 (2) \times E,
\end{equation}
\noindent where $E$ is the number of cycles elapsed from the initial epoch.

\IBVSfig{6.5cm}{5207-f1.ps}{Differential (with respect to GSC\,4456\,1751) 
CCD $V$ measurements of NSV\,12223 (dots) with synthetic 
light curve (solid line) fitted to derive the times of minimum for the three 
nights.}

\centerline{Table 1. Times of minimum light of NSV\,12223}
\vskip 3mm
\begin{center}
\begin{tabular}{cclcrl}
\hline\noalign{\smallskip}
& Type of & \multicolumn{1}{c}{Time of minimum} && Epoch & O $-$ C\\
Observer & photometry & \multicolumn{1}{c}{HJD 2400000.+} &Weight&
    \multicolumn{1}{c}{$E$} & \multicolumn{1}{c}{[d]}\\
\noalign{\smallskip}\hline\noalign{\smallskip}
VBR & visual & 51470.332(5) & 1 & 0.5 & $-$0.002 \\
VBR & visual & 51757.462(5) & 1 & 820.0 & $-$0.003 \\
VBR & visual & 51762.376(5) & 1 & 834.0 & +0.006 \\
VBR & visual & 51769.381(5) & 1 & 854.0 & +0.003 \\
VBR & visual & 51779.536(5) & 1 & 883.0 & $-$0.003 \\
VBR & visual & 51798.453(5) & 1 & 937.0 & $-$0.006 \\
PVC & CCD & 51901.4691(6) & 8 & 1231.0 & +0.0003 \\
PVC & CCD & 51907.4245(11) & 2 & 1248.0 & $-$0.0007 \\
PVC & CCD & 51922.4904(9) & 4 & 1291.0 & $-$0.0008 \\
VBR & visual & 52136.397(5) & 1 & 1901.5 & +0.003 \\
VBR & visual & 52145.500(5) & 1 & 1927.5 & $-$0.004 \\
VBR & visual & 52146.379(5) & 1 & 1930.0 & $-$0.001 \\
VBR & visual & 52167.401(5) & 1 & 1990.0 & $-$0.001 \\
\noalign{\smallskip}\hline\noalign{\medskip}
\end{tabular}

VBR = J.\,Vandenbroere, PVC = P.\,Van Cauteren.  HJD is given with
an estimated accuracy of the last digit(s).
\end{center}

In order to obtain the parameters of the binary system with the WD code, 
the CCD data (both in $B$ and $V$) were first phased with the new value of the 
orbital period (Eq.~(1)).
In the case of NSV\,12223, we have $B$ and $V$ light curves and we suspect that the 
system is a contact binary.  In Fig.~1, we can see that the maxima are not 
equal (O'Connell effect).  This means that there is a spot (or spots) on the 
side surface of one of the stars.  Because we have only 26 B CCD measurements,
it is rather impossible to adjust accurately the four parameters of a 
spot.  Therefore, it was assumed that the spot resides in star 1 (that 
one which is eclipsed near phase 0, at primary, deeper eclipse).  By trial 
and error, we found roughly the latitude (90$^{\rm o}$), longitude (310$^{\rm o}$) 
and the angular radius (25$^{\rm o}$) of the spot.  The only spot parameter 
adjusted was the temperature factor.
 
Furthermore, gravity darkenings (0.32), bolometric albedos 
(0.5), and limb darkening coefficients have been taken from tables of Van Hamme 
(1993). The average temperature of star 1, which is roughly correlated 
to the orbital period, was assumed to be $T_1$ = 5500~K.

The following parameters of NSV\,12223 were next iterated:
\begin{itemize}
\item phase shift, $\phi$,
\item orbital inclination, $i$,
\item average surface temperature of star 2, $T_2$,
\item surface potential, $\Omega$ = $\Omega_1$ = $\Omega_2$,
\item relative monochromatic luminosity for star 1, $L_1$,
\item temperature factor for the spot.
\end{itemize}

For a contact binary, it is practically the mass ratio $q = M_2/M_1$ which 
determines the geometry of the system.  The best solution is found by checking 
the changes of the weighted sum of squares of residuals as a function of the 
assumed mass ratio $q$ (see Fig.~2).  We can see that in a wide range of $q$ 
(between 0.7 and 1.8) all fits give practically the same residuals and 
therefore are equally good.  This means that we cannot accurately determine the mass 
ratio, and thus say which star is bigger.  This is the consequence of
the fact that the eclipses are partial.
\IBVSfig{6.5cm}{5207-f2.ps}{The weighted sum of squares of the residuals (SSR) 
taken from the best fit, plotted against the assumed value of the mass ratio, $q$.}

Nevertheless, it appears that some parameters which were iterated do not change 
considerably in the best solutions for 0.7 $< q <$ 1.8.  First of all, 
the inclination 
angle, $i$, equals to 72\fdeg 0 $\pm 0\fdeg 5$, and the average surface temperature 
of star 2, $T_2$, is lower by about 110 $\pm$ 10 K in comparison with $T_1$. 
Finally, the overfill 
factor equals to about 5--7\%, depending on $q$. This is quite typical for 
W~UMa systems.
In Fig.~3 we show one of the best solutions, that with $q$ = 1.4.  
The standard deviation of the residuals from the fit is 0.0097~mag for B and 
0.0082~mag for $V$-filter observations.

\IBVSfig{10cm}{5207-f3.ps}{The differential light curve of NSV\,12223 in B (circles) and $V$ 
(dots) filter compared to the best fit with $q$ = 1.4 (continuous line).  
The light curves shown with thin lines are those if there were no spot.  
Lower panel shows the residuals from the fit (the ordinate is in scale).}

Concluding, NSV\,12223 is a contact binary of the W~UMa type with 
orbital period given by Eq.~(1).  The eclipses are partial.  The inclination 
of the system is 72\fdeg 0 $\pm 0\fdeg 5$.  Mass ratio is in the range between 
0.7 and 1.8.
There is a spot at the surface of one of the stars resulting in a small O'Connell
effect.  Moreover, star 2 is cooler than star 1 by about 110~K.

\bigskip
{\bf Acknowledgement:} P.~Van Cauteren is grateful to the Royal Observatory of 
Belgium for putting at his disposal material acquired by project G.0265.97 
of the Fund for Scientific Research (FWO)-Flanders (Belgium).

\references

Strohmeier, W., 1958, {\it KVB}, Band II, {\bf Nr.~24}

Vandenbroere, J., 2000, {\it Note Circulaire GEOS NC} {\bf 923}

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

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

\endreferences

\end{document}
