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4 Photometric solutions

The Wilson & Devinney (1971) method was applied in solving the present light curves of V382 Cygni. This method has been described by many authors. For our solutions, the revised version of the program (Wilson 1992) was used. The method assumes the star surfaces to be equipotentials and computes the light curves as a function of the following parameters: the orbital inclination i, surface potentials $\Omega_{\rm h,c}$, flux-weighted average surface temperatures $T_{\rm h,c}$, mass ratio $q=m_{\rm c} / m_{\rm h}$, unnormalized monochromatic luminosities $L_{\rm h,c}$, linear limb-darkening coefficients $x_{\rm h,c}$, gravity darkening exponents $g_{\rm h,c}$, and bolometric albedos $A_{\rm h,c}$. Throughout this paper, the subscripts h and c refer to the primary (hotter) and secondary (cooler) component, respectively. For the solution of the present light curves, first the independent sets of B and V observations made at two observatories were combined after normalization to form single B and V light curves. The observational points in each B and V light curves were then combined into normal points and weighted directly according to the number of individual observations including in a point. The temperature of the primary component was taken from Morton & Adams (1968) as equal to 36100 K, corresponding to the O6.5 spectral class given by Pearce (1952). This temperature is in accord with the discussion in Hilditch et al. (1996) and in Harries et al. (1997). The linear limb darkening coefficients were taken from Wade & Rucinski (1985), the gravity darkening exponents and the bolometric albedos were set to be equal to 1.0 for radiative atmospheres. These parameters were kept constant during the iterations.

  
\begin{figure}
\includegraphics[width=8cm,clip]{fig2.eps}\vspace*{2mm} 
 \end{figure} Figure 2: The behavior $\Sigma W{\rm (O{-}C)}^2$ as a function of the mass ratio q
The spectroscopic mass ratio of the system was given by Pearce (1952) as $q = m_{\rm c} / m_{\rm h} = 0.88$. Popper & Hill (1991) and Harries et al. (1997) obtained slightly different values for the mass ratio as 0.70 and 0.74, respectively. Therefore, we decided to apply a q-search procedure for determining the photometric mass ratio of the system. For this, the B and V light curves were solved simultaneously by choosing i, $T_{\rm c}$, $\Omega_{\rm h,c}$ $(\Omega_{\rm h} = \Omega_{\rm c})$, $L_{\rm h}$ as adjustable parameters. The analysis was made with contact configuration (i.e. MODE 3). The weighted sum of the squared residuals $[\sum W{\rm (O{-}C)}^{2}]$ for the corresponding mass ratios are shown in Fig. 2. As can be seen from the figure, the lowest value of $[\sum W{\rm (O{-}C)}^{2}]$ around q=0.68 supports the spectroscopic mass ratio (q=0.702) given by Popper & Hill (1991), which was used subsequently as a starting input parameter in the solutions. The convergent simultaneous solutions of the B and V light curves were obtained with the free parameters by iterating until the corrections on the parameters became smaller than the corresponding probable errors. Because of the larger scatter in the U observations, the U light curve has not been included in the analysis. The results of the present analysis are given in Table 2. The theoretical light curves calculated with the final elements obtained from simultaneous solution of the combined B and V light curves are shown in Fig. 3 and 4 among four observational light curves (two in B, and two in V) from two observatories. As seen from the figures, the agreements between theoretical and observational light curves are very good. The over contact configuration of V382 Cygni calculated with the Roche model is shown in Fig. 5. The degree of overcontact is 22%.
  
\begin{figure}
\includegraphics[width=8.8cm]{7633f3.eps} 
\vspace*{1mm}\vspace*{2.5mm} 
 \end{figure} Figure 3: EUO light curves of V382 Cygni. The upper panel shows the theoretical B and V light curves (solid lines) formed by Wilson-Devinney model among the observations obtained at EUO, while the bottom panel shows the ${\rm (O{-}C)}$ differences between the observations and theoretical fits


  
Table 2: The results obtained by the method of Wilson-Devinney

\begin{tabular}
{llll} 
 \hline 
 \noalign{\smallskip} 
 Parameter & $B$\space &...
 ...e & 0.0018 & 0.0021 & 0.0039 \\  
 \noalign{\smallskip} 
 \hline 
 \end{tabular}

The absolute elements of the system were also obtained by combining our photometric results and the spectroscopic elements given by Harries et al. (1997). The results are given in Table 3.


  
Table 3: The absolute elements of V382 Cygni

\begin{tabular}
{ll@{$\pm$}rl@{$\pm$}r} 
 \hline 
 \noalign{\smallskip} 
 & \mul...
 ....13 & \,0.02 & 4.93 & \,0.02 \\  
 \noalign{\smallskip} 
 \hline 
 \end{tabular}

  
\begin{figure}
\includegraphics[width=8.8cm]{7633f4.eps}\vspace*{-5mm} 
 \end{figure} Figure 4: AUO light curves of V382 Cygni. The upper panel shows the theoretical B and V light curves (solid lines) formed by Wilson-Devinney model among the observations obtained at AUO, while the bottom panel shows the ${\rm (O{-}C)}$ differences between the observations and theoretical fits

  
\begin{figure}
\includegraphics[width=8.5cm,clip]{fig5.eps} \end{figure} Figure 5: The Roche configuration of V382 Cygni for q=0.677

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