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\IBVShead{5726}{12 September 2006}

\IBVStitletl{Photometric Analysis of}{ the W UM\lowercase{a} Type Binary V566 Ophiuchi}


\IBVSauth{De\v{g}\.{i}rmenc\.{i}, \"{O}.L.}

\IBVSinsto{Ege University Observatory, 35100, Bornova, \.{I}zmir, Turkey, e-mail: omer.degirmenci@ege.edu.tr}

\SIMBADobjAlias{V566 Oph}{HD 163611}
\IBVStyp{ CWA }
\IBVSkey{photometry}

\begintext

The variability of V566 Ophiuchi (BD +05\deg3547) was discovered by Hoffmeister (1935). According to 
Binnendijk (1970), the system is an A-type W UMa eclipsing binary. Important photoelectric light curves exist 
in the literature are: $B$, $V$ light curves obtained by Binnendijk (1959), Bookmyer (1969, 1976) and 
Niarchos et al.\ (1993) and ultraviolet ($\lambda$ 2585--3200 band) light curve obtained with IUE satellite 
by Eaton (1986).

The photometric solutions of the system were given by Binnendijk (1965), Bookmyer (1969, 1976), 
Mochnacki \& Doughty (1972), Hutchings \& Hill (1973), Berthier (1975), Nagy (1977), Van Hamme \& Wilson (1985), 
Eaton (1986), Niarchos et al.\ (1993) and Niarchos \& Manimanis (2003). These solutions give the values of 
photometric mass ratio in the range $0.23 < q_{\rm ptm} < 0.24$.

Radial velocities of the system were published by Heard (1965), McLean (1983), Hill et al.\ (1989) and 
Pribulla et al.\ (2006). The first spectroscopic mass ratio of the system was given by Heard (1965) as 
$q_{\rm sp}=0.34$ but McLean (1983) found $q_{\rm sp} = 0.24 \pm 0.03$ which agrees well  with the photometric 
mass ratio derived previously. Later Van Hamme \& Wilson (1985) reanalyzed the radial velocity curves of McLean 
by taking into account the proximity and eclipsing effects and obtained $q_{\rm sp} = 0.216 \pm 0.018$. 
Hill et al.\ (1989) obtained new radial velocity curves based on reticon observations and found 
$q_{\rm sp} = 0.266 \pm 0.006$. 
They obtained the mean spectral type of the system as F2 and mean effective temperature as 6700 K using 
the mean reddening in the field. Lastly, Pribulla et al.\ (2006) obtained $q_{\rm sp} = 0.263 \pm 0.012$ using the BF
(broadening function) extraction technique and the rotational-profile fitting. They also obtained the 
spectral classification of the system as F4V, indicates a slightly later spectral type than that found 
by Hill et al.\ (1989).   

The observations of V566 Oph were carried from June 18 to 21 (four nights) at the T\"{U}BITAK National 
Observatory (TUG) using 40-cm (F/12.5) reflector and on July 24 at the Ege University Observatory (EUO) 
with the 48-cm (F/13) Cassegrain telescope in 1997. The SSP5 photometers were used at both observatory; 
the observations were made in $U$, $B$, $V$, $R$ filters at TUG and in $B$, $V$, $R$ filters at EUO{}. A total of 
201, 232, 234 and 233 observational points were obtained in $U$, $B$, $V$ and $R$ filters, respectively. Differential 
measurements were made using BD+04\deg3553 as a comparison and BD+04\deg3556 as a check star. 
The differential magnitudes, in the sense variable minus comparison, were corrected for atmospheric 
extinction and the times of individual observations were reduced to the Sun's center. The extinction 
coefficients were determined for each night from the observations of the comparison and the color effect on 
the atmospheric extinction was taken into account.

The unpublished differential magnitudes in $U$, $B$, $V$ and $R$ filters are available on request 
from the author. The instrumental differential $U-B$, $B-V$ and $V-R$ color and the $U$, $B$, $V$, $R$ light curves 
of the system are also plotted against the orbital phases in Fig.~1. As seen from the figure the levels of maxima I
and II are almost equal to each other in $B$, $V$, $R$ light curves while in $U$ band the system is slightly brighter 
at maximum II than that at maximum I. 

\IBVSfig{10cm}{5726-f1.ps}{Observed differential (a) color and (b) light 
curves of V566 Oph. 
The upper panel shows the observed $U-B$, $B-V$ and $V-R$ color curves while the bottom panel shows
computed light curves among the observations}
\IBVSfigKey{5726-f1.ps}{V566 Oph}{light curve}

We used the Wilson--Devinney method (Wilson \& Devinney, 1971; Wilson, 1994) to analyze the light curves.  The analyses
were made in MODE 3 which corresponds to over-contact configurations. The temperature of the primary component was taken
from Popper (1980) as 7000 K, corresponding to F2 spectral type (Hill et al., 1989).  The logarithmic limb darkening
coefficients were used in the computations. Assuming a solar chemical composition and $\log g = 4.25$, bolometric and
monochromatic limb darkening coefficients were taken from Claret (2000).  The bolometric albedos $A_h$ and $A_c$ were
set to be equal to 0.5 and synchronized rotation ($F_h = F_c =1.0$) was assumed. The solutions were obtained with model
atmosphere approximation and multiple reflections were assumed. The results are given in Table~1 and the agreements of
the computed curves with the observed light curves are shown in Fig.~1. For comparison, the results obtained by Van
Hamme \& Wilson (1985)  (H\&W85), in which they also used the Wilson--Devinney method, are also presented in Table 1.  
The parameters obtained in the solution are in good agreement with those of van Hamme and Wilson.

\begin{table}
\normalsize
\caption{Comparison of the photometric results with those of Van Hamme \& Wilson (1985)}
\begin{center}
\begin{tabular}{lll}
\hline
Parameter & This study  & H\&W85\\
\hline
  Pshift               & $-0.0015 \pm 0.0002$                          &  0.0001                       \\
  $i$ (degree)         & $80.8 \pm 0.2$                                &  $80.32 \pm 0.17$             \\ 
  $x_h=x_c$            & 0.786 ($U$), 0.770 ($B$), 0.674 ($V$), 0.596 ($R$) & 0.564 ($B$), 0.452 ($V$) \\ 
  $A_h=A_c$            & 0.5                                           &  0.5                          \\ 
  $g_h=g_c$            & $0.39 \pm 0.06$                               &  $0.399 \pm 0.030$            \\ 
  $T_h$                & 7000 K                                        &  7000 K                       \\ 
  $T_c$                & $6902 \pm 19$ K                               &  $6881 \pm 9$ K               \\ 
  $\Omega_h=\Omega_c$  & $2.288 \pm 0.004$                             &  $2.2575 \pm 0.0026$          \\ 
  $q$                  & $0.2389 \pm 0.0007$                           &  $0.23686 \pm 0.00084$        \\ 
  $L_h/(L_h+L_c)_U$    & $0.792 \pm 0.005~(U)$                         &  --                           \\ 
  $L_h/(L_h+L_c)_B$    & $0.792 \pm 0.004~(B)$                         &  $0.7901 \pm 0.0023$          \\ 
  $L_h/(L_h+L_c)_V$    & $0.789 \pm 0.003~(V)$                         &  $0.7879 \pm 0.0019$          \\ 
  $L_h/(L_h+L_c)_R$    & $0.788 \pm 0.002~(R)$                         &  --                           \\
  $r_h$ (mean)         & $0.519 \pm 0.001$                             &  $0.5278 \pm 0.0010$          \\ 
  $r_c$ (mean)         & $0.275 \pm 0.002$                             &  $0.2848 \pm 0.0014$          \\ 
  $\sum W(O-C)^{2}  $  & 0.0020                                        &  --                           \\
\hline
\end{tabular}
\end{center}
\end{table}

Van Hamme \& Wilson (1985) solved the radial velocity curves of McLean (1983) and found the semi-major 
axis of the relative orbit of V566 Oph as $2.788 \pm 0.097~R_\odot$. Using this value and 
the photometric parameters given in Table 1 (column 2), the absolute parameters of the components were obtained 
and presented in Table 2 together with those given by Van Hamme \& Wilson (1985) and Niarchos et al.\ (1993) 
(NEA93). According to the Hipparcos Catalogue, the $B-V$ color of the system is $0.449 \pm 0.025$. So, I have estimated
the errors on the temperatures of the components as about 100 K using the above value in Popper (1980) table. 
The large errors in the absolute parameters are due to uncertainties in the determination of 
radial velocities. If we take into account Kopal's theoretical approach (Kopal, 1978) for W UMa systems, 
$L \sim M^{2{\beta}}$ with $\beta=0.49$, our results seem to be more acceptable.

\begin{table}
\normalsize
\caption{The absolute parameters of the components}
\begin{center}
\begin{tabular}{llll}
\hline
Parameter & Present work  & H\&W85 & NEA93 \\
\hline
    $M_h/M_\odot$         & $1.41 \pm 0.18$  & 1.40  & 1.56  \\ 
    $M_c/M_\odot$         & $0.34 \pm 0.08$  & 0.33  & 0.41  \\ 
    $R_h/R_\odot$         & $1.45 \pm 0.07$  & 1.47  & 1.51  \\ 
    $R_c/R_\odot$         & $0.77 \pm 0.04$  & 0.79  & 0.86  \\ 
    $(T_e)_h$ (K)           & $7000 \pm 100$   & 7000  & --    \\   
    $(T_e)_c$ (K)           & $6902 \pm 100$   & 6881  & --    \\   
    $\log (L_h/L_\odot)$   & $0.65 \pm 0.04$  & 0.66  & 0.62  \\ 
    $\log (L_c/L_\odot)$   & $0.09 \pm 0.04$  & 0.10  & 0.12  \\ 
    $\log g_h$ (cgs)        & $4.26 \pm 0.10$  & --    & --    \\ 
    $\log g_c$ (cgs)        & $4.19 \pm 0.10$  & --    & --    \\ 
\hline
\end{tabular}
\end{center}
\end{table}

\references

Berthier, E., 1975, {\it A\&A}, {\bf 40}, 237

Binnendijk,  L., 1959, {\it AJ}, {\bf 64}, 65

Binnendijk,  L., 1965, {\it AJ}, {\bf 70}, 209

Binnendijk,  L., 1970, {\it Vistas in Astr.}, {\bf 12}, 217

Bookmyer, B.B., 1969, {\it AJ}, {\bf 74}, 1197

Bookmyer, B.B., 1976, {\it PASP}, {\bf 88}, 473

Claret, A., 2000, {\it A\&A}, {\bf 363}, 1081

Eaton, J.A., 1986, {\it AcA}, {\bf 36}, 275

Heard, J.F., 1965, {\it JRASC}, {\bf 59}, 258

Hill, G., Fisher, W.A., Holmgren, D., 1989, {\it A\&A}, {\bf 218}, 152

Hoffmeister, C., 1935, {\it AN}, {\bf 255}, 401

Hutchings, J.B., Hill, G., 1973, {\it ApJ}, {\bf 179}, 539

Kopal, Z., 1978, 
  {\it Astrophysics and Space Science Library}, {\bf 68}, 1,
Dynamics of Close Binary Systems, Dordrecht, D. Reidel Publishing Co.
\ADSBIBCODE{1978assl...68.....K}

McLean, B.J., 1983, {\it MNRAS}, {\bf 204}, 817

Mochnacki, S.W., Doughty, N.A., 1972, {\it MNRAS}, {\bf 156}, 51

Nagy, T.A., 1977, {\it PASP}, {\bf 89}, 366

Niarchos, P.G., Manimanis, V.N., 2003, {\it A\&A}, {\bf 405}, 263

Niarchos, P.G., Rovithis-Livaniou, H., Rovithis, P., 1993, {\it Ap\&SS}, {\bf 203}, 197

Popper, D.M., 1980, {\it ARA\&A}, {\bf 18}, 115

Pribulla, T., Rucinski, S.M., Lu, W., Mochnacki, W., Conidis, G., Blake, R.M., 
DeBond, H., Thomson, J.R., Pych, W., Ogloza, W., Siwak, M., 2006, 
astro-ph/0605357 

Van Hamme, W., Wilson, R.E., 1985, {\it A\&A}, {\bf 152}, 25

Wilson, R.E., 1994, {\it PASP}, {\bf 106}, 921

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

\endreferences

\vfill

\IBVSerratum{5714}

The true shape of the eclipsing binary light curve and the modified,
correct period of V1898 Cyg was already published in IBVS 5699/76
(2005, July 20) by Caton \& Smith \hfill\break
(http://www.konkoly.hu/cgi-bin/IBVS?5699\#76).

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\bigskip

The Editors


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