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\IBVShead{5400}{7 April 2003}

\IBVStitletl{Spectroscopic and Photometric Solution of}{ the Binary System BD+14\deg 5016}

\IBVSauth{Maciejewski, Gracjan$^{1}$; Lig\c{e}za, Piotr$^{2}$; Karska, Agata$^{1}$}

\IBVSinst{Toru\'n Centre for Astronomy, Nicholas Copernicus University, ul. Gagarina 11, 87-100 Toru\'n,  Poland; \\ e-mail: {\tt gm@astri.uni.torun.pl}, {\tt agata@astri.uni.torun.pl}}

\IBVSinst{Astronomical Observatory of the Adam Mickiewicz University, ul. S{\l}oneczna 36, 60-286 Pozna\'n, Poland; \\ e-mail: {\tt piotrl@amu.edu.pl}}

\SIMBADobjAlias{BD+14 5016}{SAO 108714}

\IBVStyp{ spectroscopic binary  }
\IBVSkey{EW - orbital solutions}
\IBVSkey{spectroscopic binaries}

\IBVSabs{We present preliminary solution of the eclipsing binary star}
\IBVSabs{BD+14 5016. The obtained model indicates that the investigated star}
\IBVSabs{is an A-type W UMa system with a hot spot located on the surface of}
\IBVSabs{the more massive component. The system is in a large degree of}
\IBVSabs{overcontact of about 54 percent.}

\begintext

BD+14\deg 5016 (SAO 108714, GSC 01720-00658) was discovered as a
variable of W~UMa type by Maciejewski et al. (2002). It is
recorded in SIMBAD database as a $V$=9\fmm50 magnitude star of F2
spectral type, with $B-V$=0\fmm31. Photometric measurements from
Tycho-2 Catalogue give $B-V$=0\fmm34 which is more consistent with
the spectral type. The binary shows a light curve with an
amplitude slightly smaller than 0.5 mag and with unequal minima
and maxima. Up to the present the classification of variability
type has based on a light-curve morphology, typical for contact
binaries. The presented three spectral observations show lines of
both components and allow to determine preliminary radial velocity
amplitudes and hence mass ratio of component stars. That quantity
together with photometric data allows us to find preliminary
solution of the system.

The spectroscopic observations were collected at the David Dunlap
Observatory (DDO), University of Toronto, with the 1.9 m telescope and the
Cassegrain spectrograph giving a dispersion of 10.8 {\AA}
mm$^{-1}$, corresponding to about 0.2 {\AA} pixel$^{-1}$ or about
12 km s$^{-1}$ pixel$^{-1}$. The spectra were centered at 5185
{\AA} with a spectrum coverage of 210 {\AA}. The exposure time of
20 min was used for all spectra. For reduction standard
IRAF\IBVSfm, procedures were employed. The velocity
determinations were done with broadening function algorithm
(Rucinski 1999) against a sharp-line standard star used as a
template.

\IBVSfoot{IRAF is distributed by the National Optical
Astronomy Observatories, which are operated by the Association of
Universities for Research in Astronomy, Inc., under cooperative
agreement with the National Science Foundation.}

The radial velocity data are listed in Table 1. For every spectrum the Heliocentric Julian Date
of the exposure, phase and radial velocity measurements with errors are given. The phase
was calculated according to ephemeris given in Maciejewski et al. (2002). Because of
light curve peculiarities (described below) the ephemeris for a secondary minimum was
taken. As a template the star HD 89021 with radial velocity of $V_{t}=18.1$ km s$^{-1}$
(Evans, 1967) was used. Radial velocities were transformed to the solar system barycenter.

\begin{center}
{\normalsize {\bf Table 1.} Radial velocities measurements for BD+14\deg 5016} \vskip 2mm
\begin{tabular}{ccrr}
\hline
HJD & Phase & $V_{1}$ [km s$^{-1}$] & $V_{2}$ [km s$^{-1}$]\\
\hline
2452571.698462 & 0.2410 & $-47.1 \pm 1.5$ & $238.7 \pm 0.7$ \\
2452572.629192 & 0.7024 & $62.1 \pm 0.5$ & $-219.0 \pm 1.2$ \\
2452576.711157 & 0.1116 & $-44.6 \pm 0.2$ & $155.8 \pm 1.2$ \\
\hline
\end{tabular}
\end{center}

\clearpage

\IBVSfig{9cm}{5400-f1.eps}{Radial velocities of BD+14\deg 5016 plotted versus
orbital phase.}
%%\IBVSfigKey{5400-f1.eps}{BD+14 5016}{radial velocity curve}

The radial velocity orbits were solved by least squares fitting of a sinusoid for each
component from the form $V(\phi)=\gamma+K_{i}$sin$\phi$, with $\phi$ being the phase,
$\gamma$ -- the velocity of system's barycenter and $K_{i}$ -- the velocity amplitude. The
results are shown in Figure~1. The sine curves and the straight line denote
circular-orbit fits and the average radial velocity $\gamma$, respectively. The derived
orbital elements: the velocity amplitudes $K_{1}$ and $K_{2}$, average radial velocity
$\gamma$, mass ratio $q$, orbit dimensions $a$, $a_{1}$, $a_{2}$ and component masses
$m_{1}$, $m_{2}$ are presented in Table 2.

\begin{center}
{\normalsize {\bf Table 2.} Spectroscopic orbital elements of BD+14\deg 5016} \vskip 2mm
\begin{tabular}{lrc}
\hline
Element & & Value \\
\hline
$K_{1}$ & [km s$^{-1}$]            & $59.2 \pm 7.9$ \\
$K_{2}$ & [km s$^{-1}$]            & $234.2 \pm 0.2$ \\
$\gamma$ & [km s$^{-1}$]           & $4.2 \pm 0.8$\\
$q=m_{2}/m_{1}$&                   & $0.253 \pm 0.034$\\
$a\sin i$ & [R$_{\odot}$]          & $3.69 \pm 0.11$ \\
$a_{1}\sin i$ & [R$_{\odot}$]      & $0.74 \pm 0.10$ \\
$a_{2}\sin i$ & [R$_{\odot}$]      & $2.947 \pm 0.003$ \\
$m_{1}\sin^3$$i$ & [M$_{\odot}$]  & $1.33 \pm 0.08$ \\
$m_{2}\sin^3$$i$ & [M$_{\odot}$]  & $0.34 \pm 0.12$ \\
\hline
\end{tabular}
\end{center}

The photometric data were adopted from Maciejewski et al. (2002). The observations were
obtained on 16 nights during September-November 2002 with the 135 mm f/2.8 semi-automatic
CCD camera operating at the Piwnice Observatory of the Nicholas Copernicus University.
From the original CCD $V$-band light curve a few bad points have been excluded. The final
light curve, composed of 255 data points marked with crosses, is plotted in Figure 2. The
different brightness maxima heights suggest the presence of a spot on the surface of one
of the components (O'Connell effect). The primary minimum and brighter maximum are
shifted in phase and falls in phase 0.98 and 0.23, respectively. The brighter maximum
seems to be relatively broader at the side of primary minimum.

The data were analyzed with the Wilson-Devinney (WD) light and radial velocity curves
analysis code (Wilson and Devinney, 1971; Wilson, 1979, 1990). The synthetic light curve
was computed using the light curve (LC) program and the differential corrections
procedure was performed with the DC program. WD software was operated in Mode 3. The
temperature of the primary component $T_1$ was set at $6900$ K, typical for dwarfs of F2
spectral type. That value places the primary below a boundary of 7200 K between stars
with convective and radiative envelopes, therefore the convective model was finally
considered. We also developed a radiative model, however the obtained solution turned out
to be less consistent with data. Standard values of bolometric albedos, $A_1=A_2=0.5$,
and gravity darkening coefficients, $g_1=g_2=0.32$ (Lucy, 1967), for convective envelopes
were used. Limb darkening values for logarithmic law were interpolated from van Hamme's
tables (van Hamme, 1993). The central wavelength for a near-Johnson $V$ filter was assumed
to be 5400 {\AA}. Because of the light-curve peculiarities we assumed a spot solution
from the beginning.

\IBVSfig{9cm}{5400-f2.eps}{Observed (crosses) and computed (solid curve) light
curve of BD+14\deg 5016.}
%%\IBVSfigKey{5400-f2.eps}{BD+14 5016}{light curve}

The calculated final light curve is displayed in Figure 2 (solid curve). The best results
were obtained with a model including a hot spot located on the surface of the more
massive component, near the neck connecting both stars. This superluminous region may be
interpreted as a place where the gas stream from the secondary component strikes the
surface of the primary. The final solution parameters are listed in Table 3 and the
geometric representation of the model is shown in Figure 3. The system is in a large
degree of overcontact of about 54\%. The primary minimum is a transit indicating that
BD+14\deg 5016 is an A-type W UMa system. That is in agreement with its early spectral
type.

\begin{center}
{\normalsize {\bf Table 3.} Solution parameters of BD+14\deg 5016} \vskip2mm
\begin{tabular}{|lc|lc|}
\hline
Parameter  & Value & Parameter & Value\\
\hline
$g_1 = g_2$           & $0.32 ^\dagger$    & $r_1$ (pole)    & $0.493$  \\
$A_1 = A_2$           & $0.50 ^\dagger$    & $r_1$ (side)    & $0.540$  \\
$x_1 = x_2 (V)$       & $0.694 ^\dagger$   & $r_1$ (back)    & $0.573$  \\
$y_1 = y_2 (V)$       & $0.286 ^\dagger$   & $r_2$ (pole)    & $0.275$  \\
$x_1 = x_2$ (bol)     & $0.638 ^\dagger$   & $r_2$ (side)    & $0.290$  \\
$y_1 = y_2$ (bol)     & $0.252 ^\dagger$   & $r_2$ (back)    & $0.356$  \\
$i$ [\deg]            & $72.6 \pm 0.3$     & $M_1$ [M$_{\odot}$] & $1.53$   \\
$T_1$ [K]             & $6900 ^\dagger$    & $M_2$ [M$_{\odot}$] & $0.39$   \\
$T_2$ [K]             & $6571 \pm 25$      & $R_1$ [R$_{\odot}$] & $2.076$   \\
$\Omega_1 = \Omega_2$ & $2.255 \pm 0.005$  & $R_2$ [R$_{\odot}$] & $1.181$   \\
Spot Latitude  [\deg] & $90 ^\dagger$      & $L_1/(L_1+L_2)$ & $0.791 \pm 0.003$  \\
Spot Longitude [\deg] & $333 \pm 1$        & $L_2/(L_1+L_2)$ & $0.209 \pm 0.003$  \\
Spot Radius [\deg]    & $7.8 \pm 0.4$      & M$_{bol1}$ [mag]& $2.43$  \\
Spot Temp. Factor     & $1.55 \pm 0.05$    & M$_{bol2}$ [mag]& $3.87$  \\
\hline
\end{tabular}

{\normalsize $^\dagger$ assumed and unadjusted}
\end{center}

\IBVSfig{4cm}{5400-f3.eps}{A three-dimensional model of BD+14\deg 5016 for phases 0.1 and 0.25.}
%%\IBVSfigKey{5400-f3.eps}{BD+14 5016}{model}

The authors wish to thank Dr. Andrzej Niedzielski, Dr. Maciej Miko{\l}ajewski and Dr. Stanis{\l}aw Zo{\l}a for helpful suggestions.

\references

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%Changed: Wed Jun 15 11:11:10 MEST 2005

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%Changed : Wed Jun  1 11:07:11 MEST 2005

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\endreferences

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