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\IBVShead{5689}{2 March 2006}
\IBVStitletl{Photometric Analysis of the}{ Contact Binary V513 Herculis}
\IBVSauth{Byboth, K.N.$^2$; Markworth, N.L.$^1$}
\IBVSinst{Department of Physics and Astronomy Stephen F. Austin State University, Nacogdoches, TX 75962-3044 USA; e-mail:nmarkworth@sfasu.edu}
\IBVSinst{Texas A\&M University Physics Department, College Station, TX 77843-4242 USA; e-mail:krisbyboth@tamu.edu}
\SIMBADobjAlias{V513 Her}{SV* Son 5300}
\begintext
\vspace*{-0.8cm}
Hoffmeister (1959) discovered variability in the light of V513
Herculis (Son 5300, GSC~2076-01720, $\alpha$(2000) = 17\hr 40\mm
22\sec, $\delta$(2000) = $+$24\deg 15\arcm 47\arcs) and classified
it as a W~UMa system. He observed 50 times of minimum (Hoffmeister
1960) and gave an ephemeris of 2430024.654 + 0.3037689 $\cdot$ E.
Two times of minimum by Krajci (see Nelson 2004) in 2004 complete
the list of previous observations. Apparently, no other
observations have been published prior to 2005 and no study of the
light curve has ever been done.
Photometric observations of V513 Her were made on seven nights
between June 18 and August 19, 2004, using the 46-cm
Ritchey-Chr\'{e}tien telescope with attached Santa Barbara
Instrument Group (SBIG) ST-8XE CCD camera equipped with standard
Johnson UBVRI filters. An SBIG ST-4 camera attached to the finder
served as the tracking camera.
The images were calibrated and the magnitudes extracted using
standard image reduction procedures with MIRA Pro (Mirametrics
Inc.). Differential magnitudes in the natural system are available
upon request of author NLM. Approximately 170 observations were made
in each of the R, I, and V filters of V513 Her.
The comparison and check star data for V513 Her were as follows:
comparison star (C)(GSC 02076-01849, $\alpha$(2000) = 17\hr 40\mm
18\fsec6, $\delta$(2000) = $+$24\deg 16\arcm 3\farcs6); check star
(K1) (GSC 02076-01976, $\alpha$(2000) = 17\hr 40\mm 24\fsec74,
$\delta$(2000) = $+$24\deg 15\arcm 11\farcs2); and check star (K2)
(GSC 02076-01885, $\alpha$(2000) = 17\hr 40\mm 25\fsec1,
$\delta$(2000) = $+$24\deg 16\arcm 43\sec). These stars are labeled
in Figure 1.
We observed two primary and three secondary minima for V513 Her. The
mean epochs of minimum light were determined from these eclipses
using the bisection of chords. Table~1 contains the average times of
minima for the three observed colors. The five minima of Table 1,
together with the previously minima yield the following new
ephemeris.
\begin{equation}
{\rm HJD\ Tmin\ I} = 2453282.58088\ + 0.3037690\ {\rm d} \times {\rm E}.
\end{equation}
\vspace*{-0.4cm}
\IBVSfig{7.5 cm}{5689-f1.eps}{Finder chart V513 Her}
\IBVSfigKey{5689-f1.eps}{finding chart}{V513 Her}
\begin{table}[!ht]
\centerline{Table 1. Times of Minimum Light} \vskip 3mm
\begin{center}
\begin{tabular}{ccc}
\hline \hline
JD Hel. & Min & O-C\\
2450000+ & & (days) \\
\hline
3175.8112 & II & 0.0023\\
3188.7198 & I & 0.0008 \\
3192.6689 & I & 0.0009\\
3193.7325 & II & 0.0013\\
3200.7194 & II & 0.0015\\
\hline
\end{tabular}
\end{center}
\end{table}
\vskip 0.5cm
We have calculated models for the light curves of V513 Her using the
Wilson-Devinney code (Wilson 1993). Common parameters that were
varied include inclination of the orbit ({\it i}), temperature of
the secondary star ($T_2$), modified potential of the stars
($\Omega_1$ = $\Omega_2$), mass ratio (q), relative luminosity of
the primary star ($L_1$), and monochromatic linear limb darkening
coefficient of the primary star ($x_1$ = $x_2$). We assumed the star
to be a contact binary system (Mode 3). The values of gravity
brightening and bolometric albedo were set at their suggested values
for convective atmospheres (Lucy 1968), i.e., $G_1$ = $G_2$ = 0.32,
$A_1$ = $A_2$ = 0.5. Synchronous rotation was assumed for each star
($F_1$ = $F_2$ = 1.0). Linear limb darkening coefficients were
initialized at the model atmosphere values of Carbon and Gingerich
(1969). The model atmosphere option was employed for each star.
Since no previous analytical work has been done on V513 Her (in
particular, no spectroscopy), we devised a method to estimate the
temperature of the primary star ($T_1$). We observed the cluster IC
4665, computing all available color indices for stars of known
spectral type (Henden and Kaitchuck 1982). This cluster was chosen
for having stars of widely ranging spectral types. We then compared
these color indices to the observed color indices for V513 Her. We
used color index values observed near secondary minimum for V513 Her
in order to minimize contributions from the secondary star. From
these comparisons, we estimate the spectral type of primary star to
be F5, resulting in a temperature of 6600 K (Johnson 1965).
The solution presented here comes from careful examination of the
matrix of correlation coefficients and the use of the method of
multiple subsets (Wilson and Biermann 1976). Solution was taken to
be achieved when the parameter corrections all fell below their
probable errors for all subsets. The errors listed in Table 2 are
the formal errors of the partial differential least squares
technique employed in the Wilson-Devinney method. The values of the
errors are used as a guide in determining the number of decimal
places each parameter is given. We should note that the actual
errors of the parameter determination may be higher.
The solution makes V513 Her a typical, A-type W UMa system. A
steady period, a temperature of 6600 K for the primary star, and no
evidence of spots supports the stable environment associated with
A-type systems. The solution indicates only a slightly over contact
system with a fill out factor of 10.3\%.
\begin{table}[!hr]
\vspace*{.5cm} \centerline{Table 2. Wilson-Devinney Solution for
V513 Her} \vskip 3mm
\begin{center}
Wavelength Independent Parameters - Mode3
{\normalsize
\begin{tabular}{cccccccccccc}
\hline \hline
{\it i} & $T_1$ & $T_2$ & $\Omega_1$ & $\Omega_2$ & q & $F_1$ & $F_2$ & $G_1$ & $G_2$ & $A_1$ &
$A_2$ \\
\hline
\hskip4pt 74.80 & 6600 K & \hskip11pt 6071 K & \hskip9pt 3.436 & 3.436 & \hskip9pt 0.840 & 1.00 & 1.00 & 0.32 & 0.32 & 0.5 &
0.5 \\
$\pm$0.34 & & \hskip3pt$\pm$65 & $\pm$0.021 & & $\pm$0.010 \\
\hline
\end{tabular}
}
\vskip 3mm
Wavelength Dependent Parameters
\begin{tabular}{ccccc}
\hline
Band & $L_1$ & $L_2$ & $x_1$ & $x_2$ \\
\hline
Vis & \hskip9pt 0.623 & 0.377 & \hskip9pt 0.6 & 0.6 \\
& $\pm$0.014 & & $\pm$0.1 \\
Red & \hskip9pt 0.606 & 0.393 & \hskip9pt 0.6 & 0.6 \\
& $\pm$0.011 & & $\pm$0.1 \\
IR & \hskip9pt 0.594 & 0.406 & \hskip9pt 0.6 & 0.6 \\
& $\pm$0.008 & & $\pm$0.1 \\
\hline
\end{tabular}
\end{center}
\vskip 0.5cm
\end{table}
\IBVSfig{8cm}{5689-f2.eps}{Light curves for V513 Her \vskip 1mm
Solid curves are the Wilson-Devinney solution given above}
\IBVSfigKey{5689-f2.eps}{V513 Her}{light curve}
\newpage
\references
Carbon, D.F. and Gingerich, O. 1969, in {\it Theory and Observation
of Normal Stellar Atmospheres}, ed. O. Gingerich, Cambridge, Mass,
MIT Press, p. 377
Henden, A.A. and Kaitchuck, R.H. 1982, in {\it Astronomical
Photometry}, Willmann-Bell, Inc. Richmond, VA., p. 304
Hoffmeister, C., 1959, {\it Astron. Nach.}, {\bf 284}, 275
Hoffmeister, C., 1960, {\it Veroeff. Sternwarte Sonneberg}, {\bf 4}
Johnson, H.L. 1965, {\it Ap.J.} {\bf 141}, 170
Lucy, L.B. 1968, {\it Ap.J.}, {\bf 151}, 1123
Nelson, B. 2004, {\it Eclipsing Binary $O-C$ Files}, from \\
{\tt http://www.aavso.org/observing/programs/eclipser/omc/nelson\_omc.shtml}
Wilson, R.E. 1993, {\it A.S.P. Conf. Ser}, {\bf 38}, 91,
in {\it New Frontiers in Binary Research}, ed. K.C. Leung and I.S. Nha
Wilson, R.E. and Biermann, P. 1976, {\it Astr. and Ap.} {\bf 48},
349
\endreferences
\end{document}