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\input ibvs2.sty

\begin{document}
\IBVShead{5554}{6 August 2004}

\IBVStitletl{Photometric Analyses of the}{ Contact Binaries FZ Orionis and AH Tauri}

\IBVSauth{Byboth, K. N.$^{1,2}$; Markworth, N. L.$^{1,3}$; Bruton, W. B.$^{1,4}$}

\IBVSinst{Department of Physics and Astronomy Stephen F. Austin
State University, Nacogdoches, TX 75962 USA}
\IBVSinst{e-mail:krisbyboth@yahoo.com}
\IBVSinst{e-mail:nmarkworth@sfasu.edu}
\IBVSinst{e-mail:astro@sfasu.edu}

\SIMBADobjAlias{FZ Ori}{HD 288166}
\SIMBADobj{AH Tau}

\begintext

\vspace*{-1cm}

Hoffmeister (1934) discovered variability in the light of {\bf FZ
Orionis} (HD~288166, GSC~119~01014, $\alpha$(2000) = 05\hr 41\mm
21\sec, $\delta$(2000) = $+$02\deg 36\arcm 23\arcs). Kippenhahn
(1953) classified the system to be of the type $\beta$ Lyr, and
estimated the period to be 1.597 days. Figer (1983) and Le Brogne
{\it et al.} (1984) suggested the system was instead of the type W
UMa and reported a period of 0.3999860 days. El-Bassuny Alaway(1993)
and Rukmini {\it et al.} (2001) suggested that the variability in
the light curve could be due to the presence of a third body and/or
mass loss from the system.

Shapley {\it et al.}\ (1934) discovered variability in the light of
{\bf AH Tauri} (HBV~6187, CSI~24 3442, $\alpha$(2000) = 03\hr 47\mm
12\sec, $\delta$(2000) = $+$25\deg 7\arcm 0\arcs). Photographic
observations were made by Binnendijk (1950) and Romano (1962),
Binnendijk classified the system as W UMa, while Romano classified
the system to be of the type $\beta$ Lyr. Further photometric
observations were made by Bookmyer (1971) and Liu {\it et al.}
(1991). Bookmyer indicated a spectral type of around G5. Liu gives a
complete Wilson-Devinney solution.

Our photometric observations of FZ Ori were made on the nights of
December 21 and 22, 2003, and of AH Tau on the nights of December
24, 30, and 31, 2003, using the 46-cm telescope with attached SBIG
ST-8XE CCD camera equipped with standard Johnson UBVRI filters. The
images were calibrated and the magnitudes extracted using standard
image reduction procedures with MIRA. Differential magnitudes in the
natural system are available upon request of author NLM.
Approximately 200 observations were made in each of the R, I, and V
filters of FZ Ori and 130 observations in these same filters of AH
Tau. The comparison and check star data for FZ Ori were as follows:
comparison star (GSC~00119-00214, $\alpha$(2000) = 05\hr 41\mm
17\fsec6, $\delta$(2000) = $+$02\deg 35\arcm 30\farcs0); check star
(GSC~00119-00771, $\alpha$(2000) = 05\hr 41\mm 05\fsec1,
$\delta$(2000) = $+$02\deg 37\arcm 12\farcs0). These stars are
labeled in Figure 1 as C and K with the variable star denoted by V.
The comparison and check star data for AH Tau were as follows:
comparison star (GSC 01804-02470, $\alpha$(2000) = 03\hr 47\mm
0\fsec0, $\delta$(2000) = $+$25\deg 5\arcm 29\farcs0); check star
(GSC 01804-02485, $\alpha$(2000) = 03\hr 47\mm 20\fsec0,
$\delta$(2000) = $+$25\deg 8\arcm 36\farcs0). These stars are
labeled in Figure 2 in the same sense as Figure 1.

We observed one primary and two secondary minima for FZ Ori and two
primary and one secondary minima for AH Tau.  The mean epochs of
minimum light were determined from these eclipses using the results
of parabolic fits.  Table 1 contains the average times of minima for
the three observed colors.  Additional times of minima for FZ Ori
were recorded by El-Bassuny, Le Brogne {\it et al.}, and Nelson
(2004). Additional times of minima for AH Tau were recorded by Liu
{\it et al.}.  A linear ephemeris was calculated using the last
18,000 orbits (FZ Ori) and the last 39,000 orbits (AH Tau) given by
Nelson (2004). Qian and Ma (2001) suggest a parabolic ephemeris for
FZ Ori based on the previous suggestion of El-Bassuny Alawy (1993).
We have examined the O-C diagram (Qian and Ma 2001) for FZ Ori. Many
of the minima given were determined visually or photographically,
giving a large scatter. We do not find the argument for a nonlinear
ephemeris compelling. The Heliocentric Julian Day of the primary
minima can be computed by the following formula.

FZ Ori
\begin{equation}
         {\rm HJD\ Tmin\ I} = 2452950.09329\ + 0.399984\ {\rm d} \times {\rm E}.
\end{equation}

AH Tau
\begin{equation}
         {\rm HJD\ Tmin\ I} = 2451824.00832\ + 0.33267174\ {\rm d} \times {\rm E}.
\end{equation}

\vspace*{-0.5cm}

\IBVS2fig{7 cm}{5554-f1.eps}{Finder Chart FZ Ori}{5554-f2.eps}{Finder Chart AH Tau}
\IBVSfigKey{5554-f1.eps}{FZ Ori}{finding chart}
\IBVSfigKey{5554-f2.eps}{AH Tau}{finding chart}

\begin{table}[!hb]
\vspace*{-1cm}
\centerline{Table 1. Times of Minimum Light} \vskip 3mm
\begin{center}
\begin{tabular}{cccc}
\hline \hline
Star & JD Hel. & Min & O$-$C\\
 & 2450000+  & & (days) \\
 \hline\\
FZ Ori & 2994.6868 & II & -0.0048\\
FZ Ori & 2995.6863 & I & -0.0051 \\
FZ Ori & 2995.8865 & II & -0.0050\\
AH Tau & 2997.6735 & I & -0.0007\\
AH Tau & 3004.8272 & II & 0.0005\\
AH Tau & 3005.6595 & I & 0.0012\\
\end{tabular}
\end{center}
\end{table}

\vspace*{-0.5cm}

We have calculated models for the light curves of both stars using
the Wilson-Devinney code (Wilson 1993, henceforth WD). 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 ($x_1$ = $x_2$). Both
stars were assumed to be contact binary systems (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.

A previous WD solution for FZ Ori has been published (Rukmini, et
al. 2001).  We used their value of $T_1$ and did not vary it.  The
two solutions compared very well, except in the value of the mass
ratio (0.92 compared to our 0.792).  Their value was based upon
numerical experiments in which q was varied within a range.  Their
data have considerable scatter and we find evidence of a star spot.
We ran the stellar spot model for FZ Ori and found that the presence
of a hot spot on the primary star resulted in an accurate fit of the
observed light curve.  Table 2 presents our WD solution including
the spot parameters.

AH Tau also has a previous WD solution (Liu, {\it et al.} 1991). We
fixed the value of $T_1$ using a combination of the solution of Liu,
et al. (1991) and the spectral type given by Bookmyer (1971) in
conjunction with the calculations of Schmidt-Kaler (1982).
Differences occur between our solutions in the values of $L_1$
(0.657 compared to our 0.574), q (0.503 compared to our 0.773), and
{\it i} (84\fdeg3 compared to our 80\fdeg7). Differences in the mass
ratio also results in a difference in the modified potentials. The
larger inclination in their solution produced larger stars to
account for the depth and duration of the eclipses. Solution space
for contact systems is filled with local minima, making accurate
solutions difficult to obtain. The solutions presented here come
from careful examination of the matrix of correlation coefficients
and the use of the method of multiple subsets (Wilson and Biermann
1976).  Both of these solutions for AH Tau call for component stars
which are virtually identical and very close to solar values. It is
difficult to see how two stars so nearly identical in their
properties could be different by a factor of two in their masses. We
also note that our mass ratio falls in a gap in the mass ratio grid
of Liu, {\it et al.}  Our WD solution for AH Tau is presented in
Table 3.

The errors listed in Tables 2 and 3 are the formal errors of the
partial differential least squares technique employed in the WD
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.

\begin{table}[!hb]
\centerline{Table 2. Wilson-Devinney Solution for {\bf FZ Ori}}
\vskip 3mm {\bf Wavelength Independent Parameters - Mode3}
\begin{center}
\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 66.88 & 6108 K & \hskip11pt 6043 K & \hskip9pt 3.334 & 3.334 & \hskip9pt 0.792 & 1.00 & 1.00 & 0.32 & 0.32 & 0.5 &
    0.5 \\
    $\pm$0.12 & & \hskip3pt$\pm$11 & $\pm$0.007 & & $\pm$0.004 \\
\end{tabular}
\vskip 3mm 
{\bf Wavelength Dependent Parameters} \\
\begin{tabular}{ccccc}
\hline
Band & $L_1$ & $L_2$ & $x_1$ & $x_2$ \\
\hline
Vis & \hskip9pt 0.562 & 0.438 & \hskip9pt 0.61 & 0.61 \\
& $\pm$0.001 & & $\pm$0.05 \\
Red &  \hskip9pt 0.561  &   0.439   &  \hskip9pt 0.60    &     0.60 \\
& $\pm$0.001 & & $\pm$0.05 \\
IR  &  \hskip9pt 0.560  &   0.440   &  \hskip9pt 0.59   &     0.59 \\
& $\pm$0.001 & & $\pm$0.04 \\
\end{tabular}
\vskip 3mm 
{\bf Spot Parameters} \\
\begin{tabular}{ccccc}
\hline \hskip30ptCo-Latitude   &     \hskip30pt Longitude   &
\hskip30pt Size    & \hskip30ptTemperature
Factor \\
\hskip30pt 1.8 rad &  \hskip30pt 6.1 rad  &  \hskip30pt 0.27 rad & \hskip9pt 1.17 \\
$\pm$0.7 & $\pm$0.5 & $\pm$0.11 & $\pm$0.06 \\
\end{tabular}
\end{center}
\end{table}


\begin{table}[!ht]
\centerline{Table 3. Wilson-Devinney Solution for {\bf AH Tau}}
\begin{center}
\vskip 3mm {\bf Wavelength Independent Parameters - Mode3}
\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 80.73 & 5900 K & \hskip11pt 5815 K & \hskip9pt 3.330 & 3.330 & \hskip9pt 0.773 & 1.00 & 1.00 & 0.32 & 0.32 & 0.5 &
    0.5 \\
    $\pm$0.12 & & \hskip3pt$\pm$11 & $\pm$0.009 & & $\pm$0.004 \\
\end{tabular}
\vskip 3mm
{\bf Wavelength Dependent Parameters} \\
\begin{tabular}{ccccc}
\hline
Band & $L_1$ & $L_2$ & $x_1$ & $x_2$ \\
\hline
Vis & \hskip9pt 0.574 & 0.426 & \hskip9pt 0.60 & 0.60 \\
& $\pm$0.001 & & $\pm$0.07 \\
Red &  \hskip9pt 0.571  &   0.429   &  \hskip9pt 0.60    &     0.60 \\
& $\pm$0.001 & & $\pm$0.06 \\
IR  &  \hskip9pt 0.569  &   0.431   &  \hskip9pt 0.60   &     0.60 \\
& $\pm$0.001 & & $\pm$0.06 \\
\end{tabular}
\end{center}
\end{table}

\IBVSfig{8cm}{5554-f3.eps}{Light curves for FZ Ori \vskip 1mm
Solid curves are the Wilson-Devinney solution given below}

\IBVSfig{8cm}{5554-f4.eps}{Light curves for AH Tau \vskip 1mm
Solid curves are the Wilson-Devinney solution given below}

\IBVSfigKey{5554-f3.eps}{FZ Ori}{light curve}
\IBVSfigKey{5554-f4.eps}{AH Tau}{light curve}

\newpage
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\endreferences

\end{document}
