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\IBVShead{4656}{29 December 1998}

\IBVStitle{1997 PHOTOMETRY OF RT\ ANDROMEDAE}

\IBVSauth{PAUL A. HECKERT}

\IBVSinsto{Dept.\ of Chem.\ \& Physics, Western Carolina University
Cullowhee, NC 28723 USA}

\SIMBADobj{RT And}
\IBVStyp{ RSCV }
\IBVSkey{photometry}

\begintext

As part of an ongoing study of short period eclipsing RS CVn stars, this
work reports 1997 light curves and spot models of RT And. Previous papers in
this series (Heckert 1995 and Heckert et al.\ 1996) report 1995 and 1996 data
and summarize previous similar work. Ar\'{e}valo et al.\ (1995) report
infrared observations from which they estimate the system parameters.

I observed RT And on the nights of 7, 8, 9, 10, and 11 January 1997 with the
61 cm telescope at Mt.\ Laguna Observatory operated by San Diego State
University. I used the instrument, technique, and calibration reported in
Heckert (1995). Figure 1 shows the BVRI differential magnitudes
(star--comparison) in the standard Johnson-Cousins system. Phases for the 93
data points in each filter, were computed with the ephemeris given by
Strassmeier et al.\ (1993): $\phi =2441141.8888+0.62892984\times E$.

As for the 1995 and 1996 data, I used the Information Limit Optimization
Technique (ILOT) of Budding and Zeilik (1987) to model the data to find the
spot structure. Figures 2 and 3 show the fits. In degrees, I get:

\vskip -6pt

\begin{table}[h]
\caption{Spot Fits}
\begin{center}
\begin{tabular}{cr@{${}\pm{}$}lr@{${}\pm{}$}lr@{${}\pm{}$}lr@{${}\pm{}$}l}
\hline
& \multicolumn{2}{c}{B band} & \multicolumn{2}{c}{V band} &
\multicolumn{2}{c}{R band} & \multicolumn{2}{c}{I band} \\ 
\hline 
Longitude & 239.5 & 4.2 & 237.9 & 4.9 & 239.4 & 6.3 &
244.2 & 8.5 \\
Latitude & 39.0 & 19.2 & 44.3 & 26.9 & \multicolumn{2}{c}{45} &
\multicolumn{2}{c}{45} \\
Radius & 11.2 & 2.4 & 12.0 & 4.1 & 11.0 & 0.7 & 11.1 & 0.7 \\ 
$\chi^{2}$ & \multicolumn{2}{c}{233.0} & \multicolumn{2}{c}{136.0} &
\multicolumn{2}{c}{127.1} & \multicolumn{2}{c}{109.0} \\
\hline
\end{tabular}
\end{center}
\end{table}

\vskip -6pt

As for most previous results, the data fit well with a single spot. It
is interesting to compare these results to those for the 1995 and 1996
data.  Figure 4 plots the spot positions. The spot is roughly the same
size and at mid latitudes for all three years. Note however that the
modeled latitudes are quite uncertain and in some cases values had to
be fixed at 45\deg\ because I was unable to fit this parameter.  The
spot migrated from the 90\deg\ Active Longitude Belt (ALB) to the
270\deg\ ALB between 1995 and 1996. In 1996 the spot was at 216\deg\
longitude, barely within the region that could be considered the
270\deg\ ALB. By 1997 the spot had migrated to 240\deg\ longitude, closer
to the center of the 270\deg\ ALB.  Heckert et al.\ (1998) notice a
similar trend for WY Cnc. Spots originate near the edge of an ALB and
migrate to increasing longitudes.

\IBVSfig{9cm}{4656-f1.eps}{}

\IBVSfig{9cm}{4656-f2.eps}{}

\IBVSfig{9cm}{4656-f3.eps}{}

\IBVSfig{9cm}{4656-f4.eps}{}

Unlike the 1995 and 1996 light curves, these light curves were complete
enough to perform clean fits with the effects of the spot distortion
wave removed. These fits provide estimates of the system parameters.
The quantities are as defined by Budding and Zeilik (1987). The result
is as follows:

\vskip -12pt

\begin{table}[h]
\caption{Clean Fits}
\begin{center}
\begin{tabular}{cr@{${}\pm{}$}lr@{${}\pm{}$}lr@{${}\pm{}$}lr@{${}\pm{}$}l}
\hline
& \multicolumn{2}{c}{B band} & \multicolumn{2}{c}{V band} &
\multicolumn{2}{c}{R band} & \multicolumn{2}{c}{I band} \\
\hline 
$L_{1}$ & 0.861 & 0.008 & 0.823 & 0.008 & 0.807 & 0.008 & 0.775 & 0.008
\\
$k (=r_{2}/r_{1}$) & 0.718 & 0.006 & 0.721 & 0.007 & 0.736 & 0.010 &
0.744 & 0.007 \\
$\Delta\theta_{0}$ & 3.660 & 0.134 & 3.921 & 0.141 & 3.961 & 0.152 &
4.098 & 0.150 \\
$r_{1}$ & 0.319 & 0.004 & 0.316 & 0.004 & 0.315 & 0.004 & 0.307 & 0.003
\\
$i$ (deg) & 90.0 & 1.7 & 89.5 & 2.3 & 86.9 & 1.1 & 90.0 & 1.9 \\
$e$ & 0.024 & 0.013 & 0.014 & 0.012 & 0.020 & 0.011 & 0.021 & 0.012 \\
$M_{0}$ & 2.929 & 0.137 & 3.015 & 0.153 & 2.998 & 0.108 & 3.051 & 0.080
\\
$L_{2}$ & 0.111 & 0.009 & 0.145 & 0.009 & 0.165 & 0.010 & 0.199 & 0.010
\\
$q (=m_{2}/m_{1})$ & 0.399 & 0.065 & 0.424 & 0.083 & 0.54 & 0.105 &
0.470 & 0.130 \\
$\chi^{2}$ & \multicolumn{2}{c}{152.5} & \multicolumn{2}{c}{82.1} &
\multicolumn{2}{c}{97.1} & \multicolumn{2}{c}{80.5} \\
\hline
\end{tabular}
\end{center}
\end{table}

\vskip -6pt

The luminosities of the primary and secondary stars, $L_{1}$ and
$L_{2}$, are normalized to sum to approximately but not exactly one.
$\Delta\theta _{0}$ is the correction in degrees that must be added to
the observed times of eclipse minima to obtain the minima times
computed with the ephemeris given by Strassmeier et al.\ (1993). The
radius of the primary, $r_{1}$, is in units of the orbital separation.
The averages of these values, $r_{1} = 0.314\pm 0.005$ and
$k=0.730\pm 0.012$, compare well with the solutions of Ar\'{e}valo et
al.\ (1995) which are: $r_{1}=0.316\pm 0.005$ and $k=0.715\pm 0.033$.
My average value of the orbital inclination, $89.1\pm 1.5$ compares to
$88.4\pm 1.1$ and 87 obtained by Zeilik et al.\ (1989) and Ar\'{e}valo
et al.\ (1995). $M_{0}$ and $e$ are the mean anomaly and ellipticity.
Zeilik et al.\ (1989) find that RT And has a slightly elliptical orbit
rather than the circular orbit more common for these systems. They get
values of $3.03\pm 0.22$ and $0.026\pm 0.013$ which agree with the
averages of these values of $3.00\pm 0.04$ and $0.020\pm 0.04$. My
values of the mass ratio are lower than the previous values of 0.65
used by Budding and Zeilik (1987) and the spectroscopically determined
value of 0.73 (Popper 1994). However photometric mass ratios,
especially when determined from a single set of light curves, are less
reliable than those from spectroscopic data.

I thank Ron Angione for scheduling generous amounts of observing time
at Mt.\ Laguna. I also acknowledge support from a Cottrell College
Science Award of The Research Corporation for this work.

\vskip -6pt

\references

Ar\'{e}valo, M.J., L\'{a}zaro, C., and Claret, A., 1995, {\it Astron.\
J}., {\bf 110}, 1376

Budding, E. and Zeilik, M., 1987, {\it Astrophys.\ J.}, {\bf 319}, 827

Heckert, P.A., 1995, {\it Inf.\ Bull.\ Var.\ Stars}, No.4224

Heckert, P.A., Beaver, M.R., and Phillips, K., 1996, {\it Inf.\ Bull.\
Var.\  Stars}, No. 4384

Heckert, P.A., Maloney, G.V., Stewart, M.C., Ordway, J.I., Hickman,
M.A., and Zeilik, M., 1998, {\it Astron.\ J}., {\bf 115}, 1145

Popper, D.M., 1994, {\it Astron.\ J}., {\bf 108}, 1091

Strassmeier, K., et al., 1993, {\it Astron.\ \& Astrophys.\ Suppl}., {\bf
100}, 173

Zeilik, M., Cox, D.A., De Blasi, C., Rhodes, M., and Budding, E., 1989,
{\it  Astrophys.\ J}., {\bf 345}, 991
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