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\IBVShead{5169}{12 September 2001}

\IBVStitletl{1999 Observations of the Solar Type}{ Eclipsing Binary, TY Ursae Majoris}

\IBVSauth{Stoddard, Michelle L.$^1$; Samec, R.G.$^{1,3}$; Faulkner, D.R.$^{2,3}$; Walker, R.L.$^4$}

\IBVSinst{Astronomy Program, Dept.\ of Physics, Bob Jones University,
Greenville, SC 29614, rsamec@bju.edu, \\ \indent stripe313@hotmail.com} %email


\IBVSinst{University of South Carolina, Lancaster, SC 29721 USA,
faulkner@gwm.sc.edu} %email


\IBVSinst{Visiting Astronomer, Lowell Observatory, Flagstaff, Arizona}

\IBVSinst{U.S. Naval Observatory, Flagstaff Station, P.O. Box 1149,
Flagstaff, AZ 86002-1149}

\SIMBADobj{TY UMa}

\begintext

TY Ursae Majoris [GSC 3837-135, SVS 366, RA(2000)${} = 12\hr 9\mm
2\fsec656$, DEC(2000)${} = 56\deg 01\arcm 53\farcs54$] was observed as
a part of our program to detect solar type, eclipsing binaries coming
into contact through the use of precision multi-band photometry.
Broglia \& Conconi (1983) had modeled TY UMa in both near contact and
a shallow contact configurations, so we added this binary to our list
of program stars. TY UMa was discovered by Beljawsky (1933).  Broglia
\& Conconi  (1983) presented 2 complete light curves from 1981 and
1982 as well as a partial one from 1967. They found moderate
asymmetries in the light curves and calculated the following light
elements:
\begin{equation}
{\rm J.D.~Hel~Min\,I} = 2439532\fday4965 + 0.354538609 \times E.
\end{equation}

Their Wilson Code contact solution gave a marginal fill-out of 12\% and
a mass ratio of 0.4. Similarly, their near contact solution gave a mass
ratio of 0.42.  Later, Lister et al.\ (2000) reported $V$ and  $I$
light curves from 1993 observations. Lister et al.'s (2000) curves are
similar in characteristics to the 1981 curves of Broglia \& Conconi
(1983).  Their models, calculated with the LIGHT2 synthesis code gave a
similar inclination and mass ratio with an unusually large fill-out,
27.5\%. Such a rapid of change in the degree of contact is difficult to
explain especially for a system there describe as undergoing thermal
relaxation oscillations about shallow contact.  We suggest that spot
activity is played a role in their results. The present observations
were taken with the 0.79-m Lowell telescope, Flagstaff, Arizona on
April 9--11, 1999. Standard Johnson $UBV$ filters were used in
conjunction with a thermo-electrically cooled, blue-enhanced PMT\@. The
comparison and check star are given as Comp, and Chk in Figure!1 along
with the variable Var. Our photometry revealed that the comparison star
[HD 105859, GSC 3837-122, $V=10.226(11)$, $B-V=0.609(13)$, $U-B
=0.085(14)$] is of spectral type G0V and the check star, [GSC 3837-157,
$V=9.085(20)$, $B-V=0.286$, $U-B = 0.068(12)$] is of spectral type
A9V\@. TY UMa, at phase zero had magnitudes $V= 12.077(19)$, $B-V =
0.627(21)$, and $U-B=0.102(7)$.  Here, standard errors accompany the
values given in parentheses. All three stars show no evidence of
reddening, but lie on the main sequence $U-B$ vs.\ $B-V$ color-color
diagram.  We took 666 individual observations in $U$, 671 in $B$, and
669 in $V$. Four mean epochs of minimum light were determined from two
primary and two secondary eclipses using bisection of chords method.
Observations taken in 5, 8, 11 and 12 of May 1970, and 19 March 1972 at
the Naval Observatory, Flagstaff station by Walker, yielded nine
additional timings of minimum light which we present here.  Walker used
the tracing paper method to find these. These precision epochs of
minimum light are given in Table~1 along with the standard errors of
the last digits in parentheses.

A linear ephemeris was calculated using  198 epochs of minimum light:
\begin{equation}
{\rm J.D.~Hel~Min\,I} = 2450193\fday5785(50) +  0.35454257(26) \times E.
\end{equation}
The residuals are shown in Figure~2 and as $(O-C)_1$ in Table~1. The residuals 
in Figure~2 show a continuous period increase.

\begin{table}
\caption{Epochs of minimum light of TY UMa}
\begin{center}
\begin{tabular}{lrrrl}
\hline
JD Hel. & \lower6pt\hbox{Epoch} & \lower6pt\hbox{$(O-C)_1$} &
\lower6pt\hbox{$(O-C)_2$} & \lower6pt\hbox{Source} \\[-4pt]
2400000\,+ \\
\hline
40714.7018 & $-$26735.5    & $-$0.0037     & 0.0002      & Walker \\
40714.8788  & $-$26735.0    & $-$0.0040     & $-$0.0000     &  Walker \\
40717.7163  & $-$26727.0    & $-$0.0028     & 0.0011     &  Walker \\
40717.8951  & $-$26726.5    & $-$0.0013     & 0.0027     &  Walker \\
40718.7796  & $-$26724.0    & $-$0.0032     & 0.0008     &  Walker \\
41395.7701  & $-$24814.5    & $-$0.0117     & $-$0.0002     &  Walker \\
41395.9483  & $-$24814.0    & $-$0.0107     & 0.0007     &  Walker \\
50193.5894    &   0.0    & 0.0109     & 0.0001     &  BAV 102 \\
51278.8626(2) & 3061.0    & 0.0293     & $-$0.0041     &    PO \\
51279.7495(1) & 3063.5    & 0.0299     & $-$0.0036     &    PO \\
51279.9267(1) & 3064.0    & 0.0298     & $-$0.0036     &    PO \\
51280.8124(8) & 3066.5    & 0.0291     & $-$0.0055     &    PO \\
\hline
\end{tabular}

\normalsize PO: Present Observations
\end{center}
\end{table}

Although a quadratic fit seems suggested by the curve, it did not
represent the data well so a cubic was attempted. This ephemeris fits
the residuals surprisingly well. Such a fit is shown in Figure 2
overlaying the O-C residuals.  The cubic ephemeris is:
\begin{equation}
\begin{array}{c}
{\rm J.D.~Hel~Min\,I} =2450193\fday5893(16) +  0.35454911(33) \times E + {} \\
{} + 2.70(15) \times 10^{-10} \times E^2 + 1.74(17) \times 10^{-15} \times E^3. \\
\end{array}
\end{equation}

\IBVSfig{10cm}{5169-f1.ps}{Finding chart of  TY UMa, Var, the comparison, 
Comp, and the check star, Chk}

\IBVSfig{10cm}{5169-f2.ps}{The $O-C$ linear residuals and the computed cubic ephemeris 
from Equation~(3)}

\IBVSfig{10cm}{5169-f3.ps}{$U$, $B$, $V$ standard magnitude light curves as defined by the 
individual observations}

\vskip-33pt

The residuals of this fit are shown in Table~1 as the $(O-C)_2$.
Physically this could mean that there is an accelerating period
increase. In the case of conservative mass transfer, this would be
caused by a continuous but increasing mass flow from the smaller to the
larger component of the binary.  The $UBV$ light curves and the $B-V$ and
$U-B$ color curves of the variable are shown in Figure~3 as differential
standard magnitudes (variable${}-{}$comparison) versus phase. We note that a
sinusoidal curve fits the data with an equally good fit with an
oscillation of 100 years. This is a rather short time interval for a
TRO oscillation and is too long for an invisible third component
orbital period unless it is a neutron star.  The probable error of a
single observation was 1.3\% in $B$, 1.2\% in $V$, and 1.3\% in $U$.  At
present, we have calculated a contact solution using the Wilson Code
(Wilson 1994, 1990, Wilson \& Devinney 1971). Tests for a third light
gave a null result. The results show that TY UMa consists of solar-type
G0 and G2V spectral type components with a mass ratio of 2.601(2) (or
0.38 for comparison to the previous mass ratios) and a very small
fill-out factor of 9\%.  The model typical is for a W-type W UMa shallow
contact system (massive star is slightly cooler). The W-type phenomena
is due to wide spread cool spot activity on the hotter more massive
star which makes its apparent temperature cooler (Hendry \& Mochnacki
2000). This binary has been heavily patroled in the past and this work
should be continued into the future. It is truly an astrophysically
important close binary.

Much of the analysis of this binary was done as an undergraduate
physics research project by MLS\@. We wish to thank Lowell Observatory
for their allocation of observing time for the travel support from the
University of South Carolina, and Bob Jones University.

\bigskip

This research was partially supported by a grant from NASA administered
by the American Astronomical Society.

\references

Beljawsky, S., 1933, {\it Perem.\ Zvezdy}, {\bf 43}, 196

Broglia, P., Conconi, P., 1983, {\it A\&AS}, {\bf 51}, 97

Hendry, P.D.,  Mochnacki, S.W., 2000, {\it ApJ}, {\bf 531}, 467

Lister, T.A., McDermid, R.M., Hilditch R.W., 2000, {\it MNRAS}, {\bf 317}, 111

van Hamme, W., 1993, {\it AJ}, {\bf 106}, 2096

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

Wilson, R.E., 1990, {\it ApJ}, {\bf 356}, 613

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

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