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\IBVShead{4138}{29 December 1994}                      % Use it with dummy or empty arguments

% Call for macro \title {Title of the paper}
\centerline{\ft TIMINGS OF SELECTED VARIABLE STARS\footnote{Visiting Observer,
Lowell Observatory, Flagstaff, Arizona, USA.
Also based in part on data collected at Cerro Tololo Inter-American
Observatory, National Optical Astronomy Observatories,
operated by the Association of Universities for Research in
Astronomy, Inc., under contract with the National Science
Foundation.}}
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Changes in the periods of variable stars can be determined by timing the
occurrence of a certain point in the light curve, usually the maximum
or minimum value.  It is necessary to have
such timings at frequent enough intervals so that cycle counts can be
reliably determined in between.  Often in the course of other routine
observations, such timings are obtained and the purpose of this paper
is to make available such data to other researchers.

Most of the photometric data were obtained with telescopes at Lowell
Observatory in Flagstaff, AZ but some came from CTIO in Chile ($\sigma$ Sco
and $\nu$ Eri).  The raw photometry was corrected for sky, and the
atmospheric extinction
was removed using a comparison star.  Then differential magnitudes were
determined and heliocentric corrections applied.  For stars with a single
mode, plots of the light curves were made and a cross-correlation
technique between the ascending and descending branch was used
to derive the time of maximum or minimum.  The uncertainty of an individual
timing varies with data quality, but is typically 0.0005 days.
It is planned to submit all of the data upon which these
timings have been made to the Journal of Astronomical Data, Twin Press,
The Netherlands.
\vskip 5mm
\centerline{Table 1. Times of Photometric Minimum of Eclipsing Binary Stars.}
\vskip 2mm
\begin{center}
\begin{tabular}{lcc}
\hline
 Star Name & HJD & notes\\
\hline
 \\
 BX And     & 2447108.7773 & primary min\\
            & 2447535.7064 & secondary min\\
            & 2447573.6826 & primary min\\
 \\
 TY Boo     & 2447641.7811 & primary min\\
            & 2447641.9398 & secondary min\\
 \\
 W Crv      & 2447234.7467 & primary min\\
            & 2447237.8561 & primary min\\
            & 2447250.8553 & secondary min\\
            & 2449108.7855 & primary min\\
            & 2449109.7580 & secondary min\\
\hline
\end{tabular}
\end{center}


\vfill
\eject

\centerline{2}
\vskip 0.1cm
\centerline{Table 2. Times of Photometric Maximum/Minimum of $\beta$ Cephei Stars.}
\vskip 1mm
\begin{center}
\begin{tabular}{lcc}
\hline
 Star Name & HJD & notes\\
\hline
\\
 $\nu$ Eri  & 2444450.8184 & max for P1 = 0.173506 d \\
            & 2444450.8937 & max for P2 = 0.178063 d \\
\\
 $\sigma$ Sco  & 2444457.6980 & max for P2 = 0.246836 d\\
            & 2444457.7130 & max for P1 = 0.239670 d\\
\\
 BW Vul     & 2447704.7345 & max\\
            & 2447704.8300 & min\\
            & 2447803.6580 & max\\
            & 2447826.6639 & min\\
            & 2447833.6100 & max\\
            & 2447827.5755 & max\\
            & 2447833.7020 & min\\
            & 2447840.6484 & max\\
            & 2447840.7373 & min\\
            & 2448062.8020 & max\\
            & 2448062.8885 & min\\
            & 2448084.8152 & min\\
            & 2448193.6753 & max\\
            & 2448193.7676 & min\\
            & 2448194.6820 & max\\
            & 2448403.8630 & min\\
            & 2448403.9713 & max\\
            & 2448421.7744 & min\\
            & 2448421.8685 & max\\
            & 2449662.6000 & min\\
            & 2449662.7120 & max\\
            & 2449663.6025 & min\\
            & 2449663.7164 & max\\
\hline
\end{tabular}
\end{center}
\vskip 3mm

Table 1 lists the times of primary and secondary minimum for three close
binary stars.  There is enough new data only for W Crv to produce a new
ephemeris at this time.  For these close binaries, it might be expected
that the orbital period might be changing due to mass exchange between
the two stars, so both a linear and quadratic ephemeris were computed,
combining 12 timings for W Crv from the literature
with the five listed in Table 1.
The least squares quadratic ephemeris yielded only marginally smaller
residuals than the linear, and in any case produced a rate of period
change of just 0.025 seconds/century, which is probably only an upper
limit.  The linear ephemeris can be used to schedule future
observations; it is:
\vskip 0.1cm
\centerline{HJD = 2427861.3634 + 0.388080835$\times$E.}
\vskip 1mm
Table 2 gives times of maximum and minimum brightness for
three $\beta$ Cephei stars.  For those with
multiple modes, cosine functions were fit using the known periods, but
solving for the best phase and amplitude of each mode, and the time of
maximum was derived.
\vfill
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\centerline{3}
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\centerline{\epsffile{4138-f1.ps}}
\centerline{Figure 1. O$-$C diagram for BW Vul}
\vskip 3mm
\vskip 0.2cm

  These timings are completely independent of each
other, and depend on the beat phase of the star at the time of the observation.
For BW Vul, times of minimum light are included because of the suggestion
by Sterken, Young, and Furenlid (1987) that the stillstand in this star's
light curve could alter the timings derived for maximum brightness.

A least squares linear ephemeris was fit to all times of maximum
brightness measured for BW Vul since 1980, which can be used for
predicting maximum brightness for the near future:
\vskip 0.2cm
\centerline{HJD = 2447700.1158 + 0.201044444$\times$E}
\vskip 0.2cm
\noindent with an rms residual of 1.25 minutes.


The period history of BW Vul has been controversial for about ten years,
since the discovery of a periodic variation of the residuals
after a quadratic ephemeris has been removed, made by Odell (1984).  The
quadratic ephemeris can be explained in terms of the star's evolution
to larger size, and the periodic residuals can be explained either by
the light-travel-time over a binary orbit or by two modes beating with a
period of about 30 years.  The controversy arises from the claim of
Chapellier (1985) that the period has been constant except for sudden
jumps in 1945 and 1968, and again in 1980 (Chapellier and Garrido, 1990).
Pigulski (1993) has derived the properties of the binary star orbit, including
an orbital period of 33.5 years.

In order to distinguish between the two proposed behaviors of this star,
a linear ephemeris was fit to the previously published timings of
maximum between 1968 and 1980, and the residuals computed for all
timings since 1950; these are shown in Figure~1.  \vfill \eject

\centerline{4}
\vskip 2mm
The diamond symbols in
the figure represent timings used in the linear fit, while the pluses
represent eras in which a different ephemeris must be used.  It can be seen
that the residuals are fit well by three straight lines, but the residuals
predicted from a quadratic ephemeris also agree reasonably well,
especially if a periodic variation on either side of the quadratic is
allowed for.


Figure 1 gives a method of determining which of the two types of
ephemeris is the correct one.  If the quadratic-with-variations
ephemeris is correct, the figure predicts that there must be another
increase in the
period by about 0.25 seconds at HJD about 2452000, or in the year 2000.
If the piecewise-linear ephemeris is correct, there is no way to predict
when the next period change will occur, or the magnitude, or even the
sign of the change.  Thus the monitoring of this star for the next ten
years becomes important to distinguishing the correct ephemeris form.

\vskip 1cm
% Call for macros \authors - \authorsrightcol - \endauthors
\beginauthors
\authorsrightcol
Andrew P. ODELL
Northern Arizona University
Dept of Physics and Astronomy
Flagstaff, AZ 86011, U.S.A.
Internet: odell@nauvax.ucc.nau.edu
\endauthors

% Call for macro \references
\references

Chapellier, E., 1985, {\it Astron. Astrophys.}, {\bf 147}, 135

Chapellier, E. and Garrido, R., 1990, {\it Astron. Astrophys.}, {\bf 230}, 304

Odell, A. P., 1984, {\it P.A.S.P.}, {\bf 96}, 657

Pigulski, A., 1993, {\it Astron. Astrophys.}, {\bf 274}, 269

Sterken, C., Young, A., Furenlid, I. 1987, {\it Astron. Astrophys.}, {\bf 177}, 150
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