\documentstyle[epsf]{article}
\input ibvs.sty
\begin{document}
\IBVShead{4293}{31 January 1996}
\centerline{\ft CONFIRMATION OF THE PERIOD OF GW Cep}
\centerline{\ft FOUND BY HOUGH TRANSFORM}
\vskip 8mm
\begintext
In two previous papers (Ragazzoni \& Barbieri 1993, 1994, RB94),
we have shown how the
application of the Hough Transform HT (Hough 1962, Ballester 1991, Leavers
1992) can help to detect cycle--numbering errors in sparsely observed time
series, leading to incorrect values of the periods and to spuriously high time
derivatives. Whilst the correct value of the period is {\it per se} not
of utmost physical importance, a spurious time derivative can led to incorrect
conclusions about for instance the mass loss rate or the geometrical
variations of the system.
As an example, we applied those considerations to the eclipsing
binary GW Cep, showing that an error of one cycle every $\approx 16600$
could have
lead to a wrong period, the commonly accepted one being 0.31885 days, and
the most likely one given by the HT, and that at the same time minimizes the
time derivative, being 0.31883 days. In the present paper, using the new
observations, we reinforce those conclusions and add further weight to the
value of the HT to handle this class of problems.
The recent determination by Agerer and H\"ubscher (1995, AH95) of the time of an eclipse provides the
opportunity to verify our prediction.
The data by AH95 were taken at $(JD-2400000) = 49592.545$ whilst the latest
available ones by Landolt (1992, L92) were at $(JD-2400000)=48544.871$; using
the commonly accepted period of $0.31885$ days, the number of cycles between
the two dates is estimated as:
\begin{equation}
\left[\frac{49592.545 - 48544.871}{0.3188}\right]=\left[
3286.305\right] = 3286
\end{equation}
\noindent where $[ x ]$ is the nearest integer of $x$,
and the expected time difference between the observed and the calculated
minimum (in the present case, a delay) after one cycle is lost is therefore
approximately given by:
\begin{equation}
\frac{3286}{16600} \times 0.3188 = 0.0631\,{\rm days} = 1.51\,{\rm hours}
\end{equation}
Notice that the delays in the observations are of this
order, being $0.048$ days at the date of L92, and of $0.054$ at the date of
AH95, thus reinforcing our determination.
As a further check, we report in Table 1 the O$-$C for the {\it General
Catalogue of Variable Stars} GCVS, Hoffman 1992 (H92), L92 and RB94.
Whilst they show an erratic behaviour in the three first papers, they
are consistent with the constant $dP/dt = -2.327 \times 10^{-10}$ as
given in RB94 (see Figure 1).
Finally the sum of their squares is one order
of magnitude smaller in RB94.
We conclude therefore that the application of HT can be very beneficial to the
proper analysis of sparsely sampled light curves, helping to put the physics
of the phenomena on sounder grounds.
\vfill \eject
\centerline{2}
\epsfysize=7cm
\centerline{\epsffile{4293-f1.ps}}
\normalsize
\begin{center}
Figure 1. The $O-C$ for the grouped data available in the literature
fitted by the $1^{st}$ order ephemeris given in RB94. The $2^{nd}$ order
given in RB94 is here shown as a fitting parabola.
\end{center}
\large
\begin{center}
\normalsize
Table 1. O$-$C residuals for four different ephemerides of
GW Cep, without any second order term.
\end{center}
\large
\begin{center}
\begin{tabular}{lcccc}
\hline
\hline
& GCVS & H82 & L92 &
RB94 \\
\hline
Epoch (JD$-$2\,400\,000) & 38383.711 & 38651.545 & 38651.5445 & 38651.550 \\
Period [days] & 0.31885 & 0.31884945 & 0.318851065 & 0.31883082 \\
\hline
$_{MW65}$ [days] &\ \ 0.0022 & 0.0019 &\ \ 0.0030 & $-$0.0097 \\
$O-C_{H82}$ [days] & $-$0.0095 & 0.0000 & $-$0.0276 & \ \ 0.0004 \\
$O-C_{L92}$ [days] & \ \ 0.0483 & 0.0653 & \ \ 0.0156 &\ \ 0.0007 \\
$O-C_{AH95}$ [days] & $-$0.0186 & 0.0002 & $-$0.0547 & $-$0.0032 \\
\hline
$\sum(O-C)^2$ [days$^2\times10^{-6}$] & 2771 & 4263 & 4011 & 105.7 \\
\hline
\hline
\end{tabular}
\end{center}
\vskip .4cm
\beginauthors
Roberto RAGAZZONI
Astronomical Observatory of Padova,
vicolo dell'Osservatorio 5, I--35122 Italy
e-mail: {\tt ragazzoni@astrpd.pd.astro.it}
\vskip 10mm
\authorsrightcol
Cesare BARBIERI
Department of Astronomy,
University of Padova,
vicolo dell'Osservatorio 5,
I--35122 Italy
e-mail: {\tt barbieri@astrpd.pd.astro.it}
\authorsrightcol
\endauthors
\vskip -4mm
\references
Agerer F. \& H\"ubscher J., 1995, {\it IBVS}, No.\,4222, (AH95)
Ballester, P., 1991, {\it A\&A}, {\bf 286}, 1011
Hoffman, M., 1982, {\it Ap\&SS}, {\bf 83}, 195 (H82)
Hough, P.V.C., 1962, Methods and Means for Recognizing Complex Patterns,
U.S. Patent 3069654
Kholopov P.N., 1985, GCVS 4$^{th}$ edition, Moscow "Nauka" Publishing
House
Landolt A.U., 1992, {\it PASP}, {\bf 104}, 336 (L92)
Leavers, V.F., 1992, Shape Detection in Computer Vision using the Hough
Transform (Berlin, Springer)
Ragazzoni R. \& Barbieri C., 1993, in Conference on Application of Time
Series in Astronomy and meteorology, ed. O. Lessi, p.233
Ragazzoni R. \& Barbieri C., 1994, {\it PASP}, {\bf 106}, 683 (RB94)
\end{document}