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\IBVShead{4798}{15 November 1999}

\IBVStitletl{The Variable Period of V366~Cassiopeiae}{ \rm BAV Mitteilungen Nr.\ 116}

\IBVSauth{Franz AGERER$^1$, Thomas Berthold$^1$, Peter Kroll$^{1,2}$}
\IBVSinst{Bundesdeutsche Arbeitsge\-mein\-schaft f\"{u}r Ver\"{a}nderliche Sterne e.V. (BAV), Munsterdamm 90, D--12169\\ \indent Berlin, Germany, E-mail: agerer.zweik@t-online.de, berthold.mtl@t-online.de}
\IBVSinst{Sternwarte Sonneberg, Sternwartestr. 32, D--96515 Sonneberg, Germany, E-mail: pk@stw.tu-ilmenau.de}
\SIMBADobj{V366 Cas}
\IBVStyp{ EW }
\IBVSkey{photometry}

\begintext

V366~Cas (spectr.~G1) = GSC~3681.494 = CSV~122 = S~3875 was
discovered by Hoffmei\-ster (1949). He announced it as a short periodic
variable star between 10\fmm 5 and 11\fmm 0 (pg.). Further investigations on sky patrol plates were done by Perova (1957). She found the star to be of W~UMa~type and gave first elements including a period of 0\fday 7292714. These elements could be confirmed in an early paper by Berthold (1978). Using the minima given by Perova and 17 new ones using sky patrol plates of Hartha Observatory, the following refined ephemeris has been derived:
\begin{equation} 
{\rm Min~I = HJD~} 2435075.461 + 0\fday72927425 \times\rm E. \label{1}
\end{equation}
With these elements V366 Cas is listed in the fourth edition of the
GCVS (Kholopov et al.,~1985).

F.A. recently made CCD photometry with a SBIG ST6 camera without filters attached to a 20-cm~SC--telescope, from which 14 minima times using the Kwee--van Woerden algorithm (Kwee, van Woerden 1956) could be derived. We also obtained a CCD--based light-curve given in Fig.~2. Since the amplitudes in Min~I and Min~II differ less than the scattering from night to night, we were not able to unambiguously distinct between the respective minima. We therefore left the definition of the primary minimum (Min~I)
unchanged.

In order to check the long--term behaviour of the period and to bridge
the gap between the Hartha plates and the CCD measurements, additional
observations on 279 sky patrol plates of Sonneberg Observatory were
performed by T.B\@. They cover a period of time between J.D.~2441039 and
2450370.  In order to obtain more accurate minimum times, we
calculated mean lightcurves of 5 consecutive subsections using
ephemeris (\ref{1}) and thus, derived times of normal minima.

As comparison stars the ones given in the paper of Perova were used. However, we derived new photographic magnitudes based on the Harvard--Groningen SA8:

\begin{center}
\begin{tabular}{clcclc}
Perova & GSC & mpg & Perova & GSC & mpg \\
a & 3681.374 & 11.40 & b & 3681.1033 & 12.44\\
c & 3681.493 & 12.64 & d & 3681.988  & 12.98\\
\end{tabular}
\end{center}

\IBVSfig{8.5cm}{4798-f1.eps}{$O-C$ diagram of all available minima according to ephemeris (\ref{1}). Symbols are identified as follows: $\Box:$ Photographic minima, $\circ:$ Photographic normal minima 
of Berthold (this paper) and $\bullet:$ CCD minima.}

\IBVSfig{8cm}{4798-f2.eps}{CCD light curve of V366~Cas, according to elements (\ref{3}).}

\begin{table}[t]
\begin{center}
\caption{Times of minima for V366 Cas, epochs and residuals
 computed according to the ephemeris (2) and (3), respectively.}
\footnotesize
\vspace{1ex} 
\begin{tabular}{r@{.}lrlr@{.}lr@{.}lc|r@{.}lrlr@{.}lr@{.}lc}
\hline
\multicolumn{2}{c}{JD hel.} & \lower4pt\hbox{W} & \lower4pt\hbox{T$^*$} &  \multicolumn{2}{c}{\lower4pt\hbox{Epoch$_2$}} & \multicolumn{2}{l}{\lower4pt\hbox{$O-C_2$}} & \lower4pt\hbox{Ref.} & \multicolumn{2}{c}{JD hel.} & \lower4pt\hbox{W} & \lower4pt\hbox{T$^*$} & \multicolumn{2}{c}{\lower4pt\hbox{Epoch$_3$}} & \multicolumn{2}{r}{\lower4pt\hbox{$O-C_3$}} & \lower4pt\hbox{Ref.} \\[-2pt]
\multicolumn{2}{c}{2400000+} & & & \multicolumn{2}{c}{} & \multicolumn{2}{l}{} & & \multicolumn{2}{c}{2400000+} & & & \multicolumn{2}{c}{} & \multicolumn{2}{l}{} & \\
\hline
19255 & 415 & 1&P &$-21693$& 0 &$+0$& 089 & [1] & 41567 & 495 & 2&F &$-11976$& 0 &$+0$& 024 & [3] \\
29166 & 519 & 1&P &$ -8102$& 5 &$-0$& 004 & [1] & 41598 & 442 & 1&P &$-11934$& 5 &$-0$& 024 & [2] \\
29287 & 228 & 1&P &$ -7937$& 0 &$+0$& 011 & [1] & 41973 & 318 & 1&P &$-11420$& 5 &$-0$& 002 & [2] \\
29848 & 419 & 1&P &$ -7167$& 5 &$+0$& 025 & [1] & 43138 & 360 & 2&F &$ -9822$& 0 &$+0$& 001 & [3] \\
29879 & 397 & 1&P &$ -7125$& 0 &$+0$& 009 & [1] & 44847 & 442 & 2&F &$ -7479$& 5 &$-0$& 005 & [3] \\
33183 & 333 & 1&P &$ -2594$& 5 &$-0$& 030 & [1] & 46706 & 393 & 2&F &$ -4930$& 5 &$-0$& 010 & [3] \\
33209 & 244 & 1&P &$ -2559$& 0 &$-0$& 008 & [1] & 48888 & 424 & 2&F &$ -1938$& 5 &$-0$& 010 & [3] \\
33856 & 466 & 1&P &$ -1671$& 5 &$-0$& 017 & [1] & 50301 & 4298&10&E &$     0$& 0 &$-0$& 0013& [4] \\
34681 & 285 & 1&P &$  -540$& 5 &$-0$& 006 & [1] & 50379 & 4651&10&E &$   107$& 0 &$+0$& 0001& [4] \\
35075 & 455 & 1&P &$     0$& 0 &$-0$& 009 & [1] & 50380 & 5592&10&E &$   108$& 5 &$+0$& 0003& [4] \\
35076 & 190 & 1&P &$     1$& 0 &$-0$& 003 & [1] & 50423 & 2229&10&E &$   167$& 0 &$+0$& 0006& [4] \\
35077 & 280 & 1&P &$     2$& 5 &$-0$& 007 & [1] & 50716 & 3925&10&E &$   569$& 0 &$-0$& 0038& [4] \\
35363 & 517 & 1&P &$   395$& 0 &$-0$& 010 & [1] & 50718 & 5845&10&E &$   572$& 0 &$+0$& 0003& [4] \\
35394 & 522 & 1&P &$   437$& 5 &$+0$& 001 & [1] & 50728 & 4295&10&E &$   585$& 5 &$-0$& 0001& [4] \\
35401 & 455 & 1&P &$   447$& 0 &$+0$& 006 & [1] & 50739 & 3669&10&E &$   600$& 5 &$-0$& 0020& [4] \\
35431 & 365 & 1&P &$   488$& 0 &$+0$& 015 & [1] & 50754 & 3192&10&E &$   621$& 0 &$-0$& 0001& [4] \\
37016 & 431 & 1&P &$  2661$& 5 &$+0$& 005 & [2] & 50755 & 4130&10&E &$   622$& 5 &$-0$& 0002& [4] \\
37044 & 492 & 1&P &$  2700$& 0 &$-0$& 011 & [2] & 50756 & 5069&10&E &$   624$& 0 &$-0$& 0003& [4] \\
37082 & 437 & 1&P &$  2752$& 0 &$+0$& 011 & [2] & 50863 & 3481&10&E &$   770$& 5 &$+0$& 0002& [5] \\
38142 & 437 & 1&P &$  4205$& 5 &$+0$& 012 & [2] & 51100 & 373 & 5&E:&$  1095$& 5 &$+0$& 006 & [4] \\
39024 & 484 & 1&P &$  5415$& 0 &$+0$& 002 & [2] & 51177 & 3098&10&E &$  1201$& 0 &$+0$& 0031& [4] \\
39035 & 430 & 1&P &$  5430$& 0 &$+0$& 009 & [2] & 51185 & 3316&10&E &$  1212$& 0 &$+0$& 0028& [4] \\
39146 & 261 & 1&P &$  5582$& 0 &$-0$& 010 & [2] & \multicolumn{9}{c}{} \\
39381 & 441 & 1&P &$  5904$& 5 &$-0$& 020 & [2] & \multicolumn{9}{c}{} \\
39389 & 476 & 1&P &$  5915$& 5 &$-0$& 007 & [2] & \multicolumn{9}{c}{} \\
40825 & 429 & 1&P &$  7884$& 5 &$+0$& 005 & [2] & \multicolumn{9}{c}{} \\
40851 & 312 & 1&P &$  7920$& 0 &$-0$& 001 & [2] & \multicolumn{9}{c}{} \\
40853 & 503 & 1&P &$  7923$& 0 &$+0$& 002 & [2] & \multicolumn{9}{c}{} \\
40856 & 426 & 1&P &$  7927$& 0 &$+0$& 008 & [2] & \multicolumn{9}{c}{} \\
40863 & 357 & 1&P &$  7936$& 5 &$+0$& 011 & [2] & \multicolumn{9}{c}{} \\
40924 & 238 & 1&P &$  8020$& 0 &$-0$& 002 & [2] & \multicolumn{9}{c}{} \\ \hline
\end{tabular}

\normalsize $^*$ P\, denotes photographic minima, F\, photographic normal minima  and   E\, CCD observed minima. Those marked with `:' got reduced weight.

[1]: Perova (1957), [2]: Berthold (1978), [3]: Berthold: this paper, [4]: Agerer: this paper,\\{} [5]: Diethelm (1998)
\end{center}
\end{table}

As it is clearly to be seen, the period of V366 Cas is significantly
changing. For describing such a behaviour, two different approaches can
be made: (1) we assume the period was constant during certain periods
of time with distinct period jumps in between, (2) we apply a
continuously increasing changing period with a quadratic $O-C$ fit.

Assuming two consecutive constant periods, the following set of linear
elements can be derived: 

From JD 2427500 (approx.)\ to JD 2441000 (approx.): 
\begin{equation} \begin{array}{r@{}r@{}l}
{\rm  Min~I = HJD~} 2435075.464 & {} + 0\fday72927385 & {} \times E. \\
                          \pm 2 &              \pm 42 \\
\end{array}
\label{2}
\end{equation}
 
From JD 2441000 (approx.)\ to JD 2451185 (last observed minimum): 
\begin{equation}
\begin{array}{r@{}r@{}l}
{\rm  Min~I = HJD~} 2450301.4311 & {} + 0\fday72928857 & {} \times E. \\
                           \pm 3 &              \pm 13 \\
\end{array}
\label{3}
\end{equation}

If Perova's first moment of minimum is correct, it is obvious that a 
further change has occurred sometimes in the first third of this 
century.

Alternatively -- and the $O-C$ diagram suggests this strongly -- a
weighted quadratic least squares fit is also possible to achieve that
yields the following elements:
\begin{equation} \begin{array}{r@{}r@{}l}
{\rm  Min~I = HJD~} 2435075.449 & {} + 0\fday72927554 & {} \times E. \\
                          \pm 1 &              \pm 15 \\
\end{array}
\label{4}
\end{equation}

Based on the quadratic elements we can derive the rate of change of
the period as $dP \sim 7\fday6 \times 10^{-10}$ per orbital revolution. Under the assumption that this change is caused by mass exchange between the stars, the mass transfer proceeds from the less massive component to the more massive component since the period increases. If we knew the stellar masses we were able to derive the mass transfer rate $|\delta m|$ using the well-known relation (Kopal, 1978)
\begin{equation}
\frac{dP}{P} = 3 \left( 1 - \frac{m_1}{m_2} \right) \frac{|\delta  m_1|}{m_1}, \label{5}
\end{equation}
where $m_1$ (more massive component) and $m_2$ represent the stellar
masses. Although the CCD light-curve (Fig.~2) clearly indicates a 
close binary system and that one or both stars must be heavily
distorted, an estimate of the mass ratio is hard to achieve. Provided
the stars are similar and, thus, assuming a mass ratio in the order of
0.9 and (roughly) a solar mass for both components (spectrum
G1), we obtain a mass transfer rate of $1.75 \times 10^{-6}
M_\odot$/yr. 

The improved electronic version of the GCVS (Kholopov et al.\ 1998)
lists only 4 other objects of similar periods (0.65\dots0.85 days) and
spectra between F8 and G5 showing W-UMa-like lightcurves: VY Cnc, UZ
CMi, RS Col, and ER Vul. Although described as EW/DW, this
classification is erroneous in at least one case (RS Col).
Insufficiently studied until today, UZ CMi might be also a contact  
binary (Giuricin, Mardirossian and Mezzetti 1983). ER Vul, on the
contrary, is a short-period RS CVn-type star. This makes V~366~Cas an 
interesting case to which more attention should be paid. We therefore
suggest time-resolved spectroscopy and multicolor CCD photometry of this
object. 
 
\references 

Berthold, T., 1978, {\it Hartha Mitt.,} {\bf 12}, 2

Diethelm, R., 1998, {\it BBSAG Bull.,} No.\, 117

Giuricin, G., Mardirossian, F., Mezzetti, M., 1983, {\it Astron.\
Astrophys.\ Suppl.\ Ser.}, {\bf 54}, 211

Hoffmeister, C., 1949, {\it Erg.\ Astron.\ Nachr.,} {\bf 12}, 1

Kholopov, P.N. et al., 1998, {\tt http://www.sai.msu.su/database.html}

Kopal, Z., 1978, {\it Dynamics of close binary systems,} Reidel,
Dordrecht 

Perova, N.B., 1957, {\it Perem.\ Zvezdy,} {\bf 96}, 467

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