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\IBVShead{4679}{9 March 1999}

\IBVStitle{The Sudden Period Change of VV~Cephei}

\IBVSauth{D.~GRACZYK, M.~MIKO{\L}AJEWSKI, J.{\L}.~JANOWSKI}

\IBVSinsto{Centre for Astronomy, Nicolaus Copernicus University, ul.\ Gagarina 11, PL-87\,100 Toru\'n, Poland}


\IBVStyp{ EA/GS+SRC }
\IBVSkey{photometry}
\SIMBADobj{VV Cep}

\begintext


VV~Cep (HD 208816, HR 8383) is known as a massive eclipsing binary
consisting of an M supergiant and a Be companion showing strong Balmer
and [FeII] emission lines (Cowley 1969). The orbital period, based on
photometric data, is 7430\day\ (Gaposchkin 1937, Sait{\=o}
et~al.\ 1980) and the eclipses are apparently total.  Wright (1977) has
found the spectroscopic orbits of both components from the radial
velocity measurements of some neutral atomic lines of the M component
and the H$\alpha$ emissions from an envelope of the hot companion.
Assuming the inclination 77\deg\ he calculated the masses and sizes of
both components concluding that M supergiant does not fill up its Roche
lobe. However, quite large eccentricity ($e = 0.346$) indicates that
some mass transfer events may exist near the periastron passage, when
temporary Roche-lobe overflow drives a stream which forms an accretion
disk around the Be companion (Wright 1977, Stencel et~al.\ 1993).

The nature of the hot companion has attracted much attention over the
last years.  In particular the spectral type and temperature of the B
star remain very uncertain.  Estimates range from early B or even O
(Hutchings \& Wright 1971, Stencel et~al.\ 1993) to as late as A0 (Hack
et~al.\ 1989).

We have observed VV~Cep as a part of a project of UBVRI photometric
monitoring of long period binaries. We used one-channel photometer with
the 60-cm Cassegrain telescope at the Piwnice Observatory.  The UBV
realization was very close to the original Johnson's response  curves,
while R and I bands were centered at {\it shorter\/} effective
wavelengths of 638~nm and 740~nm, respectively.  As the comparison star
20~Cep has been used.


Figure 1~presents our light curves of VV~Cep in the UBV bands, covering
the period from 1991 to the end of 1998.  The large scatter of the
observed magnitudes is due to intrinsic variability of both components:
semiregular pulsations of the M supergiant (visible in B and V light
curves) and random fluctuations of the hot component (seen mainly in U
light curve). The amplitudes of the variations were about 0\fmm 3 in
the UBV bands and about 0\fmm 2 in the I and R bands.  The eclipse is
very well seen in ultraviolet and blue light. In the V light the
eclipse is difficult to detect because the amplitude of the M
supergiant's pulsations is over three times larger than the depth of
the minimum. The period of the semiregular pulsation over the whole
eclipse is about 114~d and corresponds very well to the previously
reported periods which range from 110 to 118~d (Sait{\=o}
et~al.\ 1980).


We have analyzed the U$-$B, B$-$V, V$-$R colour curves. This allows us
to remove much of the intrinsic variations of the supergiant, in
particular its pulsations.

The eclipse duration was calculated using U$-$B, B$-$V curves where the
eclipse is clearly visible. The eclipse began just after JD~2450541 and
ended just before JD~2451177 in both colours. The totality phase seems
not to be longer than 450~d in U$-$B and 477~d in B$-$V colour.  This
indicates that the 1997/98 eclipse was similar to the 1957/58 one
(Larsson-Leander 1957, 1959) in the duration of totality phase and
partial phases (Fig.~2).  The previous 1977/78 eclipse (Fig.~3) seems
to be different in some aspects: it was asymmetric, with shorter
totality phase and longer total duration (Sait{\=o} et~al.\ 1980).

The most surprising feature of the eclipse is the disagreement between
the observed time of mid-eclipse and the predicted time based on the
Gaposchkin's (1937) ephemeris (Fig.~4).  The ephemeris gives JD~2450790
for the mid-eclipse time, while the observations (Fig.~2,\,3) clearly
show that it occurred at around JD~2450855.  This means that the
mid-eclipse occurred 65~d {\it later\/} than expected from the
ephemeris.  There are two probable reasons for such event: (i)
inappropriate Gaposchkin's elements; (ii) the secular or even sudden
change of period in VV~Cep.  We inspected diagram O$-$C (Fig.~4) for
the past five eclipses observed since 1890 and recalculated the times
of minima, but we did not find any systematic deviation from the
Gaposchkin's elements (see e.g.\ Sait{\=o} et~al.\ 1980).  This means
that a sudden increase of about 1\% in the orbital period occurred
between the two last eclipses!


\IBVSfig{10cm}{4679-f1.ps}{The latest part of the UBV light curves of
VV~Cep  including the 1997/98 eclipse. The comparison star was 20 Cep
and its variability was smaller than reported by Sait{\=o} (1978). The
B and V light curves are shifted by +0.2 mag.~and +1.0
mag.~respectively. The errors of individual observations are drawn with
bars and for most of the nights are  smaller than 0.006 for B,\,V and
0.010 for U band.}

The well-known reasons for the period change in binaries are: 1) mass
transfer between components, 2) ejection of some amount of mass from a
system, or 3) presence of a third body.  The sudden increase of the
period suggests the first possibility (that is the mass transfer
between less massive donor to more massive gainer) or the second one.

Assuming, that the change in the period is caused entirely by a rapid
mass-loss event from the M star (the second scenario) we can calculate
the total mass ejected during the period of last 20 years.  There are
two dynamical solutions conceivable in the case of VV~Cep system.  The
first one is the result of the Wright's spectroscopic orbit of the hot
component. It is a massive system ($40 M_\odot$) with the mass ratio $q
= M_{\rm M}/M_{\rm B}$ very close to unity. In this case we obtained
the value of  the total ejected mass of the order of 0.1 solar mass!
This gives the lower limit of the mass loss rate of $ \dot M = 5\times
10^{-3} M_\odot\,{\rm yr}^{-1}$.  We propose the second possibility:
the {\it medium mass model\/} with mass ratio $0.2 \le q\le 0.3$. In
such a case, rejecting questionable spectroscopic solution for the hot
component and using well-defined mass function for the M star
$f(m)=4.68\pm 0.44$, we get the mass of a B star of about $8 M_\odot$
(typical for early B main-sequence star) and the mass of M star about
$2.5 M_\odot$ (it corresponds to early AGB phase rather than to
supergiants).  This gives the total mass ejection of about $0.008
M_\odot$ and mass loss rate of $\dot M = 4\times 10^{-4} M_\odot\,{\rm
yr}^{-1}$ which is consistent with the estimates of the upper limits of
mass loss rate from the M-component in VV~Cep (Stencel et~al.\ 1993,
Kawabata \& Sait{\=o} 1997).  Assuming that the change of period is
caused by a mass transfer (the first scenario) we get the mass transfer
rate of $5\times 10^{-2} M_\odot\,{\rm yr}^{-1}$ for $q=1$ and $5\times
10^{-4} M_\odot\,{\rm yr}^{-1}$ for $q=0.3$.  These calculations also
advocate the low mass model of the VV~Cep system.

\IBVS2fig{7.5cm}{4679-f2.eps}{The 1997/98 eclipse in B$-$V (points) and the 1956/57 eclipse in similar P$-$V (solid line, Larsson-Leander 1957, 1959) shifted according to Gaposchkin's ephemeris by $+2\times 7430\day$.  The dashed line is a simple parabolic fit to the shoulders of the eclipse setting the time of mid-eclipse at JD~2450858. Note that both eclipses are symmetric and of similarity in the depth and shape.}{4679-f3.eps}{The 1997/98 eclipse in U$-$B (points) and 1976/78
eclipse in 3500~\AA--4170~\AA\ colour (solid line, Sait{\=o}
et~al.\ 1980) shifted by +7430\day.  The dashed line is a parabolic fit
to observed shoulders and the time of mid-eclipse is JD +2450854. The
minima are slightly different in the shape and the duration of the
totality.}

Table 1 reports colours and V magnitudes of VV~Cep and 20 Cep.  The
depth of the eclipse does not differ significantly from the last one in
1977 (Sait{\=o} et~al.\ 1980).  The colours of the B component
corresponds to B1 V main sequence star with $E$(B$-$V)${} = 0.63$.
However, this reddening seems to be overestimated in the case of M
component.


{\it Acknowledgments}: We are much indebted to prof.~J.~Kre{\l}owski for correcting the English text. This paper was supported by 
{\it Nicolaus Copernicus Univ.\/}~Grant No.\,352A.

\newpage

\begin{table}
\begin{center}
\caption{Colours and V magnitudes for the both components of
VV~Cep and the comparison star 20 Cep. The colours of VV~Cep during
totality were adopted for the M component. The UBVR magnitudes of 20
Cep were transformed to Johnson system from Argue (1966, 1967).}
\vskip2mm
\begin{tabular}{lrrrr}
\hline
\multicolumn{1}{c}{Star} & \multicolumn{1}{c}{U$-$B} & \multicolumn{1}{c}{B$-$V} & \multicolumn{1}{c}{V$-$R} &  \multicolumn{1}{c}{V} \\
\hline
VV~Cep, outside eclipse  &    0.43 & 1.73 & 1.45      & 5.14 \\ 
VV~Cep, M component      &    1.82 & 2.07 & 1.52      & 5.25 \\
VV~Cep, B component      & $-$0.52 & 0.36 & $\sim$0.4 & 7.68 \\
20 Cep 			 &    1.78 & 1.41 & 1.10      & 5.27 \\ 
\hline
\end{tabular}
\end{center}
\end{table}

\vskip-2cm

\IBVSfig{8.5cm}{4679-f4.ps}{The O$-$C diagram for the orbital period of the VV~Cep 
system. The times and errors of the first three eclipses were estimated
graphically using published photographic light curves by Gaposchkin (1937).
The O$-$C of 1997/1998 eclipse obviously indicates a sudden large change 
in the orbital period between the last two minima.}


\vskip-1cm


\references

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