Up: A period study of
The (O-C)1 residuals in Table 2 are calculated by
using the ephemeris given by Cereda et al. (1988), i.e.
The (O-C) diagram of the change in the orbital period
of V 781 Tau is shown in Fig. 1, where (O-C)1 residuals listed in Table 2
are used. It is clear that the
period of this binary star decreased continually from
1949 to 1998. All epochs in Table 2 are used for a least square solution
to obtain a quadratic
ephemeris. The improved ephemeris is described as follows:
which is used to calculate the (O-C)2 in Table 2.
The period change rate of V781 Tau is
.
![\begin{figure}\includegraphics[width=7.2cm,clip]{ds8864f1.eps}\end{figure}](/articles/aas/full/2000/04/ds8864/Timg11.gif) |
Figure 1:
The O-C diagram of the period change for V 781 Tau. The solid circles
indicate the photoelectric observations and the crosses express the photographic
one |
The secular instability of the secondary
component of a W UMa type binary arises because they
obtain the luminosity transferred from the primary
component (Lucy & Wilson 1979; Hazlehurst 1985; Wang
1994). So it could be suggested that decrease in the period of V 781 Tau
is caused by the contraction of the
secondary component, then its shrinking velocity can be calculated
from the decrease rate in the
orbital period.
The Kepler's third law can be written as
where A is the separation between the two components
in solar radii, p represents the orbital period in
days and M indicates the total mass of the two
components in solar mass. From the definition of the
relative radius of one of the two components, one may have
 |
(2) |
According to Binnendijk (1970) and Lacy (1977), one may have
and
 |
(4) |
Inserting the Eqs. (4), (3) and (2) into the
Eq. (1), one may acquire
 |
(5) |
Assuming conservation of total mass of the system,
from the Eq. (5), one can obtain
 |
(6) |
Since the period of V 781 Tau decreases, from the Eq. (6) and the
parameters published by Lu (1993), one may find a contracting velocity of the
secondary component,
,
namely the
contraction of 21.4 m/year, which is in agreement with
the results shown in the study of the thermal
relaxation oscillation of contact binaries by Wang
(1994).
Up: A period study of
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