The decrease in the orbital period of V 781 Tau
has presented the evidence to test the interesting results
presented by Wang (1994), who suggested that the two
subtypes of W UMa binaries should be in two different
thermal relaxation oscillation states: the secondary
components of the W-subtypes of W UMa type binaries are
shrinking whereas the ones of A-subtypes are swelling.
According to Wang (1994), a W-subtype W UMa binary
has a contracting secondary component, which
releases some gravitational energy to support its
surface effective temperature higher than that of the
primary component. The luminosity radiated by the
secondary component consists of the three parts, the
first is from the nuclear reaction in the secondary, the
second is from the transferred luminosity from the
primary and the third is from the released
gravitational luminosity by the secondary component.
Suppose the secondary component with a mass of m2 and a radius of R2 spherically
symmetric, then its gravitational
energy
is written (Kippenhahn & Weigert 1990) as
follows:
![]() |
(7) |
![]() |
(8) |
The paradox of the over-luminous secondary
component of the W UMa binary was explained by the
introduction of large-scale energy transfer from the
primary to the secondary (Lucy 1968). In the
present discussion for V 781 Tau, the secondary
component of the system is continuously shrinking at the
velocity of
and releasing the
gravitational luminosity of
,
while the
orbital period of the system was continuously
decreasing with the change ratio of
.
Then the transferred luminosity from the primary
component may be only a part of the over-luminosity,
the other
part may be from the gravitational
luminosity released by the secondary component when it
shrinks. According to Mochnacki (1981), the ratio
of energy transfer of V 781 Tau should be of
,
but in the present discussion, that is only of
.
It is interesting to notice that the W-phenomena of W UMa binaries arise also because of the contracting secondary components rather than only because the energy transfer from the primary to the secondary. The transferred luminosity from the primary should never cause the temperature of the secondary component to be higher than that of the primary if there were non-gravitational luminosity released by the secondary component.
In order to test the contracting model of the secondary components of the W-subtype W UMa Binaries, observations and analyses in the orbital period of more systems will be needed.
Acknowledgements
The authors would like to thank Dr. F. Li for his assistance in the observation and Dr. P.G. Niarchos for his useful advice. The authors would also like to express their gratitude for the support from the Chinese National Science Foundation Committee and the Chinese Academy of Sciences.
Copyright The European Southern Observatory (ESO)