A&A 414, 317-333 (2004)
The structure of contact binariesH. Kähler
Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
(Received 7 July 2003 / Accepted 16 October 2003 )
In radiative layers of rotating stars the luminosity carried by
circulation currents through a surface of constant entropy (circulation luminosity)
is shown to be positive.
The corresponding decrease in the temperature gradient is important in the secondary
of contact binaries. This result removes the deadlock in the theory of
The resulting treatment of contact binaries is investigated, assuming thermal
equilibrium. The sources of the circulation luminosity in the secondary
can be written as the product of a circulation function (a normalized non-negative
function of the fractional mass) and an amplitude. If the amplitude is adjusted
to give a prescribed temperature difference
the choice of the circulation function is (in a broad range) unimportant.
This invariance extends in a close approximation to all observable properties
as well as to the internal structure.
The temperature difference is bound to be positive. The fractional extent of
radiative regions is larger in the secondary than in the primary.
In the course of evolution the period increases and the mass ratio decreases.
Comparing thermodynamic quantites on level surfaces, pressure and density are
larger in the secondary than in the primary. The specific entropy is larger in the
primary than in the secondary. The temperature difference is remarkably small and
almost vanishing when averaged over the level surfaces occupied in both components.
The only free parameter (apart from
) is the efficiency
of the energy transfer from the primary to the secondary.
Using standard values for the parameters,
a survey of unevolved and evolved contact configurations is presented.
Observational tests are passed. In stable systems the degree of contact is small.
Stable systems in the period-colour diagram, unevolved and evolved, cover the strip
(and only the strip) of observed systems in this diagram. Lower limits for period and
effective temperature, compatible with the observed limits, are caused
by the requirement of thermal stability. Stable systems with mass ratios very close
to unity are possible, in accordance with recent observations.
Since stability considerations are essential in these observational tests
the results support the assumption of thermal equilibrium as well as
the treatment of the stability problem.
Models for individual observed systems with reliable data are well-determined (apart
from some freedom in
) and can be used to calibrate the efficiency
and to determine metallicity and age. All models obtained so far are stable.
This again supports the assumption of thermal stability. The results show that evolutionary effects
are important and that the efficiency is very small (
Arguments are presented that the velocity field in the common envelope
has a reversing layer, with motions from the secondary to the primary in the layers
just above the critical surface and from the primary to the secondary in the
stars: binaries: close --
© ESO 2004