Tidal heating in close binary stellar systems

Tidal heating of a low-mass star in a close binary system, resulting from the conjugate effect of angular momentum loss and tidal action, is investigated via a detailed study of the flow inside the secondary. In the case of cataclysmic binaries we find that viscous dissipation is at most |10⁻³\,×| the nuclear luminosity of the star; we thus confirm by a more exact model the result of Verbunt & Hut. It is shown, however, that the dissipation is very sensitive to the turbulent viscosity in the envelope of the secondary. The lack of reliable theory for such a viscosity, especially in presence of fast rotation, makes the estimation of total dissipation rather uncertain. This uncertainty leaves the possibility open that when the evolution is driven by magnetic braking, tidal dissipation may reach the luminosity of the star. We also consider the case of very close pairs of white dwarfs. We show that such pairs, which are thought to be the progenitors of Type I Supernovae (Webbink), may dissipate a power as large as |10³⁸\,erg\,s⁻¹|⁠, provided that they reach synchronization; such a heating will strongly modify the conditions in which the nuclear explosion starts. We show that the detection of such objects is quite difficult.