Irradiation and mass transfer in low-mass compact binaries

This paper studies the reaction of low-mass stars to anisotropic irradiation and its implications for the long-term evolution of compact binaries (cataclysmic variables and low- mass X-ray binaries). First, we show by means of simple homology considerations that if the energy outflow through the surface layers of a low- mass main sequence star is blocked over a fraction se 0:7M systems may be unstable, subject to the efficiency of irradiation. Low- mass X-ray binaries, despite providing much higher irradiating fluxes, are even less susceptible to this instability. If a binary is unstable, mass transfer must evolve through a limit cycle in which phases of irradiation-induced high mass transfer alternate with phases of small (or no) mass transfer. At the peak rate mass transfer proceeds on se times the thermal time scale rate of the convective envelope. A necessary condition for the cycles to be maintained is that this time scale has to be much shorter (< 0:05) than the time scale on which mass