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 lowmass X-ray binaries). First, we show by means of simple homology considerations that if the energy outflow through the surface layers of a lowmass main sequence star is blocked over a fraction seff < 1 of its surface (e.g. as a consequence of anisotropic irradiation) it will inflate only modestly, by a factor ∼ (1 − seff)−0.1. The maximum contribution to mass transfer of the thermal relaxation of the donor star is seff times what one obtains for isotropic (seff = 1) irradiation. The duration of this irradiation-enhanced mass transfer is of the order of 0.1| ln(1−seff)| times the thermal time scale of the convective envelope. Numerical computations involving full 1D stellar models confirm these results. Second, we present a simple analytic one-zone model for computing the blocking effect by irradiation which gives results in acceptable quantitative agreement with detailed numerical computations. Third, we show in a detailed stability analysis that if mass transfer is not strongly enhanced by consequential angular momentum losses, cataclysmic variables are stable against irradiation-induced runaway mass transfer if the mass of the main sequence donor is M <∼ 0.7M . If M >∼ 0.7M systems may be unstable, subject to the efficiency of irradiation. Lowmass 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 seff 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 transfer is driven.