2000A&A...360..969R

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 s_eff<1 of its surface (e.g. as a consequence of anisotropic irradiation) it will inflate only modestly, by a factor ~(1-s_eff)^–0.1. The maximum contribution to mass transfer of the thermal relaxation of the donor star is s_eff times what one obtains for isotropic (s_eff=1) irradiation. The duration of this irradiation-enhanced mass transfer is of the order of 0.1|ln((1-s)_eff)| 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. 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 s_eff 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.