Irradiation and mass transfer in low-mass compact binaries

This paper studies the reaction of low-mass stars to anisotropic irradiatio n and its implications for the long-term evolution of compact binaries (cat aclysmic variables and low-mass X-ray binaries). First, we show by means of simple homology considerations that if the energ y outflow through the surface layers of a low-mass main sequence star is bl ocked over a fraction s(eff) < 1 of its surface (e.g. as a consequence of a nisotropic irradiation) it will inflate only modestly, by a factor similar to (1 - s(eff))(-0.1). The maximum contribution to mass transfer of the the rmal relaxation of the donor star is s(eff) times what one obtains for isot ropic (s(eff) = 1) irradiation. The duration of this irradiation-enhanced m ass 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 give s results in acceptable quantitative agreement with detailed numerical comp utations. Third, we show in a detailed stability analysis that if mass transfer is no t strongly enhanced by consequential angular momentum losses, cataclysmic v ariables are stable against irradiation-induced runaway mass transfer if th e mass of the main sequence donor is M less than or similar to 0.7M.. If M greater than or similar to 0.7M. systems may be unstable, subject to the ef ficiency of irradiation. Low-mass X-ray binaries, despite providing much hi gher 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 phas es 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 n ecessary condition for the cycles to be maintained is that this time scale has to be much shorter (less than or similar to 0.05) than the time scale o n which mass transfer is driven.