Long-term evolution of compact binaries with irradiation feedback

We resume the discussion about irradiation-driven mass transfer cycles in semi- detached compact binary systems. The analytical model that describes the onset of these cycles, which occur on a thermal timescale of the donor star, is reexamined. We take into account a contribution of the thermal relaxation which is not related to the irradiation of the donor star and which was neglected in previous studies. Cataclysmic variables (CVs) containing extended giant donors are more stable than previously thought. CVs close to the upper edge of the period gap can undergo cycles for low angular momentum loss rates, as they have been suggested by recent magnetic braking prescriptions, while they are stable for high braking rates. A model for the irradiation geometry that takes into account surface elements near the terminator of the donor star indicates that possibly also low-mass X-ray binaries (LMXBs) can undergo mass transfer cycles. Regarding the braking rate, which is necessary to drive cycles, basically the same restrictions apply for short period LMXBs as they do for short period CVs. We confirm that LMXBs containing giants can undergo cyles. In terms of an irradiation efficiency parameter \alpha CVs are susceptible to the irradiation instability for \alpha >= 0.1 while LMXBs are susceptible for \alpha <= 0.1. The predictions of the analytical model are checked by the first long-term evolutionary computations of systems undergoing mass transfer cycles with full 1D stellar models. For unevolved main sequence (MS) and giant donors the analytic model provides reasonable values for the boundaries of the stable and unstable regions while CVs containing highly evolved MS donors are more stable at high braking rates than expected.Taking into account irradiation the minimum period of CVs is increased by up to 1-2 minutes, depending on \alpha.