Common envelope: on the mass and the fate of the remnant

One of the most important and uncertain stages in the binary evolution is the common envelope (CE) event. Significant attention has been devoted in the literature so far to the energy balance during the CE event, expected to determine the outcome. However this question is intrinsically coupled with the problem of what is left from the donor star after the CE and its immediate evolution. In this paper we argue that an important stage has been overlooked: post-CE remnant thermal readjustment phase. We propose a methodology for unambiguously defining the post-CE remnant mass after it has been thermally readjusted, namely by calling the core boundary the radius in the hydrogen shell corresponding to the local maximum of the sonic velocity. We argue that the important consequences of the thermal readjustment phase are: (i) a change in the energy budget requirement for the CE binaries and (ii) a companion spin-up and chemical enrichment, as a result of the mass transfer that occurs during the remnant thermal readjustment (TR). More CE binaries are expected to merge. If the companion is a neutron star, it will be mildly recycled during the TR phase. The mass transfer during the TR phase is much stronger than the accretion rate during the common envelope, and therefore satisfies the condition for a hypercritical accretion better. We also argue that the TR phase is responsible for a production of mildly recycled pulsars in double neutron stars.