Considerations on the role of fall-back discs in the final stages of the common envelope binary interaction

The common envelope interaction is thought to be the gateway to all evolved compact binaries and mergers. Hydrodynamic simulations of the common envelope interaction between giant stars and their companions are restricted to the dynamical, fast, in-spiral phase. They find that the giant envelope is lifted during this phase, but remains mostly bound to the system. At the same time, the orbital separation is greatly reduced, but in most simulations it levels off at values larger than measured from observations. We conjectured that during the post-in-spiral phase the bound envelope gas will return to the system. Using hydrodynamic simulations, we generate initial conditions for our simulation that result in a fall-back disc with total mass and angular momentum in line with quantities from the simulations of Passy et al. We find that the simulated fall-back event reduces the orbital separation efficiently, but fails to unbind the gas before the separation levels off once again. We also find that more massive fall-back discs reduce the orbital separation more efficiently, but the efficiency of unbinding remains invariably very low. From these results we deduce that unless a further energy source contributes to unbinding the envelope (such as was recently tested by Nandez et al.), all common envelope interactions would result in mergers. On the other hand, additional energy sources are unlikely to help, on their own, to reduce the orbital separation. We conclude by discussing our dynamical fall-back event in the context of a thermally regulated post-common envelope phase.