ABSTRACT
We investigate the common envelope binary interaction, that leads to the formation of compact binaries, such as the progenitors of Type Ia supernovae or of mergers that emit detectable gravitational waves. In this work, we diverge from the classic numerical approach that models the dynamic inspiral. We focus instead on the asymptotic behaviour of the common envelope expansion after the dynamic inspiral terminates. We use the SPH code phantom to simulate one of the set-ups from Passy et al., with a 0.88 M⊙, 83 R⊙ RGB primary and a 0.6 M⊙ companion, then we follow the ejecta expansion for 50 yr. Additionally, we utilize a tabulated equation of state including the envelope recombination energy in the simulation (Reichardt et al.), achieving a full unbinding. We show that, as time passes, the envelope’s radial velocities dominate over the tangential ones, hence allowing us to apply an homologous expansion kinematic model to the ejecta. The external layers of the envelope become homologous as soon as they are ejected, but it takes 5000 d (14 yr) for the bulk of the unbound gas to achieve the homologously expanding regime. We observe that the complex distribution generated by the dynamic inspiral evolves into a more ordered, shell-like shaped one in the asymptotic regime. We show that the thermodynamics of the expanding envelope are in very good agreement with those expected for an adiabatically expanding sphere under the homologous condition and give a prediction for the location and temperature of the photosphere assuming dust to be the main source of opacity. This technique ploughs the way to determining the long-term light behaviour of common envelope transients.
Energy Transfer by Circulation in W Ursae Majoris Systems