On the formation and evolution of common envelope systems

We discuss the formation of a common envelope system following dynamically unstable mass transfer in a close binary and the subsequent dynamical evolution and final fate of the envelope. We base our discussion on new three-dimensional hydrodynamic calculations that we have performed for a close binary system containing a 4 M_⊙ red giant with a 0.7 M_⊙ main-sequence star companion. The initial parameters are chosen to model the formation of a system resembling V471 Tau, a typical progenitor of a cataclysmic variable binary. The calculations are performed using the smoothed particle hydrodynamics (SPH) method with up to 5 × 10⁴ particles. As initial condition we use an exact hydrostatic equilibrium configuration at the onset of dynamically unstable mass transfer. The nonlinear development of the instability is followed using SPH until a quasi-static common envelope configuration is formed. In our highest resolution calculation, we find evidence for a corotating region of gas around the central binary. This is in agreement with the theoretical model proposed by Meyer & Meyer-Hofmeister for the evolution of common envelope systems, in which this central corotating region is coupled to the envelope through viscous angular momentum transport only. We also find evidence that the envelope is convectively unstable, in which case the viscous dissipation time could be as short as ∼ 100 dynamical times, leading to rapid ejection of the envelope. For V471 Tau our results, and the observed parameters of the system, are entirely consistent with rapid envelope ejection on a timescale ∼ 1 yr and an efficiency parameter α_CE ≃ 1.