Extending common envelope simulations from Roche lobe overflow to the nebular phase

We have simulated a common envelope interaction between a 0.88 M⊙, 90 R⊙, red giant branch star, and a 0.6 M⊙, compact companion with the smoothed particle hydrodynamics code, PHANTOM, from the beginning of the Roche lobe overflow phase to the beginning of the self-regulated inspiral, at three different resolutions. The duration of the Roche lobe overflow phase is resolution dependent and would lengthen with increased resolution beyond the ∼20 yr observed, while the inspiral phase and the post-common envelope separation are largely independent of (average) resolution. Mass transfer rates through the Lagrangian points drive the orbital evolution during the Roche lobe overflow phase, as predicted analytically. The absolute mass transfer rate is resolution dependent, but always within a factor of two of the analytical value. Similarly, the gravitational drag in the simulations is close to the analytical approximation. This verifies simulations and shows that these analytical approximations are reasonable. The L₂ and L₃ outflows observed during Roche lobe overflow remain bound, forming a circumbinary disc that is largely disrupted by the common envelope ejection. However, a longer phase of Roche lobe overflow and weaker common envelope ejection typical of a more stable Roche lobe phase may result in a surviving circumbinary disc. Finally, we examine the density distribution resulting from the interaction for simulations that include or omit the phase of Roche lobe overflow. We conclude that the degree of stability of the Roche lobe phase modulates the shape of the subsequent planetary nebula, explaining the wide range of post-common envelope planetary nebula shapes observed.