The effect of binding energy and resolution in simulations of the common envelope binary interaction

The common envelope binary interaction remains one of the least understood phases in the evolution of compact binaries, including those that result in Type Ia supernovae and in mergers that emit detectable gravitational waves. In this work, we continue the detailed and systematic analysis of 3D hydrodynamic simulations of the common envelope interaction aimed at understanding the reliability of the results. Our first set of simulations replicate the five simulations of Passy et al. (a 0.88M(circle dot), 90R(circle dot) red giant branch (RGB) primary with companions in the range 0.1-0.9M(circle dot)) using a new adaptive mesh refinement gravity solver implemented on our modified version of the hydrodynamic code ENZO. Despite smaller final separations obtained, these more resolved simulations do not alter the nature of the conclusions that are drawn. We also carry out five identical simulations but with a 2.0M(circle dot) primary RGB star with the same core mass as the Passy et al. simulations, isolating the effect of the envelope binding energy. With a more bound envelope, all the companions in-spiral faster and deeper, though relatively less gas is unbound. Even at the highest resolution, the final separation attained by simulations with a heavier primary is similar to the size of the smoothed potential even if we account for the loss of some angular momentum by the simulation. As a result, we suggest that an similar to 2.0 M-circle dot RGB primary may possibly end in a merger with companions as massive as 0.6 M-circle dot , something that would not be deduced using analytical arguments based on energy conservation.