Journey to the center of the common envelope evolution

          Three-dimensional hydrodynamical simulations of common envelope evolution are often terminated soon after the initial dynamical plunge of the companion transitions into a long-lasting post-dynamical inspiral with a slowly varying semimajor axis,
          a
          b
          . This premature termination is often due to insufficient numerical resolution and challenges associated with the softening of the gravitational potential of the two cores. In this work we used statically refined 3D hydrodynamical simulations to study non-accreting binaries orbiting inside a common envelope, exploring the effects of varying numerical resolution,
          δ
          , gravitational potential softening prescriptions, and the associated softening length scale,
          ϵ
          . We find that quantities such as the binary inspiral timescale or the volume-averaged shearing rate typically converge to asymptotic values only for
          ϵ
          ≤0.1
          a
          b
          and
          δ
          ≤6×10
          −3
          a
          b
          , with smaller
          ϵ
          requiring correspondingly smaller
          δ
          . This suggests that many of the contemporary simulations could effectively be under-resolved. After a few tens of binary orbits, the two cores become surrounded by a corotating, nearly hydrostatic gas structure that resembles the shared envelope of a contact binary. We propose that this structure is responsible for the slowing of the dynamical inspiral, leading to an asymptotic inspiral timescale of approximately 10
          5
          orbital periods for a binary mass ratio
          q
          =1/3, and approximately 10
          6
          orbital periods for a binary mass ratio
          q
          =1. Even in the absence of magnetic fields, we observe intermittent polar outflows collimated by partially centrifugally evacuated polar funnels. We discuss the implications for the long-term evolution in the post-dynamical inspiral phase and the ultimate emergence of the post-common-envelope binary.