  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 5
simulations of Passy et al. (a 0.88Msun, 90Rsun RGB primary with companions in
the range 0.1 to 0.9Msun) using a new AMR 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 5 identical simulations
but with a 2.0Msun 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 a ~2.0$Msun RGB primary may
possibly end in a merger with companions as massive as 0.6Msun, something that
would not be deduced using analytical arguments based on energy conservation.
