The role of mass transfer and common envelope evolution in the formation of merging binary black holes

As the number of observed merging binary black holes (BHs) grows, accurate models are required to disentangle multiple formation channels. In models with isolated binaries, important uncertainties remain regarding the stability of mass transfer (MT) and common-envelope (CE) evolution. To study some of these uncertainties, we have computed simulations using MESA of a $30M_\odot$, low metallicity ($Z_\odot/10$) star with a BH companion. We developed a prescription to compute MT rates including possible outflows from outer Lagrangian points, and a method to self-consistently determine the core-envelope boundary in the case of CE evolution. We find that binaries survive a CE only if unstable MT happens after the formation of a deep convective envelope, resulting in a narrow range (0.2 dex) in period for envelope ejection. All cases where interaction is initiated with a radiative envelope have large binding energies ($\sim 10^{50}$ erg), and merge during CE even under the assumption that all the internal and recombination energy of the envelope, as well as the energy from an inspiral, is used for ejection. This is independent of core helium ignition for the donor, a condition under which various rapid-population synthesis calculations assume a successful ejection is possible. Moreover, we find that the critical mass ratio for instability is such that for periods between $\sim 1-1000$ days merging binary BHs can be formed via stable MT. A large fraction of these systems overflow their L$_2$ equipotential, in which case we find stable MT produces merging binary BHs even under extreme assumptions of mass and angular momentum outflows. Our conclusions are limited to the study of one donor star, but suggest that population synthesis calculations overestimate the formation rate of merging binary BHs produced by CE evolution, and that stable MT could dominate the rate from isolated binaries.