It has to be cool: Supergiant progenitors of binary black hole mergers from common-envelope evolution

Abstract

Common-envelope (CE) evolution in massive binary systems is thought to be one of the most promising channels for the formation of compact binary mergers. In the case of merging binary black holes (BBHs), the essential CE phase takes place at a stage when the first BH is already formed and the companion star expands as a supergiant. We aim to decipher the kinds of BH binaries with supergiant companions that could potentially evolve through and survive a CE phase. To this end, we compute envelope binding energies from detailed massive stellar models at different evolutionary stages and metallicities. We make multiple physically extreme choices of assumptions that favor easier CE ejection as well as account for recent advancements in mass-transfer stability criteria. We find that even with the most optimistic assumptions, a successful CE ejection in BH binaries is only possible if the donor is a massive convective-envelope giant, namely a red supergiant (RSG). The same is true for neutron-star binaries with massive companions. In other words, pre-CE progenitors of BBH mergers are BH binaries with RSG companions. We find that because of its influence on the radial expansion of massive giants, metallicity has an indirect but a very strong effect on the chemical profile, density structure, and the binding energies of RSG envelopes. Our results suggest that merger rates from population-synthesis models could be severely overestimated, especially at low metallicity. Additionally, the lack of observed RSGs with luminosities above log(L/L⊙) ≈ 5.6 − 5.8, corresponding to stars with M ≳ 40 M⊙, puts into question the viability of the CE channel for the formation of the most massive BBH mergers. Either such RSGs elude detection due to very short lifetimes, or they do not exist and the CE channel can only produce BBH systems with total mass ≲50 M⊙. Finally, we discuss an alternative CE scenario in which a partial envelope ejection is followed by a phase of possibly long and stable mass transfer.