Development of convective envelopes in massive stars

Context. The structure of stellar envelopes strongly influences the course and outcome of binary mass transfer, in particular of common-envelope (CE) evolution. Convective envelopes can most easily be ejected during CE events, leading to short-period binaries and, potentially, gravitational-wave (GW) sources. Conversely, radiative envelopes are thought to lead to CE mergers and Thorne-Żytkow objects (TŻOs) or quasi-stars (QSs). Aims. Rapid binary models based on Hurley et al. (2000, MNRAS, 315, 543) often assume that any CE event with a Hertzsprung gap donor results in a CE merger, in tension with the literature. We improve on this assumption with a more self-consistent criterion based on the presence of a convective envelope. Methods. Using 1D stellar models ( MESA ), we systematically investigated the development of convective envelopes in massive stars. We provided fitting formulae for rapid binary codes and implemented them into the StarTrack population synthesis code to refine the CE treatment and examined the impact on GW sources, TŻOs, and QSs. Results. We show that convective envelopes in massive stars are highly sensitive to the treatment of superadiabacity and the mixing length. Our revised CE model significantly reduces (by a factor ∼20) the predicted merger rate of binary black hole (BH-BH) mergers with total masses between ∼20 and 50 M ⊙ . This leads to a bimodal mass distribution with a strong metallicity dependence. We also predict that the current TŻO–QS formation rate in the Galaxy (up to ∼10 −4 yr −1 ), combined with their predicted lifetimes, makes their detection unlikely. Conclusions. Our study strongly suggests that the role of CE evolution in the formation of BH-BH mergers has been considerably overestimated for BH-BH mergers with M tot ≥ 20 M ⊙ . We highlight that any prediction from the CE channel for massive BH-BH mergers (> 50 M ⊙ ) heavily hinges on our limited understanding of stellar structure and mass loss close to the Eddington limit.