The role of stellar expansion on the formation of gravitational wave sources

Massive stars are the progenitors of black holes and neutron stars, the mergers of which can be detected with gravitational waves (GW). The expansion of massive stars is one of the key factors affecting their evolution in close binary systems, but it remains subject to large uncertainties in stellar astrophysics. For population studies and predictions of GW sources, the stellar expansion is often simulated with the analytic formulae from Hurley et al. (2000). These formulae need to be extrapolated and are often considered outdated. In this work, we present five different prescriptions developed from 1D stellar models to constrain the maximum expansion of massive stars. We adopt these prescriptions to investigate how stellar expansion affects mass transfer interactions and in turn the formation of GW sources. We show that limiting radial expansion with updated 1D stellar models, when compared to the use of Hurley et al. (2000) radial expansion formulae, does not significantly affect GW source properties (rates and masses). This is because most mass transfer events leading to GW sources are initialized in our models before the donor star reaches its maximum expansion. The only significant difference was found for the mass distribution of massive binary black hole mergers (M_tot > 50 M_⊙) formed from stars that may evolve beyond the Humphreys-Davidson limit, whose radial expansion is the most uncertain. We conclude that understanding the expansion of massive stars and the origin of the Humphrey-Davidson limit is a key factor for the study of GW sources.