Expansion of accreting main-sequence stars during rapid mass transfer

Accreting main-sequence stars expand significantly when the mass accretion timescale is much shorter than their thermal timescales. This occurs during mass transfer from an evolved giant star onto a main-sequence companion in a binary system, and is an important phase in the formation of compact binaries including X-ray binaries, cataclysmic variables, and gravitational-wave sources. In this study, we compute 1D stellar models of main-sequence accretors with different initial masses and accretion rates. The calculations are used to derive semi-analytical approximations to the maximum expansion radius. We assume that mass transfer remains fully conservative as long as the inflated accretor fits within its Roche lobe, leading stars to behave like hamsters, stuffing excess material behind their expanding cheeks. We suggest a physically motivated prescription for the mass growth of such "hamstars", which can be used to determine mass-transfer efficiency in rapid binary population synthesis models. With this prescription, we estimate that progenitors of high-mass X-ray binaries and gravitational-wave sources may have experienced highly non-conservative mass transfer. In contrast, for low-mass accretors, the accretion timescale can exceed the thermal timescale by a larger factor without causing significant radial expansion.