Analytic approximations for massive close post-mass transfer binary systems

Massive binary evolution models are needed to predict massive star populations in star-forming galaxies, the supernova diversity, and the number and properties of gravitational wave sources. Such models are often computed using so-called rapid binary evolution codes, which approximate the evolution of the binary components based on detailed single star models. However, about one-third of the interacting massive binary stars undergo mass transfer during core hydrogen-burning (Case A mass transfer), whose outcome is difficult to derive from single star models. For this work, we used a large grid of detailed binary evolution models for primaries in the initial mass range 10–40 M⊙ with a Large and Small Magellanic Cloud composition, to derive analytic fits for the key quantities needed in rapid binary evolution codes, that is, the duration of core hydrogen-burning, and the resulting donor star mass. We find that systems with shorter orbital periods produce up to 50% lighter stripped donors and have a lifetime up to 30% larger than wider systems. Both quantities strongly depend on the initial binary orbital period, but the initial mass ratio and the mass-transfer efficiency of the binary have little impact on the outcome. Our results are easily parameterisable and can be used to capture the effects of Case A mass transfer more accurately in rapid binary evolution codes.