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. Here, we use a large grid of detailed binary evolution models for primaries in the initial mass range 10 to 40 Solar masses of LMC and SMC composition, to derive analytic fits for the key quantities needed in rapid binary evolution codes, i.e., the duration of core hydrogen burning, and the resulting donor star mass. Systems with shorter orbital periods produce up to 50% lighter stripped donors and have a up to 30% larger lifetime than wider systems. We find that both quantities depend strongly on the initial binary orbital period, but that 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.