The radius variations of accreting main sequence stars and mass transfer instability

Many previous works studied the dynamical timescale mass transfer stability criteria based on the donor response with neglecting the stellar structure of the accretor. In this letter, we investigate the radial response of accretors with mass accumulation and its effect on the binary mass transfer stability. We perform a series of detailed stellar evolution simulations with different types of accretors and obtain the radial variations of stars accreting at different rates. Since the time within which the donor loses half of the original mass has a correlation with the donor mass, we approximately obtain the mean mass transfer rate as a function of mass ratio. Assuming that the common envelope (CE) phase occurs if the accretor radius exceeds the outer Roche lobe radius, we obtain the critical mass ratio of dynamically unstable mass transfer. We find the critical mass ratios for donors filling their Roche lobes at the Main Sequence (MS) and Hertzsprung Gap (HG) stages are smaller than that derived from the radial response of the donor in the traditional way. Our results may suggest that the binary is easier to enter into the CE phase for a donor star at the MS or HG stage than previously believed.