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Abstract

Context. The stability of mass transfer is critical in determining pathways towards various kinds of compact binaries, such as compact main-sequence white-dwarf binaries, and transients, such as double white-dwarf mergers and luminous red novae. Despite its importance, very few systematic studies of the stability of mass transfer exist.
Aims. We study the behaviour of mass-losing donor stars in binary systems in a systematic way. We focus on identifying and understanding the parameter space for stable mass transfer in low- and intermediate-mass binaries with post-main-sequence donor stars as well as the properties of ultimately unstable binary systems at the onset of the instabilities.
Methods. We employed the 1D stellar evolution code MESA to simulate the mass-transfer evolution of 1404 binary systems with donor-star masses between 1 M_⊙ and 8 M_⊙. We studied the behaviour of the binaries during mass transfer, without assuming that the donor star responds adiabatically to mass loss. We treated the accretor as a point mass, which we do not evolve, and assumed the mass transfer is conservative.
Results. We considered several criteria to define when unstable mass transfer occurs. We find that the criterion that best predicts the onset of runaway mass transfer is based on the transition to an effectively adiabatic donor response to mass loss. Using this quasi-adiabatic criterion, we determine the location of the stability boundary to within a relative uncertainty of five per cent in the mass ratio at the onset of mass transfer. Defining this critical mass ratio (q_qad) in terms of accretor mass over donor mass, we find that q_qad ∼ 0.25 for stars with radiative envelopes that cross the Hertzsprung gap, while for convective giants q_qad decreases from ∼1 at the base of the red giant branch to ∼0.1 at the onset of thermal pulses on the asymptotic giant branch. Compared with recent similar studies, we find increased stability of mass transfer from convective giants. This is because an effectively adiabatic response of the donor star only occurs at a very high critical mass-transfer rate due to the short local thermal timescale in the outermost layers of a red giant. Furthermore, we find that for q > q_qad mass transfer is self-regulated, but that for evolved giants the resulting mass-transfer rates can be so high that the evolution becomes dynamical and/or the donor can overflow its outer lobe.
Conclusions. Our results indicate that mass transfer is stable for a wider range of binary parameter space than typically assumed in rapid binary population synthesis. Moreover, we find a systematic dependence of the critical mass ratio on the donor star mass and radius, which may have significant consequences for predictions of post-mass-transfer populations.