  The distinguishing feature of the evolution of close binary stars is the role
played by the mass exchange between the component stars. Whether the mass
transfer is dynamically stable is one of the essential questions in binary
evolution. In the limit of extremely rapid mass transfer, the response of a
donor star in an interacting binary becomes asymptotically one of adiabatic
expansion. We use the adiabatic mass loss model to systematically survey the
thresholds for dynamical timescale mass transfer over the entire span of
possible donor star evolutionary states. We also simulate mass loss process
with isentropic envelopes, the specific entropy of which is fixed to be that at
the base of the convective envelope, to artificially mimic the effect of such
mass loss in superadiabatic surface convection regions, where the adiabatic
approximation fails. We illustrate the general adiabatic response of 3.2 Msun
donor stars at different evolutionary stages. We extend our study to a grid of
donor stars with different masses (from 0.1 to 100 Msun with Z = 0.02) and at
different evolutionary stages. We proceed to present our criteria for
dynamically unstable mass transfer in both tabular and graphical forms. For red
giant branch and asymptotic giant branch donors in systems with such mass
ratios, they may have convective envelopes deep enough to evolve into common
envelopes on a thermal timescale, if the donor star overfills its outer
Lagrangian radius. Our results show that the red giant branch and asymptotic
giant branch stars tend to be more stable than previously believed, and this
may be helpful to explain the abundance of observed post-AGB binary stars with
an orbital period of around 1000 days.

Solar and Stellar Astrophysics