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Description
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 survey here adiabatic mass loss from Population I stars (Z=0.02) of mass 0.10M_{sun}_-100M_{sun}_ from the zero-age main sequence to the base of the giant branch, or to central hydrogen exhaustion for lower main sequence stars. The logarithmic derivatives of radius with respect to mass along adiabatic mass-loss sequences translate into critical mass ratios for runaway (dynamical timescale) mass transfer, evaluated here under the assumption of conservative mass transfer. For intermediate- and high-mass stars, dynamical mass transfer is preceded by an extended phase of thermal timescale mass transfer as the star is stripped of most of its envelope mass. The critical mass ratio q_ad_ (throughout this paper, we follow the convention of defining the binary mass ratio as q{equiv}M_donor_/M_accretor_) above which this delayed dynamical instability occurs increases with advancing evolutionary age of the donor star, by ever-increasing factors for more massive donors. Most intermediate- or high-mass binaries with nondegenerate accretors probably evolve into contact before manifesting this instability. As they approach the base of the giant branch, however, and begin developing a convective envelope, q_ad_ plummets dramatically among intermediate-mass stars, to values of order unity, and a prompt dynamical instability occurs. Among low-mass stars, the prompt instability prevails throughout main sequence evolution, with q_ad_ declining with decreasing mass, and asymptotically approaching q_ad_=2/3, appropriate to a classical isentropic n=3/2 polytrope. Our calculated q_ad_ values agree well with the behavior of time-dependent models by Chen & Han (2003MNRAS.341..662C) of intermediate-mass stars initiating mass transfer in the Hertzsprung gap. Application of our results to cataclysmic variables, as systems that must be stable against rapid mass transfer, nicely circumscribes the range in q_ad_ as a function of the orbital period in which they are found. These results are intended to advance the verisimilitude of population synthesis models of close binary evolution.
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