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 0.10 M _ { \sun } to 100 M _ { \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 time scale ) 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 time scale 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 } agree well with the behavior of time-dependent models by Chen & Han ( 11 ) of intermediate-mass stars initiating mass transfer in the Hertzsprung gap .
Application of our results to cataclysmic variables , as systems which must be stable against rapid mass transfer , nicely circumscribes the range in q _ { ad } as a function of orbital period in which they are found .
These results are intended to advance the verisimilitude of population synthesis models of close binary evolution .