Thresholds for Rapid Mass Transfer in Binary System. I. Polytropic Models

The adiabatic responses to mass loss of simple and compound polytropic star models are explored. The results show that stars in thermal equilibrium with isentropic surface layers are linearly unstable if the mass ratio exceeds a finite critical threshold q(0). Unless the mass fraction in these surface layers is quite small, q(0) is of the order of unity. On the other hand, stars in thermal equilibrium with subadiabatic surface layers are linearly stable for any value of the mass ratio. A finite-amplitude instability exists to which radiative stars are subject. If the initial phases of mass transfer are sufficiently rapid, such a star may undergo a delayed transition to dynamical time scale mass loss. Red giants with small core mass fractions behave very much like fully convective stars, expanding adiabatically as they lose mass.