Mass Transfer in Binary Stellar Evolution and Its Stability

Abstract

The evolution of a binary star system by various analytical and numerical approximations of mass transfer rate normalized to the equilibrium rate and its stability conditions are investigated. We present results from investigations of mass transfer and stability in close binary star systems using the different orbital parameters. The stability and instability of mass transfer in binary star evolution depends on the exchange of material which the response of the binary to the initial Roche lobe overflow causes the donor to loose even more material. Our work is mainly focused on basic mathematical derivations, analytical and numerical solutions in order to explain the mass transfer system in different orbital parameters as well as the results are compared with previous studies in both cases. Mass transfer is usually stable, as long as the winds specific angular momentum does not exceed the angular momentum per reduced mass of the system. This holds for both dynamical and thermal time scales. Those systems which are not stable will usually transfer mass on the thermal time scale. The variation of Roche lobe radius with mass ratio in the binary, for various orbital parameters in the conservative and non-conservative mass transfer, as well as the evolution equations, orbital angular momentum of the binary system and the corresponding analytical and numerical solutions for different cases, under certain restrictive approximations is derived, simulated and discussed.