Theory of mass transfer in binary stars

Calculation of the mass-transfer rate of a Roche lobe overflowing star is a fundamental task in binary star evolution theory. First, we introduce existing mass-transfer prescriptions that are based on a common set of assumptions that combine optically-thick and optically-thin regimes with different flow geometries. Next, we present our new model of mass transfer based on the assumption that the Roche potential sets up a nozzle converging on the inner Lagrangian point and that the gas flows mostly along the axis connecting both stars. We derive a set of 1D hydrodynamic equations governing the gas flow with the value of the mass-transfer rate being determined as the eigenvalue of the system. The inner boundary condition directly relates our model to the structure of the donor obtained from 1D stellar evolution codes. For the polytropic equation of state we obtain an algebraic solution that gives the mass-transfer rate within a factor of 0.9 to 1.0 of existing optically-thick prescriptions and reduces to the existing optically-thin prescription for isothermal gas. For a realistic EOS, we find that the mass-transfer rate differs by up to a factor of 4 from existing prescriptions. We illustrate the effects of our new model on a realistic binary star system. Finally, we explain how additional physics such as radiation or magnetic fields can be implemented into our new model.