Numerical Methods for the Simulation of Dynamical Mass Transfer in Binaries

Abstract

We describe computational tools that have been developed to simulate dynamical mass transfer in semidetached, polytropic binaries that are initially executing synchronous rotation upon circular orbits. Initial equilibrium models are generated with a self-consistent Ðeld algorithm; models are then evolved in time with a parallel, explicit, Eulerian hydrodynamics code with no assumptions made about the symmetry of the system. PoissonÏs equation is solved along with the equations of ideal Ñuid mechanics to allow us to treat the nonlinear tidal distortion of the components in a fully self-consistent manner. We present results from several standard numerical experiments that have been conducted to assess the general viability and validity of our tools, and from benchmark simulations that follow the evolution of two detached systems through Ðve full orbits (up to approximately 90 stellar dynamical times). These benchmark runs allow us to gauge the level of quantitative accuracy with which simulations of semidetached systems can be performed using presently available computing resources. We Ðnd that we should be able to resolve mass transfer at levels M0 /M[few]10~5 per orbit through approximately 20 orbits with each orbit taking about 30 hours of computing time on parallel computing platforms.