ar X iv : a st ro - p h / 94 06 03 2 v 1 1 0 Ju n 19 94 Hydrodynamics of Binary Coalescence

We present a new numerical study of the equilibrium and stability properties of close binary systems. We use the smoothed-particle hydrodynamics (SPH) technique both to construct accurate equilibrium configurations in three dimensions and to follow their hydrodynamic evolution. We adopt a simple polytropic equation of state p = Kρ with Γ = 5/3 and K =constant within each star, applicable to low-mass degenerate dwarfs as well as low-mass main-sequence stars. For degenerate configurations, we set K = K ′ independent of the mass ratio. For main-sequence stars, we adjust K and K ′ so as to obtain a simple mass-radius relation of the form R/R = M/M . Along a sequence of binary equilibrium configurations for two identical stars, we demonstrate the existence of both secular and dynamical instabilities, confirming directly the results of recent analytic work. We use the SPH method to calculate the nonlinear development of the dynamical instability and to determine the final fate of the system. We find that the two stars merge together into a single, rapidly rotating object in just a few orbital periods. Equilibrium sequences are also constructed for systems containing two nonidentical stars. These sequences terminate at a Roche limit, which we can determine very accurately using SPH. For two low-mass main-sequence stars with mass ratio q ∼< 0.4 we find that the Hubble Fellow. Departments of Astronomy and Physics, Cornell University.