Newtonian hydrodynamics of the coalescence of black holes with neutron stars. I. Tidally locked binaries with a stiff equation of state

We present a detailed Newtonian study of the last stages of binary evolution of a black hole and a neutron star, when the components are separated by a few stellar radii. Our simulations are carried out using a three-dimensional smooth particle hydrodynamics (SPH) code. We calculate the gravitational radiation waveforms as well as the gravitational radiation luminosity in the quadrupole approximation. The neutron star is modeled with a stiff polytropic equation of state, P = K rho(Gamma), with the adiabatic index Gamma = 3. We have performed runs with two different resolutions, using 16,944 and 8121 particles initially. Our equilibrium initial conditions correspond to tidally locked binaries with different initial values of the mass ratio q = M/M-BH (where M is the mass of the neutron star and M-BH is that of the black hole). The dynamical evolution of the system was simulated using an ideal gas equation of state for a time equivalent to several initial orbital periods. We find that for high mass ratios (q = 1 and q = 0.8, but not for q = 0.31) there is a critical separation at which the binary becomes unstable due to hydrodynamical effects and decays on a dynamical timescale. The neutron star is not completely tidally disrupted, and its core continues to orbit the black hole. For a mass ratio of unity, an accretion torus forms around the black hole and survives for several dynamical times, but no comparable accretion structure is present for lower mass ratios. For q = 0.31 we have performed two separate runs, one with gravitational radiation reaction included in our calculations, and one with no gravitational radiation reaction - in both cases we find intermittent mass transfer through Roche lobe overflow. For the stiff polytrope considered here, the binary system always survives the initial mass transfer - the encounter results in a decreased mass ratio and increased separation. In all cases, the binary axis is free of baryons.