Newtonian hydrodynamics of the coalescence of black holes with neutron stars III: Irrotational binaries with a stiff equation of state

We present a numerical study of the hydrodynamics in the final stages of inspiral in a black hole–neutron star binary, when the binary separation becomes comparable to the stellar radius. We use a Newtonian three–dimensional Smooth Particle Hydrodynamics (SPH) code, and model the neutron star with a stiff (adiabatic index Γ = 3 and Γ = 2.5) polytropic equation of state and the black hole as a Newtonian point mass which accretes matter via an absorbing boundary at the Schwarzschild radius. Our initial conditions correspond to irrotational binaries in equilibrium (approximating the neutron star as a compressible tri–axial ellipsoid), and we have explored configurations with different values of the initial mass ratio q = MNS/MBH, ranging from q = 0.5 to q = 0.2. The dynamical evolution is followed using an ideal gas equation of state for approximately 23 ms. We have included gravitational radiation losses in the quadrupole approximation for a point–mass binary. For the less compressible case (Γ = 3), we find that after an initial episode of intense mass transfer, the neutron star is not completely disrupted and a remnant core remains in orbit about the black hole in a stable binary configuration. For Γ = 2.5—which is believed to be appropriate for matter at nuclear densities—the tidal disruption process is more complex, with the core of the neutron star surviving the initial mass transfer episode but being totally disrupted during a second periastron passage. The resulting accretion disc formed around the black hole contains a few tenths of a solar mass. A nearly baryon–free axis is present in the system throughout the coalescence, and only modest beaming of a relativistic fireball that could give rise to a gamma–ray burst would be sufficient to avoid excessive baryon contamination. We find that some mass (on the order of 10 M⊙) may be dynamically ejected from the system, and could thus contribute substantially to the amount of observed r–process material in the galaxy. We calculate the gravitational radiation waveforms and luminosity emitted during the coalescence in the quadrupole approximation, and show that they directly reflect the morphology of the coalescence process. Finally, we present the results of dynamical simulations that have used spherical neutron stars relaxed in isolation as initial conditions, in order to gauge the effect of using non–equilibrium initial conditions on the evolution of the system.