Newtonian Hydrodynamics of the Coalescence of Black Holes with Neutron Stars. I. Tidally Locked Binaries with a Stiff Equation of State

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Abstract
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 = KρΓ, with the adiabatic index Γ = 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/MBH (where M is the mass of the neutron star and MBH 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.

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