Polytropic neutron star - black hole merger simulations with a Paczynski-Wiita potential

Context: Mergers of neutron stars (NS) and black holes (BH) are among the strongest sources of gravitational waves and are potential central engines for short gamma-ray bursts. Aims: We aim to compare the general relativistic (GR) results by other groups with Newtonian calculations of models with equivalent parameters. We vary the mass ratios between NS and BH and the compactness of the NS. The mass of the NS is 1.4 M_sol. We compare the dynamics in the parameter-space regions where the NS is expected to reach the innermost stable circular orbit (ISCO) before being tidally disrupted (mass shedding, MS) and vice versa. Methods: The hydrodynamics is evolved by a Newtonian PPM scheme with four levels of nested grids. We use a polytropic EoS (Gamma=2), as was done in the GR simulations. However, instead of full GR we use a Newtonian potential supplemented by a Paczynski-Wiita-Artemova potential for the BH, both disregarding and including rotation of the BH. Results: If the NS is compact (C=0.18) it is accreted by the BH more quickly, and only a small amount of mass remains outside the BH. If the mass ratio is small (Q=2 or 3) or the NS is less compact (C=0.16 or less) the NS is tidally torn apart before being accreted. Although most of the mass is absorbed by the BH, some 0.1 M_sol remain in a tidal arm. For small mass ratios the tidal arm can wrap around the BH to form a thick disk. When including the effects of BH spin-up or spin-down by the accreted matter, more mass remains in the surroundings (0.2-0.3 M_sol). Conclusions: Although details and quantitative results differ, the general trends of our Newtonian calculations are similar to the GR calculations. A clear delimiting line that separates ISCO from the MS cases is not found. Inclusion of BH rotation as well as sufficient numerical resolution are extremely important.