1999A&A...344..573R

By means of three-dimensional hydrodynamic simulations with a Eulerian PPM code we investigate the formation and the properties of the accretion torus around the stellar mass black hole which we assume to originate from the remnant of a neutron star merger within the dynamical time scale of a few milliseconds. The simulations are performed with four nested cartesian grids which allow for both a good resolution near the central black hole and a large computational volume. They include the use of a physical equation of state as well as the neutrino emission from the hot matter of the torus. The gravity of the black hole is described with a Newtonian and alternatively with a Paczynski-Wiita potential. In a post-processing step, we evaluate our models for the energy deposition by νν annihilation around the accretion torus. We find that the torus formed after neutron star merging has a mass between several 10^–2M_☉ and a few 10^–1M_☉ with maximum densities around 10¹²g/cm³ and maximum temperatures of about 10MeV (entropies around 5k_B per nucleon). Correspondingly, the neutrino emission is huge with a total luminosity near 10⁵³erg/s. Neutrino-antineutrino annihilation deposits energy in the vicinity of the torus at a rate of (3-5)x10⁵⁰erg/s. It is most efficient near the rotation axis where 10 to 30% of this energy or up to a total of 10⁴⁹erg are dumped within an estimated emission period of 0.02-0.1s in a region with a low integral baryonic mass of about 10^–5M_☉. This baryon pollution is still dangerously high, and the estimated maximum relativistic Lorentz factors Γ-1 are around unity. The conversion of neutrino energy into a pair plasma, however, is sufficiently powerful to blow out the baryons along the axis so that a clean funnel should be produced within only milliseconds. Our models show that accretion on the black hole formed after neutron star merging can yield enough energy by νν annihilation to account for weak, short gamma-ray bursts, if moderate beaming is involved. In fact, the barrier of the dense baryonic gas of the torus suggests that the low-density e^±γ plasma is beamed as axial jets into a fraction f_Ω= 2δΩ/(4π) between 1/100 and 1/10 of the sky, corresponding to opening half-angles of roughly ten to several tens of degrees. Thus γ-burst energies of E_γ≃E_νν/f_Ω≲ 10⁵⁰-10⁵¹erg seem to be within the reach of accreting black holes formed in neutron star mergers (if the source is interpreted as radiating isotropically), corresponding to luminosities around 10⁵¹erg/s for typical burst durations of 0.1-1s. Gravitational capture of radiation by the black hole, redshift and ray bending do not reduce the jet energy significantly, because most of the neutrino emission comes from parts of the torus at distances of several Schwarzschild radii from the black hole. Effects associated with the Kerr character of the rapidly rotating black hole, however, could increase the γ-burst energy considerably, and effects due to magnetic fields might even be required to get the energies for long complex gamma-ray bursts.