Gamma-ray bursts from accreting black holes in neutron star mergers

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 r emnant of a neutron star merger within the dynamical time scale of a few mi lliseconds. The simulations are performed with four nested cartesian grids which allow for both a good resolution near the central black hole and a la rge computational volume. They include the use of a physical equation of st ate 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 w ith a Paczynski-Wiita potential. In a post-processing step, we evaluate our models for the energy deposition by nu<(nu)over bar> annihilation around t he accretion torus. We find that the torus formed after neutron star merging has a mass between several 10(-2) M. and a few 10(-1) M. with maximum densities around 10(12) g cm(-3) and maximum temperatures of about 10 MeV (entropies around 5 k(B) per nucleon). Correspondingly, the neutrino emission is huge with a total luminosity near 10(53) erg s(-1). Neutrino-antineutrino annihilation deposi ts energy in the vicinity of the torus at a rate of (3-5) x 10(50) erg s(-1 ). It is most efficient near the rotation axis where 10 to 30% of this ener gy or up to a total of 10(49) erg are dumped within an estimated emission p eriod of 0.02-0.1 s in a region with a low integral baryonic mass of about 10(-5) M.. This baryon pollution is still dangerously high, and the estimat ed maximum relativistic Lorentz factors Gamma - 1 are around unity. The con version of neutrino energy into a pair plasma, however, is sufficiently pow erful 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 nu <(nu)over bar> annihilation to account for weak, short gamma-ray bursts, if moderate beaming is involved. In fact, the barrier of the dense baryonic g as of the torus suggests that the low-density e(+/-)gamma plasma is beamed as axial jets into a fraction f(Omega) = 2 delta Omega/(4 pi) between 1/100 and 1/10 of the sky, corresponding to opening half-angles of roughly ten t o several tens of degrees. Thus gamma-burst energies of E gamma approximate to E(nu<(nu)over bar>)/f(Omega) less than or similar to 10(50)-10(51) erg seem to be within the reach of accreting black holes formed in neutron star mergers (if the source is interpreted as radiating isotropically), corresp onding to luminosities around 10(51) erg s(-1) for typical burst durations of 0.1-1 s. 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 severa l Schwarzschild radii from the black hole. Effects associated with the Kerr character of the rapidly rotating black hole, however, could increase the gamma-burst energy considerably, and effects due to magnetic fields might e ven be required to get the energies for long complex gamma-ray bursts.