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Gamma-ray bursts from accreting black holes in neutron star mergers
M. Ruffert 1 and
H.-Th. Janka 2
Received 28 September 1998 / Accepted 11 January 1999
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 Paczyski-Wiita potential. In a post-processing step, we evaluate our models for the energy deposition by annihilation around the accretion torus.
We find that the torus formed after neutron star merging has a mass between several and a few with maximum densities around and maximum temperatures of about MeV (entropies around 5 per nucleon). Correspondingly, the neutrino emission is huge with a total luminosity near . Neutrino-antineutrino annihilation deposits energy in the vicinity of the torus at a rate of (3-. It is most efficient near the rotation axis where 10 to 30% of this energy or up to a total of are dumped within an estimated emission period of 0.02-0.1 s in a region with a low integral baryonic mass of about . This baryon pollution is still dangerously high, and the estimated maximum relativistic Lorentz factors 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 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 plasma is beamed as axial jets into a fraction between and of the sky, corresponding to opening half-angles of roughly ten to several tens of degrees. Thus -burst energies of -erg 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 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 several Schwarzschild radii from the black hole. Effects associated with the Kerr character of the rapidly rotating black hole, however, could increase the -burst energy considerably, and effects due to magnetic fields might even be required to get the energies for long complex gamma-ray bursts.
Key words: elementary particles hydrodynamics stars: binaries: close stars: neutron gamma rays: bursts
Present address: Department of Mathematics & Statistics, University of Edinburgh, Scotland, EH9 3JZ, U.K.
Send offprint requests to: H.-Th. Janka
Online publication: March 18, 1999