Relativistic outflows from remnants of compact object mergers and their viability for short gamma-ray bursts

Max-Planck-Institut für Astrophysik, Postfach 1317, 85741 Garching, Germany e-mail: maa@mpa-garching.mpg.de

Received: 19 August 2004
Accepted: 20 January 2005

Abstract

We present the first general relativistic hydrodynamic models of the launch and evolution of relativistic jets and winds, driven by thermal energy deposition, possibly due to neutrino-antineutrino annihilation, in the close vicinity of black hole-accretion torus systems. The latter are considered to be the remnants of compact object mergers. Our two-dimensional simulations establish the link between models of such mergers and future observations of short gamma-ray bursts by the SWIFT satellite. They show that ultrarelativistic outflow with maximum terminal Lorentz factors around 1000 develops for polar energy deposition rates above some erg s^-1 per steradian, provided the merger environment has a sufficiently low baryon density. By the interaction with the dense accretion torus the ultrarelativistic outflow with Lorentz factors Γ above 100 is collimated into a sharp-edged cone that is embedded laterally by a wind with steeply declining Lorentz factor. The typical semi-opening angles of the cone are , corresponding to about of the hemisphere and apparent isotropized energies (kinetic plus internal) up to ≈erg although at most of the deposited energy is transferred to the outflow with . The viability of post-merger black hole-torus systems as engines of short, hard gamma-ray bursts is therefore confirmed. The annihilation of neutrino-antineutrino pairs radiated from the hot accretion torus appears as a suitable energy source for powerful axial outflow even if only ≈erg are deposited within a cone of half-opening angle around the system axis. Although the torus lifetimes are expected to be only between some 0.01 s and several 0.1 s, our models can explain the durations of all observed short gamma-ray bursts, because different propagation velocities of the front and rear ends will lead to a radial stretching of the ultrarelativistic fireball before transparency is reached. The ultrarelativistic flow reveals a highly non-uniform structure caused by the action of Kelvin-Helmholtz instabilities that originate at the fireball-torus interface. Large radial variations of the baryon density (up to several orders of magnitude) are uncorrelated with moderate variations of the Lorentz factor (factors of a few) and fluctuations of the gently declining radiation-dominated pressure. In the angular direction the Lorentz factor reveals a nearly flat plateau-like maximum with values of several hundreds, that can be located up to  off the symmetry axis, and a steep decrease to less than 10 for polar angles larger than . Lateral expansion of the ultrarelativistic core of the flow is prevented by a subsonic velocity component of about  towards the symmetry axis, whereas the moderately relativistic wings show a subsonic sideways inflation with less than  (measured in the frame comoving with the radial flow).