Magnetohydrodynamics of neutrino-cooled accretion tori around a rotating black hole in general relativity

We present our first numerical results of axisymmetric magnetohydrodynamic simulations for neutrino-cooled accretion tori around rotating black holes in general relativity. We consider tori of mass similar to 0.1-0.4M circle dot around a black hole of mass M = 4M circle dot and spin a = 0-0.9M; such systems are candidates for the central engines of gamma-ray bursts (GRBs) formed after the collapse of massive rotating stellar cores and the merger of a black hole and a neutron star. In this paper, we consider the short-term evolution of a torus for a duration of approximate to 60 ms, focusing on short-hard GRBs. Simulations were performed with a plausible microphysical equation of state that takes into account neutronization, the nuclear statistical equilibrium of a gas of free nucleons and cc-particles, black body radiation, and a relativistic Fermi gas (neutrinos, electrons, and positrons). Neutrino-emission processes, such as e capture onto free nucleons, e pair annihilation, plasmon decay, and nucleon-nucleon bremsstrahlung are taken into account as cooling processes. Magnetic braking and the magnetorotational instability in the accretion tori play a role in angular momentum redistribution, which causes turbulent motion, resultant shock heating, and mass accretion onto the black hole. The mass accretion rate is found to be M-*similar to 1-10M circle dot/s, and the shock heating increases the temperature to similar to 10(11) K. This results in a maximum neutrino emission rate of L-nu = several X 10(53) ergs/s and a conversion efficiency L-nu/M(*)c(2) on the order of a few percent for tori with mass M-t approximate to 0.1-0.4M circle dot and for moderately high black hole spins. These results are similar to previous results in which the phenomenological a-viscosity prescription with the alpha-parameter of alpha(v) = 0.01-0.1 is used. It is also found that the neutrino luminosity can be enhanced by the black hole spin, in particular for large spins, i.e., a greater than or similar to 0.75M; if the accretion flow is optically thin with respect to neutrinos, the conversion efficiency may be greater than or similar to 10% for a greater than or similar to 0.9M. Angular momentum transport, and the resulting shock heating caused by magnetic stress induce time-varying neutrino luminosity, which is a favorable property for explaining the variability of the luminosity curve of GRBs.