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

Abstract

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 ∼ 0.1-0.4M⊙ around a black hole of mass M = 4M⊙ 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 ≈ 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 α-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 Ṁ* ∼ 1-10M⊙/s, and the shock heating increases the temperature to ∼ 1011 K. This results in a maximum neutrino emission rate of Lν = several ×1053 ergs/s and a conversion efficiency Lν/Ṁ*c2 on the order of a few percent for tori with mass Mt ≈ 0.1-0.4M⊙ and for moderately high black hole spins. These results are similar to previous results in which the phenomenological α-viscosity prescription with the a-parameter of αv = 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 ≳ 0.75M; if the accretion flow is optically thin with respect to neutrinos, the conversion efficiency may be ≳ 10% for o ≳ 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.