Accretion disks around black holes: Dynamical evolution, meridional circulations, and gamma-ray bursts

We study the hydrodynamic evolution of massive accretion disks around black holes, formed when a neutron star is disrupted by a black hole in a binary system. The initial conditions are taken from three-dimensional calculations of coalescing binaries. By assuming azimuthal symmetry we are able to follow the time dependence of the disk structure for 0.2 s in cylindrical coordinates (r, z). We use an ideal gas equation of state and assume that all the dissipated energy is radiated away. The disks evolve because of viscous stresses, modeled with an alpha law. We study the disk structure and, in particular, the strong meridional circulations that are established and persist throughout our calculations. These consist of strong outflows along the equatorial plane that reverse direction close to the surface of the disk and converge on the accretor. In the context of gamma-ray bursts (GRBs), we estimate the energy released from the system in neutrinos and through magnetic-dominated mechanisms and find it can be as high as E-nu approximate to 10(52) ergs and E-BZ approximate to 10(51) ergs, respectively, during an estimated accretion timescale of 0.1-0.2 s. The nu(ν) over bar annihilation is likely to produce bursts from only a short, impulsive energy input Lnu(ν) over bar proportional to t(-5/2) and so would be unable to account for a large fraction of bursts that show complicated light curves. On the other hand, a gas mass approximate to0.1-0.25 M. survives in the orbiting debris, which enables strong magnetic fields approximate to10(16) G to be anchored in the dense matter long enough to power short duration GRBs. We highlight the effects that the initial disk and black holes masses, viscosity, and binary mass ratio have on the evolution of the disk structure. Finally, we investigate the continuous energy injection that arises as the black hole slowly swallows the rest of the disk and discuss its consequences on the GRB afterglow emission.