General relativistic, neutrino-assisted magnetohydrodynamic winds - Theory and application to gamma-ray bursts. I. Schwarzschild geometry

A model for general relativistic magnetohydrodynamic (GRMHD) disk outflows with neutrino-driven mass ejection is developed and employed to calculate the structure of the outflow in the subslow magnetosonic region and the mass loading of the outflow, under conditions anticipated in the central engines of gamma-ray bursts (GRBs). The dependence of the mass flux on the conditions in the disk, on magnetic field geometry, and on other factors is carefully examined for a range of neutrino luminosities expected in hyperaccreting black holes. The fraction of neutrino luminosity that is ultimately being converted to kinetic energy flux is shown to be a sensitive function of the effective neutrino temperature at the flow injection point and the shape of magnetic field lines in the subslow region but is practically independent of the strength of poloidal and toroidal magnetic fields. We conclude that magnetic launching of ultrarelativistic polar outflows from the innermost parts of the disk is in principle possible provided the neutrino luminosity is sufficiently low, L-v less than or similar to 10(52) ergs s(-1) or so. The conditions found to be optimal for the launching of an ultrarelativistic jet are also the conditions favorable for a large neutron-to-proton ratio in the disk, suggesting that a large neutron excess in GRB jets, as often conjectured, may be possible. However, the outflow time appears to be comparable to the neutronization timescale, implying that the electron fraction should evolve during the initial acceleration phase. Further analysis is required to determine the composition profile in the wind.