General Relativistic, Neutrino-Assisted MHD winds - Theory and Application to GRBs. I. Schwarzschild Geometry

(short version) - A model for GRMHD disk outflows with neutrino-driven mass ejection is developed,and employed to calculate the structure of the outflow in the sub-slow magnetosonic region and the mass loading of the outflow, under conditions anticipated in the central engines of gamma-ray bursts. 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 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 sub-slow region, but is practically independent of the strength of poloidal and toroidal magnetic fields. We conclude that magnetic launching of ultra-relativistic polar outflows from the innermost parts of the disk is in principle possible provided the neutrino luminosity is sufficiently low, $L_\nu\simlt10^{52}$ erg s$^{-1}$ or so. The conditions found to be optimal for the launching of an ultra-relativistic jet are also the conditions favorable for large neutron-to-proton ratio in the disk.