Mass loss from a magnetically driven wind emitted by a disk orbiting a stellar mass black hole

The source of cosmic gamma-ray bursts (hereafter GRBs) is usually believed to be a stellar mass black hole accreting material from a thick disk. The mechanism for the production of a relativistic wind by such a system is still unknown. We investigate here one of the proposal where the disk energy is extracted by a magnetic field amplified to very large values B \sim 10^15 G. Using some very simple assumptions we compute the mass loss rate along magnetic field lines and then estimate the Lorentz factor \Gamma at infinity. We find that \Gamma can reach high values only if severe constraints on the field geometry and the conditions of energy injection are satisfied. We discuss the results in the context of different scenarios for GRBs.