Jet formation in GRBs: A semi-analytic model of MHD flow in Kerr geometry with realistic plasma injection

We construct a semi-analytic model for MHD flows in Kerr geometry, that incorporates energy loading via neutrino annihilation on magnetic field lines threading the horizon. We compute the double-flow structure for a wide range of energy injection rates, and identify the different operation regimes. At low injection rates the outflow is powered by the spinning black hole via the Blandford-Znajek mechanism, whereas at high injection rates it is driven by the pressure of the plasma deposited on magnetic field lines. In the intermediate regime both processes contribute to the outflow formation. The parameter that quantifies the load is the ratio of the net power injected below the stagnation radius and the maximum power that can be extracted magnetically from the black hole.