Disc-jet coupling in black hole accretion systems - I. General relativistic magnetohydrodynamical models

General relativistic numerical simulations of magnetized accretion flows around black holes show a disordered electromagnetic structure in the disc and corona and a highly relativistic, Poynting-dominated funnel jet in the polar regions. The polar jet is nearly consistent with the stationary paraboloidal Blandford-Znajek model of an organized field threading the polar regions of a rotating black hole. How can a disordered accretion disc and corona lead to an ordered jet ? We show that the polar jet is associated with a strikingly simple angular-integrated toroidal current distribution dI(phi)/dr proportional to r(-5/4), where I-phi(r) is the toroidal current enclosed inside radius r. We demonstrate that the poloidal magnetic field in the simulated jet agrees well with the force-free field solution for a non-rotating thin disc with an r(-5/4) toroidal current, suggesting rotation leads to negligible self-collimation. We find that the polar field is confined/collimated by the corona. We also study the properties of the bulk of the simulated disc, which contains a turbulent magnetic field locked to the disc's Keplerian rotation except for rapidly rotating prograde black holes (a/M greater than or similar to 0.4) for which within r less than or similar to 3GM/c(2) the field locks to roughly half the black hole spin frequency. The electromagnetic field in the disc also scales as r(-5/4), which is consistent with some Newtonian accretion models that assume rough equipartition between magnetic and gas pressure. However, the agreement is accidental since towards the black hole the magnetic pressure increases faster than the gas pressure. This field dominance near the black hole is associated with magnetic stresses that imply a large effective viscosity parameter alpha similar to 1, whereas the typically assumed value of alpha similar to 0.1 holds far from the black hole.