General relativistic numerical simulations of magnetized accretion flows around black holes show a disordered electromagnetic structure in the disk 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 disk 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 \propto 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 disk 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 disk , which contains a turbulent magnetic field locked to the disk ’ s Keplerian rotation except for rapidly rotating prograde black holes ( a / M \gtrsim 0.4 ) for which within r \lesssim 3 GM / c ^ { 2 } the field locks to roughly half the black hole spin frequency .
The electromagnetic field in the disk 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 toward 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 \sim 1 , whereas the typically assumed value of \alpha \sim 0.1 holds far from the black hole .