Disc-jet coupling in black hole accretion systems - II. Force-free electrodynamical models

In Paper I, we showed that time-dependent general relativistic magnetohydrodynamic (GRMHD) numerical models of accretion discs, although being highly turbulent, have surprisingly simple electromagnetic properties. In particular, the toroidal current density in the disc takes the form dI(phi)/dr proportional to r(-5/4). Guided by this simplicity, we use a time-dependent general relativistic force-free electrodynamics (GRFFE) code to study an idealized problem in which the accretion disc is replaced by an infinitely thin rotating equatorial current sheet. We consider both an r(-5/4) current profile and an r(-1) profile, the latter corresponding to the paraboloidal model of Blandford and Znajek. The force-free magnetosphere we obtain with the r(-5/4) current sheet matches remarkably well to the Poynting-dominated jet seen in GRMHD numerical models. By comparing to the non-rotating force-free model studied in Paper I, rotation is seen to lead to mild decollimation of the jet suggesting that hoop-stress forces nearly cancel centrifugal forces. In order to study the process that generates the corona and disc wind and destroys the ordered field in the corona in GRMHD numerical models, the force-free field with the r(-5/4) current distribution is embedded in an accretion disc and followed in a GRMHD simulation. Field at high latitudes is continuously transported to larger radii leaving a corona with only disordered field, while in the equator the turbulent field is accreted. Reconnection and magnetic stresses contribute to a magnetized, thermal wind without the aid of an ordered field threading the disc.