Magnetic field transport in geometrically thick discs: multi-dimensional effects on the field strength and inclination angle

We theoretically investigate the magnetic flux transport in geometrically thick accretion discs which may form around black holes. We utilize a two-dimensional (2D) kinematic mean-field model for poloidal field transport which is governed by both inward advection and outward diffusion of the field. Assuming a steady state, we analytically show that the multi-dimensional effects prevent the field accumulation toward the centre and reduce the field inclination angle. We also numerically investigate the radial profile of the field strength and the inclination angle for two geometrically thick discs for which (quasi-)analytic solutions exist: radiatively inefficient accretion flows (RIAFs) and super-Eddington accretion flows. We develop a 2D kinematic mean-field code and perform simulations of flux transport to study the multi-dimensional effects. The numerical simulations are consistent with our analytical prediction. We also discuss a condition for the external field strength that RIAF can be a magnetically arrested disc. This study could be important for understanding the origin of a large-scale magnetic field that drives jets and disc winds around black holes.