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

TL;DR

This paper presents a theoretical and numerical study of magnetic flux transport in thick accretion discs around black holes, revealing how multi-dimensional effects influence magnetic field strength and inclination, with implications for jet formation.

Contribution

It introduces a 2D kinematic mean-field model for poloidal magnetic flux transport in thick discs, highlighting the impact of multi-dimensional effects on field configuration and strength.

Findings

Multi-dimensional effects prevent magnetic field accumulation at the center.

Field inclination angle is reduced by multi-dimensional effects.

Numerical results agree with analytical predictions.

Abstract

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.