What really makes an accretion disc MAD

TL;DR

This paper proposes that the key to understanding magnetically arrested accretion discs (MADs) around black holes lies in the dynamics of a strong toroidal magnetic field generated by dynamo action, challenging previous emphasis on vertical flux.

Contribution

It introduces a new theoretical model emphasizing the role of a dynamo-generated toroidal field in MADs, supported by comparison with simulations, and revises the understanding of MRI's role in these discs.

Findings

Strong toroidal fields regulate MAD properties.

Convection-like instabilities can lead to two stable states, including MADs.

MRI is active and responsible for toroidal field generation in MADs.

Abstract

Magnetically arrested accretion discs (MADs) around black holes (BH) have the potential to stimulate the production of powerful jets and account for recent ultra-high-resolution observations of BH environments. Their main properties are usually attributed to the accumulation of dynamically significant net magnetic (vertical) flux throughout the arrested region, which is then regulated by interchange instabilities. Here we propose instead that it is mainly a dynamically important {\it toroidal} field -- the result of dynamo action triggered by the significant but still relatively weak vertical field -- that defines and regulates the properties of MADs. We suggest that rapid convection-like instabilities, involving interchange of toroidal flux tubes and operating concurrently with the magnetorotatonal instability (MRI), can regulate the structure of the disc and the escape of net flux. We generalize the convective stability criteria and disc structure equations to include the effects of a strong toroidal field and show that convective flows could be driven towards two distinct marginally stable states, one of which we associate with MADs. We confirm the plausibility of our theoretical model by comparing its quantitative predictions to simulations of both MAD and SANE (strongly magnetized but not "arrested") discs, and suggest a set of criteria that could help to distinguish MADs from other accretion states. Contrary to previous claims in the literature, we argue that MRI is not suppressed in MADs and is probably responsible for the existence of the strong toroidal field.