An Analytic Model For Magnetically-Dominated Accretion Disks

TL;DR

This paper introduces an analytic model for magnetically-dominated quasar accretion disks, which are distinct from classical models, and demonstrates its consistency with recent simulations and their gravitational stability at high accretion rates.

Contribution

The paper presents a simple, boundary-condition-driven analytic similarity model for magnetically-dominated accretion disks, aligning well with simulations and highlighting their stability at hyper-Eddington rates.

Findings

Model agrees with simulations across various assumptions.

Disks remain gravitationally stable at high accretion rates.

Magnetic fields dominate midplane pressure in these disks.

Abstract

Recent numerical cosmological radiation-magnetohydrodynamic-thermochemical-star formation simulations have resolved the formation of quasar accretion disks with Eddington or super-Eddington accretion rates onto supermassive black holes (SMBHs) down to a few hundred gravitational radii. These 'flux-frozen' and hyper-magnetized disks appear to be qualitatively distinct from classical $\alpha$ disks and magnetically-arrested disks: the midplane pressure is dominated by toroidal magnetic fields with plasma $\beta \ll 1$ powered by advection of magnetic flux from the interstellar medium (ISM), and they are super-sonically and trans-Alfvenically turbulent with cooling times short compared to dynamical times yet remain gravitationally stable owing to magnetic support. In this paper, we present a simple analytic similarity model for such disks. For reasonable assumptions, the model is entirely specified by the boundary conditions (inflow rate at the BH radius of influence [BHROI]). We show that the scalings from this model are robust to various detailed assumptions, agree remarkably well with the simulations (given their simplicity), and demonstrate the self-consistency and gravitational stability of such disks even in the outer accretion disk (approaching the BHROI) at hyper-Eddington accretion rates.