An Analytic Model For Magnetically-Dominated Accretion 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 $\hat{I}\pm$ disks and magnetically-arrested disks: the midplane pressure is dominated by toroidal magnetic fields with plasma ${\hat{I}}^2\ll 1$ 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.

12 pages, 1 figure. Replaced with accepted version. Companion paper to 'FORGE'D IN FIRE II' (arXiv:2310.04506, part of a series with arXiv:2309.13115 -- animations of the simulations referred to here can be viewed at http://www.tapir.caltech.edu/~phopkins/Site/animations/Movies_zoom.html)