Vertical Structure and Coronal Power of Accretion Disks Powered by MRI Turbulence

TL;DR

This paper develops an analytical model for the vertical thermal structure and coronal power fraction of MRI-driven accretion disks, highlighting the roles of parasitic instabilities and magnetic fields.

Contribution

It provides a self-consistent analytical solution for disk vertical structure and explores the impact of Parker instability on coronal power in MRI-affected disks.

Findings

Uniform turbulent dissipation rate across the disk height.

Parker instability sets a lower limit on coronal power.

Results applicable to both externally threaded and dynamo-generated magnetic fields.

Abstract

In this paper we consider two outstanding intertwined problems in modern high-energy astrophysics: (1) the vertical thermal structure of an optically thick accretion disk heated by the dissipation of magnetohydrodynamic (MHD) turbulence driven by the magneto-rotational instability (MRI), and (2) determining the fraction of the accretion power released in the corona above the disk. For simplicity, we consider a gas-pressure-dominated disk and assume a constant opacity. We argue that the local turbulent dissipation rate due to the disruption of MRI channel flows by secondary parasitic instabilities should be uniform across most of the disk, almost up to the disk photosphere. We then obtain a self-consistent analytical solution for the vertical thermal structure of the disk, governed by the balance between the heating by MRI turbulence and the cooling by radiative diffusion. Next, we argue that the coronal power fraction is determined by the competition between the Parker instability, viewed as a parasitic instability feeding off of MRI channel flows, and other parasitic instabilities. We show that the Parker instability inevitably becomes important near the disk surface, leading to a certain lower limit on the coronal power. While most of the analysis in this paper focuses on the case of a disk threaded by an externally imposed vertical magnetic field, we also discuss the zero-net-flux case, in which the magnetic field is produced by the MRI dynamo itself, and show that most of our arguments and conclusions should be valid in this case as well.