Identifying Deficiencies of Standard Accretion Disk Theory: Lessons from a Mean-Field Approach

TL;DR

This paper critically examines standard accretion disk theory, revealing that a mean-field approach necessitates two distinct transport coefficients for mass and angular momentum, and highlights overlooked turbulent diffusion effects.

Contribution

It introduces a mean-field framework that identifies two separate transport coefficients and emphasizes the importance of turbulent diffusion in accretion disk modeling.

Findings

Standard theory neglects turbulent diffusion in surface density equations.

Two transport coefficients are necessary for accurate mass and angular momentum transport.

Oscillations in surface density can occur without proper constraints.

Abstract

Turbulent viscosity is frequently used in accretion disk theory to replace the microphysical viscosity in order to accomodate the observational need for in- stabilities in disks that lead to enhanced transport. However, simply replacing the microphysical transport coefficient by a single turbulent transport coeffi- cient hides the fact that the procedure should formally arise as part of a closure in which the hydrodynamic or magnetohydrodynamic equations are averaged, and correlations of turbulent fluctuations are replaced by transport coefficients. Here we show how a mean field approach leads quite naturally two transport coefficients, not one, that govern mass and angular momentum transport. In particular, we highlight that the conventional approach suffers from a seemingly inconsistent neglect of turbulent diffusion in the surface density equation. We constrain these new transport coefficients for specific cases of inward, outward, and zero net mass transport. In addition, we find that one of the new transport terms can lead to oscillations in the mean surface density which then requires a constant or small inverse Rossby number for disks to maintain a monotonic power-law surface density.