Identifying deficiencies of standard accretion disc theory: lessons from a mean-field approach

Turbulent viscosity is frequently used in accretion disc theory to replace the microphysical viscosity in order to accommodate the observational need for instabilities in discs that lead to enhanced transport. However, simply replacing the microphysical transport coefficient by a single turbulent transport coefficient 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 to 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 discs to maintain a monotonic power-law surface density.