New constraints on turbulent transport in accretion discs

Abstract

Microphysical viscosity is too small to produce observed proto-planetary accretion disc lifetimes. Turbulent transport, in which turbulent motion takes the place of thermal motion, can provide the correct order-of-magnitude accretion rates for reasonable surface densities, though the source of such turbulence remains a matter of discussion. Here, we consider, independent of the source of turbulence, the minimal properties that turbulent motion must possess in order to adequately transport both angular momentum and mass in accretion discs. We find that the resulting angular momentum transport coefficient depends on the turbulent time scale and angular distribution, not only on the product of the turbulent length and velocity scales. More importantly, we also find that the required energy conversion efficiency is prohibitive if angular momentum transport results purely from fluid turbulence supplied by accretion energy and therefore that turbulent fluid motion mediated accretion must be powered by an outside source. Even in the case that the accretion mechanism is not a turbulent viscosity, as can be the case for a Magneto-Rotational Instability (MRI) disc, numerical simulations suggest that energy conservation is a significant constraint even on accretion driving processes such as the MRI.