Secular evolution of viscous and self-gravitating circumstellar discs

TL;DR

This study models the evolution of protostellar discs by incorporating turbulent viscosity, revealing how varying viscosity levels influence disc structure, stability, and lifetime in the context of self-gravity and gravitational torques.

Contribution

It introduces non-axisymmetric, thin-disc models with turbulent viscosity to analyze the interplay of gravitational and viscous torques during disc evolution.

Findings

Low viscosity (=10^{-4}) minimally affects disc evolution and structure.

Higher viscosity (=10^{-2}) leads to more axisymmetric, stable, and shorter-lived discs.

Self-regulation with Q  1.5-2.0 persists at low viscosities.

Abstract

We add the effect of turbulent viscosity via the \alpha-prescription to models of the self-consistent formation and evolution of protostellar discs. Our models are non-axisymmetric and carried out using the thin-disc approximation. Self-gravity plays an important role in the early evolution of a disc, and the later evolution is determined by the relative importance of gravitational and viscous torques. In the absence of viscous torques, a protostellar disc evolves into a self-regulated state with disk-averaged Toomre parameter Q \sim 1.5-2.0, non-axisymmetric structure diminishing with time, and maximum disc-to-star mass ratio \xi = 0.14. We estimate an effective viscosity parameter \alpha_eff associated with gravitational torques at the inner boundary of our simulation to be in the range 10^{-4}-10^{-3} during the late evolution. Addition of viscous torques with a low value \alpha = 10^{-4} has little effect on the evolution, structure, and accretion properties of the disc, and the self-regulated state is largely preserved. A sequence of increasing values of \alpha results in the discs becoming more axisymmetric in structure, being more gravitationally stable, having greater accretion rates, larger sizes, shorter lifetimes, and lower disc-to-star mass ratios. For \alpha=10^{-2}, the model is viscous-dominated and the self-regulated state largely disappears by late times. (Abridged)