Formation and evolution of protostellar accretion discs. I. Angular-momentum budget, gravitational self-regulation, and numerical convergence

TL;DR

This study uses advanced non-ideal MHD simulations to explore how protostellar discs form and evolve, emphasizing angular momentum dynamics, gravitational effects, and the importance of numerical convergence.

Contribution

It provides new insights into the formation of large, marginally unstable protostellar discs, highlighting the roles of magnetic braking, gravitational instability, and the necessity of proper boundary conditions in simulations.

Findings

Protostellar discs reach ~30 au within 3 kyr after formation.

Angular momentum is mainly accumulated from low-angular-momentum infalling gas.

Discs remain marginally unstable with Toomre Q~1-2, consistent with observations.

Abstract

We investigate the formation and early evolution of a protostellar disc from a magnetized pre-stellar core using non-ideal magnetohydrodynamic (MHD) simulations including ambipolar diffusion and Ohmic dissipation. The dynamical contraction of the pre-stellar core ultimately leads to the formation of a first hydrostatic core, after ambipolar diffusion decouples the magnetic field from the predominantly neutral gas. The hydrostatic core accumulates angular momentum from the infalling material, evolving into a rotationally supported torus; this `first hydrostatic torus' then forms an accreting protostar and a rotationally supported disc. The disc spreads out by gravitational instability, reaching $\sim$30 au in diameter at $\sim$3 kyr after protostar formation. The total mass and angular momentum of the protostar-disc system are determined mainly by accretion of gas from an infalling pseudo-disc, which has low specific angular momentum because of magnetic braking; their removal from the protostar-disc system by outflow and disc magnetic braking are negligible, in part because the magnetic field is poorly coupled there. The redistribution of angular momentum within the protostar-disc system is facilitated mainly by gravitational instability; this allows formation of relatively large discs even when the specific angular momentum of infalling material is low. We argue that such discs should remain marginally unstable as they grow (with Toomre $Q\sim 1$-$2$), an idea that is broadly consistent with recent observational estimates for Class 0/I discs. We discuss the numerical convergence of our results, and show that properly treating the inner boundary condition is crucial for achieving convergence at an acceptable computational cost.