Formation and evolution of protostellar accretion discs. II. From 3D simulation to a simple semi-analytic model of Class 0/I discs

TL;DR

This paper combines 3D MHD simulations and a semi-analytic model to understand the formation, evolution, and properties of early protostellar discs, providing a computationally efficient way to predict their long-term behavior.

Contribution

It introduces a semi-analytic model of Class 0/I protostellar disc evolution based on detailed 3D simulations, capturing key physical processes and matching observational data.

Findings

Disc radius saturates at about 30 au.

Discs are gravitationally unstable with spiral arms.

Model predictions align with recent observations.

Abstract

We use a 3D radiative non-ideal magnetohydrodynamic (MHD) simulation to investigate the formation and evolution of a young protostellar disc from a magnetized pre-stellar core. The simulation covers the first ${\sim}10~{\rm kyr}$ after protostar formation, and shows a massive, weakly magnetized disc with radius that initially grows and then saturates at ${\sim}30~{\rm au}$. The disc is gravitationally unstable with prominent large-amplitude spiral arms. We use our simulation results and a series of physical arguments to construct a predictive and quantitative physical picture of Class 0/I protostellar disc evolution from several aspects, including (i) the angular-momentum redistribution in the disc, self-regulated by gravitational instability to make most of the disc marginally unstable; (ii) the thermal profile of the disc, well-approximated by a balance between radiative cooling and accretion heating; and (iii) the magnetic-field strength and magnetic-braking rate inside the disc, regulated by non-ideal magnetic diffusion. Using these physical insights, we build a simple 1D semi-analytic model of disc evolution. We show that this 1D model, when coupled to a computationally inexpensive simulation for the evolution of the surrounding pseudodisc, can be used reliably to predict disc evolution in the Class 0/I phase. The predicted long-term evolution of disc size, which saturates at ${\sim}30~{\rm au}$ and eventually shrinks, is consistent with a recent observational survey of Class 0/I discs. Such hierarchical modelling of disc evolution circumvents the computational difficulty of tracing disc evolution through Class 0/I phase with direct, numerically converged simulations.