Time-dependent models of the structure and evolution of self-gravitating protoplanetary discs

TL;DR

This study models the evolution of self-gravitating protoplanetary discs using time-dependent one-dimensional simulations, revealing their quasi-steady states, temperature profiles, and stability against fragmentation, with implications for planet formation.

Contribution

It introduces a time-dependent disc model based on local cooling times to analyze the structure and stability of self-gravitating protoplanetary discs, highlighting their quasi-steady states and fragmentation thresholds.

Findings

Discs rapidly reach a quasi-steady state with low turbulence inside 5 au.

Temperatures sufficient for crystalline silicate formation can extend several au early on.

Outer regions near 20 au are close to fragmentation instability threshold.

Abstract

Angular momentum transport within young massive protoplanetary discs may be dominated by self-gravity at radii where the disk is too weakly ionized to allow the development of the magneto-rotational instability. We use time-dependent one-dimensional disc models, based on a local cooling time calculation of the efficiency of transport, to study the radial structure and stability (against fragmentation) of protoplanetary discs in which self-gravity is the sole transport mechanism. We find that self-gravitating discs rapidly attain a quasi-steady state in which the surface density in the inner disc is high and the strength of turbulence very low (alpha ~ 10^{-3} or less inside 5 au). Temperatures high enough to form crystalline silicates may extend out to several au at early times within these discs. None of our discs spontaneously develop regions that would be unambiguously unstable to fragmentation into substellar objects, though the outer regions (beyond 20 au) of the most massive discs are close enough to the threshold that fragmentation cannot be ruled out. We discuss how the mass accretion rates through such discs may vary with disc mass and with mass of the central star, and note that a determination of the \dot{M}-M_* relation for very young systems may allow a test of the model.