The fragmentation of protostellar discs: the Hill criterion for spiral arms

TL;DR

This paper introduces a new Hill radius-based criterion for predicting fragmentation in gravitationally unstable protostellar discs, supported by simulations and modeling of cooling and spiral arm formation.

Contribution

It presents a novel, simple model linking cooling, spiral arm formation, and fragmentation in protostellar discs, validated by 3D radiation hydrodynamics simulations.

Findings

The Hill criterion effectively predicts disc fragmentation.

The model aligns with Gammie's critical cooling time.

Simulations support gravitational instability as a mechanism for wide-orbit giant planet formation.

Abstract

We present a new framework to explain the link between cooling and fragmentation in gravitationally unstable protostellar discs. This framework consists of a simple model for the formation of spiral arms, as well as a criterion, based on the Hill radius, to determine if a spiral arm will fragment. This detailed model of fragmentation is based on the results of numerical simulations of marginally stable protostellar discs, including those found in the literature, as well as our new suite of 3-D radiation hydrodynamics simulations of an irradiated, optically-thick protostellar disc surrounding an A star. Our set of simulations probes the transition to fragmentation through a scaling of the physical opacity. This model allows us to directly calculate the critical cooling time of Gammie (2001), with results that are consistent with those found from numerical experiment. We demonstrate how this model can be used to predict fragmentation in irradiated protostellar discs. These numerical simulations, as well as the model that they motivate, provide strong support for the hypothesis that gravitational instability is responsible for creating systems with giant planets on wide orbits.