A Lower Angular Momentum Limit for Self-Gravitating Protostellar Disc Fragmentation

TL;DR

This study confirms that the initial angular momentum of a spherical molecular cloud can predict the fragmentation of the resulting self-gravitating disc, establishing a lower angular momentum limit for fragmentation based on simulations.

Contribution

It provides a quantitative threshold for the initial angular momentum ratio needed for disc fragmentation, extending previous semi-analytic models with hydrodynamic simulations.

Findings

Fragmentation occurs if the angular momentum ratio exceeds ~5e-3.

The threshold is insensitive to initial thermal energy.

Higher cloud masses reduce the effectiveness of the angular momentum criterion.

Abstract

We attempt to verify recent claims (made using semi-analytic models) that for the collapse of spherical homogeneous molecular clouds, fragmentation of the self-gravitating disc that subsequently forms can be predicted using the cloud's initial angular momentum alone. In effect, this condition is equivalent to requiring the resulting disc be sufficiently extended in order to fragment, in line with studies of isolated discs. We use smoothed particle hydrodynamics with hybrid radiative transfer to investigate this claim, confirming that in general, homogeneous spherical molecular clouds will produce fragmenting self-gravitating discs if the ratio of rotational kinetic energy to gravitational potential energy is greater than ~ 5e-3, where this result is relatively insensitive to the initial thermal energy. This condition begins to fail at higher cloud masses, suggesting that sufficient mass at large radii governs fragmentation. While these results are based on highly idealised initial conditions, and may not hold if the disc's accretion from the surrounding envelope is sufficiently asymmetric, or if the density structure is perturbed, they provide a sensible lower limit for the minimum angular momentum required to fragment a disc in the absence of significant external turbulence.