The effects of opacity on gravitational stability in protoplanetary discs

TL;DR

This study examines how different opacity regimes and temperature-dependent cooling affect the gravitational stability and fragmentation of protoplanetary discs, revealing critical dependencies on local temperature and opacity gaps.

Contribution

It demonstrates the significant impact of temperature-dependent cooling functions on disc stability, especially in the opacity gap, and predicts how these effects influence fragmentation thresholds.

Findings

Temperature dependence increases susceptibility to fragmentation.

Opacity gap significantly raises the critical Omega*tcool value.

Fragmentation radius and accretion rate thresholds are lowered with temperature-dependent cooling.

Abstract

In this paper we consider the effects of opacity regimes on the stability of self-gravitating protoplanetary discs to fragmentation into bound objects. Using a self-consistent 1-D viscous disc model, we show that the ratio of local cooling to dynamical timescales Omega*tcool has a strong dependence on the local temperature. We investigate the effects of temperature-dependent cooling functions on the disc's gravitational stability through controlled numerical experiments using an SPH code. We find that such cooling functions raise the susceptibility of discs to fragmentation through the influence of temperature perturbations - the average value of Omega*tcool has to increase to prevent local variability leading to collapse. We find the effects of temperature dependence to be most significant in the "opacity gap" associated with dust sublimation, where the average value of Omega*tcool at fragmentation is increased by over an order of magnitude. We then use this result to predict where protoplanetary discs will fragment into bound objects, in terms of radius and accretion rate. We find that without temperature dependence, for radii < ~10AU a very large accretion rate ~10^-3 Msun/yr is required for fragmentation, but that this is reduced to 10^-4 Msun/yr with temperature-dependent cooling. We also find that the stability of discs with accretion rates < ~10^-7 Msun/yr at radii > ~50AU is enhanced by a lower background temperature if the disc becomes optically thin.