The Role of the Cooling Prescription for Disk Fragmentation: Numerical Convergence & Critical Cooling Parameter in Self-Gravitating Disks

TL;DR

This study investigates how different cooling prescriptions affect disk fragmentation in self-gravitating protoplanetary disks, revealing that more realistic cooling models influence the critical cooling parameter and the likelihood of planet formation.

Contribution

The paper introduces a cooling law dependent on local surface density fluctuations, improving the realism of simulations and examining its impact on disk fragmentation thresholds.

Findings

Higher resolution simulations show increased stability to fragmentation.

Realistic cooling models raise the critical cooling parameter for fragmentation.

Fragmentation can occur at higher beta values with improved cooling prescriptions.

Abstract

Protoplanetary disks fragment due to gravitational instability when there is enough mass for self-gravitation, described by the Toomre parameter, and when heat can be lost at a rate comparable to the local dynamical timescale, described by t_c=beta Omega^-1. Simulations of self-gravitating disks show that the cooling parameter has a rough critical value at beta_crit=3. When below beta_crit, gas overdensities will contract under their own gravity and fragment into bound objects while otherwise maintaining a steady state of gravitoturbulence. However, previous studies of the critical cooling parameter have found dependence on simulation resolution, indicating that the simulation of self-gravitating protoplanetary disks is not so straightforward. In particular, the simplicity of the cooling timescale t_c prevents fragments from being disrupted by pressure support as temperatures rise. We alter the cooling law so that the cooling timescale is dependent on local surface density fluctuations, a means of incorporating optical depth effects into the local cooling of an object. For lower resolution simulations, this results in a lower critical cooling parameter and a disk more stable to gravitational stresses suggesting the formation of large gas giants planets in large, cool disks is generally suppressed by more realistic cooling. At our highest resolution however, the model becomes unstable to fragmentation for cooling timescales up to beta = 10.