The role of the cooling prescription for disk fragmentation: Numerical convergence and critical cooling parameter in self-gravitating disks

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 tc . = βω-1 Simulations of self-gravitating disks show that the cooling parameter has a rough critical value at bcrit = 3. When below bcrit, 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 dependences on simulation resolution, indicating that the simulation of self-gravitating protoplanetary disks is not so straightforward. In particular, the simplicity of the cooling timescale tc 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, which is 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 that is more stable to gravitational stresses, suggesting that 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 β = 10.