The Role of the Cooling Prescription for Disk Fragmentation: Numerical Convergence & 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 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.

10 pages, 6 figures. Accepted for publication in ApJ

References in corpus (7)

• Direct Imaging of Multiple Planets Orbiting the Star HR 8799
• Characterising the Gravitational Instability in Cooling Accretion Discs
• The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks III. Simulations with Radiative Cooling and Realistic Opacities
• Treating gravity in thin disk simulations
• Secular evolution of viscous and self-gravitating circumstellar discs
• Viscosity prescription for gravitationally unstable accretion disks
• The effect of external environment on the evolution of protostellar disks

Cited by in corpus (15)

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• Nonlinear outcome of gravitational instability in an irradiated protoplanetary disc
• The Effect of Protoplanetary Disk Cooling Times on the Formation of Gas Giant Planets by Gravitational Instability
• Thermal evolution of protoplanetary disks: from $\beta$-cooling to decoupled gas and dust temperatures
• The evolution of self-gravitating accretion discs
• Gravito-turbulence in irradiated protoplanetary discs
• The Concentration and Growth of Solids in Fragmenting Circumstellar Disks
• The impact of numerical oversteepening on the fragmentation boundary in self-gravitating disks
• Flux-Limited Diffusion Approximation Models of Giant Planet Formation by Disk Instability. II. Quadrupled Spatial Resolution
• Gravito-turbulence in local disk simulations with an adaptive moving mesh
• Kozai-Lidov oscillations triggered by a tilt instability of detached circumplanetary discs
• Closing the gap to convergence of gravitoturbulence in local simulations