Evolution of the Solar Nebula. V. Disk Instabilities with Varied Thermodynamics

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Abstract
Disk instability is a promising mechanism for explaining the rapid formation of the gas and ice giant planets in our solar system as well as in extrasolar planetary systems. Disk instability involves the formation of self-gravitating clumps in marginally gravitationally unstable protoplanetary disks on timescales of ~1000 yr. We present here the results of a suite of disk instability models calculated with a three-dimensional, gravitational hydrodynamics code. The models explore the effects of varying the thermodynamical assumptions, the initial degree of gravitational instability, and the numerical spatial resolution. For all models, the disk has an initial mass of 0.091 M☉ inside 20 AU, in orbit around a 1 M☉ protostar. The most realistic models are calculated with an energy equation and diffusion approximation radiative transfer, which produces results intermediate between those of models with a locally isothermal or locally adiabatic thermodynamic response to the growth of azimuthal density perturbations. Locally adiabatic models suppress the growth of clumps, while radiative transfer models permit the formation of clumps similar to those in locally isothermal models. Vertical convection is identified as the primary means for cooling the midplane in the models with radiative transfer. These models suggest that the disk instability mechanism is capable of rapidly forming self-gravitating protoplanets in marginally unstable disks with a mass similar to that inferred for the solar nebula and for other protoplanetary disks. Assuming that the protoplanets survive their subsequent evolution, the likelihood that all protoplanetary disks pass through a phase of marginal gravitational instability might then imply a high frequency of extrasolar giant planets.