Boundary Conditions of Radiative Cooling in Gravitationally Unstable Protoplanetary Disks

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In order to create 3D hydrodynamic disk simulations which reproduce the observable properties of young stellar disks and which realistically probe the possibility of planet formation by gravitational instabilities, it is crucial to include a proper treatment of the radiative energy transport within the disk. Our recent simulations (Mejía 2004, Ph.D. dissertation) suggest that the boundary conditions between optically thin and thick regions are important in treating radiative cooling in protoplanetary disks. Although the initial cooling times are shorter than one rotation period, these disks adjust their structures over a few rotations to much longer cooling times, at which Gammie's (2001) criterion predicts they are stable against fragmentation into dense clumps. In fact, the disks do not fragment in Mejía's calculations. Boss (2001, 2002), on the other hand, using different boundary conditions, finds rapid cooling and fragmentation in his own disk simulations with radiative cooling. He attributes the rapid cooling to convection, which does not occur in Mejía's calculations. This apparent disagreement is critical because disk fragmentation has been proposed as a gas giant planet formation mechanism. To test the importance of boundary conditions, we are running simulations which compare a Boss-like treatment of boundary conditions with Mejía's for the case of a disk heated from above by a hot envelope. Preliminary results will be presented.

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