2005ApJ...619.1098M

In order to investigate mass transport and planet formation through gravitational instabilities (GIs), we have extended our three-dimensional hydrodynamic simulations of protoplanetary disks from a previous paper. Our goal is to determine the asymptotic behavior of GIs and how it is affected by different constant cooling times. Initially, R_disk=40 AU, M_disk=0.07 M_☉, M_*=0.5 M_☉, and Q_min=1.5. Sustained cooling, with t_cool=2 ORPs (outer rotation periods; 1ORP~250 yr), drives the disk to instability in about 4 ORPs. This calculation is followed for 23.5 ORPs. After 12 ORPs, the disk settles into a quasi-steady state with sustained nonlinear instabilities, an average Q=1.44 over the outer disk, a well-defined power law Σ(r), and a roughly steady M{dot}~5x10^–7 M_☉yr^–1. The transport is driven by global low-order spiral modes. We restart the calculation at 11.2 ORPs with t_cool=1 and (1)/(4) ORPs. The latter case is also run at high azimuthal resolution. We find that shorter cooling times lead to increased M{dot}-values, denser and thinner spiral structures, and more violent dynamic behavior. The asymptotic total internal energy and the azimuthally averaged Q(r) are insensitive to t_cool. Fragmentation occurs only in the high-resolution t_cool=(1)/(4) ORP case; however, none of the fragments survive for even a quarter of an orbit. Ringlike density enhancements appear and grow near the boundary between GI-active and GI-inactive regions. We discuss the possible implications of these rings for gas giant planet formation.