  In order to investigate mass transport and planet formation by gravitational
instabilities (GIs), we have extended our 3-D 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, Rdisk = 40 AU, Mdisk = 0.07 Mo, M* = 0.5 Mo, and Qmin = 1.8.
Sustained cooling, with tcool = 2 orps (outer rotation periods, 1 orp ~ 250
yrs), drives the disk to instability in ~ 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 Sigma(r), and a roughly steady Mdot ~ 5(-7) Mo/yr. The
transport is driven by global low-order spiral modes. We restart the
calculation at 11.2 orps with tcool = 1 and 1/4 orp. The latter case is also
run at high azimuthal resolution. We find that shorter cooling times lead to
increased Mdots, denser and thinner spiral structures, and more violent dynamic
behavior. The asymptotic total internal energy and the azimuthally averaged
Q(r) are insensitive to tcool. Fragmentation occurs only in the high-resolution
tcool = 1/4 orp case; however, none of the fragments survive for even a quarter
of an orbit. Ring-like density enhancements appear and grow near the boundary
between GI active and inactive regions. We discuss the possible implications of
these rings for gas giant planet formation.
