Evolution of the solar nebula. VII. Formation and survival of protoplanets formed by disk instability

A major concern for the disk instability mechanism for giant planet formation is survival of the self-gravitating clumps that form in a marginally gravitationally unstable disk. Previous grid-based calculations have found that these clumps may only survive for an orbital period or two, an outcome that has been attributed to insufficient spatial resolution of the clumps. Here we use the highest spatial resolution grid-based models to date (effectively over 8 x 10(6) grid points, with a locally refined radial grid and 1024 azimuthal grid points) to demonstrate that clump formation and survival are enhanced as the numerical resolution is increased, even with a full treatment of disk thermodynamics and radiative transfer. The overall disk evolution appears to be converging toward a solution with robust spiral arms and self-gravitating protoplanets. The survival of these protoplanets is then further explored by introducing "virtual protoplanets," point masses representing massive protoplanets that accrete gas from the disk and interact with the disk as they orbit around the protostar. While growing cores and protoplanets formed by core accretion are thought to be subject to significant orbital migration, the virtual protoplanet models show that protoplanets formed by disk instability are likely to avoid rapid inward orbital migration, at least initially, because the self-gravitating disk gas flows inward, past the protoplanets, while the protoplanets orbit relatively undisturbed. Subsequent orbital migration in this case may depend primarily on the outer disk lifetime and hence on the star-forming environment, i.e., whether it is Taurus-like with relatively long-lived outer disks or Orion-like with relatively short-lived outer disks. The latter environment should lead to minimal inward orbital migration, as appears to be the case for our solar system, while the former may lead to sufficient inward migration to produce the observed short-period gas giant planets.