Challenges in Forming Planets by Gravitational Instability: Disk Irradiation and Clump Migration, Accretion, and Tidal Destruction

Abstract

We present two-dimensional hydrodynamic simulations of self-gravitating protostellar disks subject to axisymmetric, continuing mass loading from an infalling envelope and irradiation from the central star to explore the growth of gravitational instability (GI) and disk fragmentation. We assume that the disk is built gradually and smoothly by the infall, resulting in good numerical convergence. We confirm that for disks around solar-mass stars, infall at high rates at radii beyond ~50 AU leads to disk fragmentation. At lower infall rates, however, irradiation suppresses fragmentation. We find that, once formed, the fragments or clumps migrate inward on typical type I timescales of ~2 × 10 3  yr initially, but with a stochastic component superimposed due to their interaction with the GI-induced spiral arms. Migration begins to deviate from the type I timescale when the clump becomes more massive than the local disk mass, and/or when the clump begins to form a gap in the disk. As they migrate, clumps accrete from the disk at a rate between 10 –3 and 10 –1 M J yr –1 , consistent with analytic estimates that assume a 1-2 Hill radii cross section. The eventual fates of these clumps, however, diverge depending on the migration speed: 3 out of 13 clumps in our simulations become massive enough (brown dwarf mass range) to open gaps in the disk and essentially stop migrating; 4 out of 13 are tidally destroyed during inward migration; and 6 out of 13 migrate across the inner boundary of the simulated disks. A simple analytic model for clump evolution explains the different fates of the clumps and reveals some limitations of two-dimensional simulations. Overall, our results indicate that fast migration, accretion, and tidal destruction of the clumps pose challenges to the scenario of giant planet formation by GI in situ, although we cannot address whether or not remnant solid cores can survive after tidal stripping. The models where the massive clumps are not disrupted and open gaps may be relevant to the formation of close binary systems similar to Kepler 16. A clump formed by GI-induced fragmentation can be as large as 10 AU and as luminous as 2 × 10 –3 L ☉ , which will be easily detectable with ALMA, but its lifetime before dynamically collapsing is only ~1000 years.