Giant Planet Formation by Disk Instability in Low Mass Disks?

Forming giant planets by disk instability requires a gaseous disk that is massive enough to become gravitationally unstable and able to cool fast enough for self-gravitating clumps to form and survive. Models with simplified disk cooling have shown the critical importance of the ratio of the cooling to the orbital timescales. Uncertainties about the proper value of this ratio can be sidestepped by including radiative transfer. Three-dimensional radiative hydrodynamics models of a disk with a mass of $0.043 M_\odot$ from 4 to 20 AU in orbit around a $1 M_\odot$ protostar show that disk instabilities are considerably less successful in producing self-gravitating clumps than in a disk with twice this mass. The results are sensitive to the assumed initial outer disk ($T_o$) temperatures. Models with $T_o$ = 20 K are able to form a single self-gravitating clump, whereas models with $T_o$ = 25 K form clumps that are not quite self-gravitating. These models imply that disk instability requires a disk with a mass of at least $\sim 0.043 M_\odot$ inside 20 AU in order to form giant planets around solar-mass protostars with realistic disk cooling rates and outer disk temperatures. Lower mass disks around solar-mass protostars must rely upon core accretion to form inner giant planets.