Fragmentation of Gravitationally Unstable Gaseous Protoplanetary Disks with Radiative Transfer

We report on the results of the first 3D SPH simulations of gravitationally unstable protoplanetary disks with radiative transfer. We adopt a flux-limited diffusion scheme justified by the high opacity of most of the disk. The optically thin surface of the disk cools as a blackbody. We find that gravitationally bound clumps with masses close to a Jupiter mass can arise. Fragmentation appears to be driven by vertical convective-like motions capable of transporting the heat from the disk midplane to its surface on a timescale of only about 40 years at 10 AU. A larger or smaller cooling efficiency of the disk at the optically thin surface can promote or stifle fragmentation by affecting the vertical temperature profile, which determines whether convection can happen or not, and by regulating accretion from optically thin regions toward overdense regions. We also find that the chances of fragmentation increase for a higher mean molecular weight, μ, since compressional heating is reduced. Only disks with masses >0.12 M ☉ and with μ ≥ 2.4, as expected for gas with a metallicity comparable to solar or higher, can fragment.