Fragmentation of gravitationally unstable gaseous protoplanetary disks with radiative transfer

We report on the results of the first 3D SPH simulation of massive, 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. The disks grow slowly in mass starting from a Toomre-stable initial condition to the point at which they become marginally unstable. 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 the accretion flow from optically thin regions towards overdense regions. We also find that the chances of fragmentation increase for a higher mean molecular weight $\mu$ since compressional heating is reduced. Around a star with mass $1 M_{\odot}$ only disks with $\mu \ge 2.4$, as expected for gas with a metallicity comparable to solar or higher, fragment. This suggests that disk instability, like core-accretion, should be more effective in forming gas giants at higher gas metallicities, consistent with the observed correlation between metallicity of the planet-hosting stars and frequency of planet