abstract
- We present the results of high resolution SPH simulations of the evolution of gravitationally unstable protoplanetary disks. We report on calculations in which the disk is evolved using a locally isothermal or adiabatic equation of state (with shock heating), and also on new simulations in which cooling and heating by radiation are explicitly modeled. We find that disks with a minimum Toomre parameter $< 1.4$ fragment into several gravitationally bound protoplanets with masses from below to a few Jupiter masses. This is confirmed also in runs where the disk is given a quiet start, growing gradually in mass over several orbital times. A cooling time comparable to the orbital time is needed to achieve fragmentation, for disk masses in the range $0.08-0.1 M_{\odot}$. After about 30 orbital times, merging between the bound condensations always leads to 2-3 protoplanets on quite eccentric orbits.