The evolution of gravitationally unstable protoplanetary disks: fragmentation and possible giant planet formation

We carry out a large set of very high resolution, three dimensional smoothed particle hydrodynamics (SPH) simulations describing the evolution of gravitationally unstable gaseous protoplanetary disks. We consider a broad range of initial disk parameters. Disk masses out to 20 AU range from 0.075 to 0.125 M⊙, roughly consistent with the high-end of the mass distribution inferred for disks around T Tauri stars.Minimum outer temperatures range from 30 to 100 K, as expected from studies of the early protosolar nebula and suggested by the modeling of protoplanetary disks spectra. The mass of the central star is also varied although it is usually assumed equal to that of the Sun. Overall the initial disks span minimum Q parameters between 0.8 and 2, with most models being around ∼ 1.4. The disks are evolved assuming either a locally isothermal equation of state or an adiabatic equation of state with varying γ. Heating by (artificial) viscosity and shocks is included when the adiabatic equation of state is used. When overdensities above a specific threshold appear as a result of gravitational instability in a locally isothermal calculation, the equation of state is switched to adiabatic to account for the increased optical depth. We show that when a disk has a minimum Q parameter less than 1.4 strong trailing spiral instabilities, typically three or four armed modes, form and grow until fragmentation occurs along the arms after about 5 mean disk orbital times. The resulting clumps contract quickly to densities several orders of magnitude higher than the initial disk density, and the densest of them survive even under adiabatic conditions. These clumps are stable to tidal disruption and merge quickly, leaving 2-3 protoplanets on fairly eccentric orbits (the mean eccentricity being around