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 smoothedparticle hydrodynamics (SPH) simulations describing the evolution ofgravitationally unstable gaseous protoplanetary disks. We consider a broadrange of initial disk parameters. Disk masses out to 20 AU range from 0.075 to0.125 $M_{\odot}$, roughly consistent with the high-end of the massdistribution inferred for disks around T Tauri stars. The initial disks spanminimum $Q$ parameters between 0.8 and 2, with most models being around $\sim1.4$. The disks are evolved assuming either a locally isothermal equation ofstate or an adiabatic equation of state with varying $\gamma$. Whenoverdensities above a specific threshold appear as a result of gravitationalinstability in a locally isothermal calculation, the equation of state isswitched to adiabatic to account for the increased optical depth. We show thatwhen a disk has a minimum $Q$ parameter less than 1.4 strong trailing spiralinstabilities, typically three or four armed modes, form and grow untilfragmentation occurs along the arms after about 5 mean disk orbital times. Theresulting clumps contract quickly to densities several orders of magnitudehigher than the initial disk density, and the densest of them survive evenunder adiabatic conditions. These clumps are stable to tidal disruption andmerge quickly, leaving 2-3 protoplanets on fairly eccentric orbits (the meaneccentricity being around 0.2) with masses between 0.7 and more than $7M_{Jup}$, well in agreement with those of detected extrasolar planets.after$\sim 10^3$ years. Fragmentation is not strongly dependent on whether the diskstarts from a marginally unstable state or gradually achieves it, as shown by atest where the disk gradually achieves the critical $Q$ by growing in mass.