TURBULENT DISKS ARE NEVER STABLE: FRAGMENTATION AND TURBULENCE-PROMOTED PLANET FORMATION

A fundamental assumption in our understanding of disks is that when the Toomre Q >> 1, the disk is stable against fragmentation into self-gravitating objects (and so cannot form planets via direct collapse). But if disks are turbulent, this neglects a spectrum of stochastic density fluctuations that can produce rare, high-density mass concentrations. Here, we use a recently developed analytic framework to predict the statistics of these fluctuations, i.e., the rate of fragmentation and mass spectrum of fragments formed in a turbulent Keplerian disk. Turbulent disks are never completely stable: we calculate the (always finite) probability of forming self-gravitating structures via stochastic turbulent density fluctuations in such disks. Modest sub-sonic turbulence above Mach number M similar to 0.1 can produce a few stochastic fragmentation or direct collapse events over similar to Myr timescales, even if Q >> 1 and cooling is slow (t(cool) >> t(orbit)). In transsonic turbulence this extends to Q similar to 100. We derive the true Q-criterion needed to suppress such events, which scales exponentially with Mach number. We specify to turbulence driven by magneto-rotational instability, convection, or spiral waves and derive equivalent criteria in terms of Q and the cooling time. Cooling times greater than or similar to 50 t(dyn) may be required to completely suppress fragmentation. These gravo-turbulent events produce mass spectra peaked near similar to(Q M-disk/M-*)(2) M-disk (rocky-to-giant planet masses, increasing with distance from the star). We apply this to protoplanetary disk models and show that even minimum-mass solar nebulae could experience stochastic collapse events, provided a source of turbulence.