Turbulent Disks are Never Stable: Fragmentation and Turbulence-Promoted Planet Formation

TL;DR

This paper demonstrates that turbulence in disks can cause stochastic density fluctuations leading to fragmentation and potential planet formation, even when classical stability criteria suggest the disk should be stable.

Contribution

It develops an analytic framework to predict the probability and mass spectrum of turbulent fragmentation in Keplerian disks, challenging traditional stability assumptions.

Findings

Turbulent disks can produce self-gravitating fragments despite high Toomre Q.

Sub-sonic turbulence can cause fragmentation over Myr timescales.

Cooling times >50 times the dynamical time may suppress fragmentation.

Abstract

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 ~0.1 can produce a few stochastic fragmentation or 'direct collapse' events over ~Myr timescales, even if Q>>1 and cooling is slow (t_cool>>t_orbit). In trans-sonic turbulence this extends to Q~100. We derive the true Q-criterion needed to suppress such events, which scales exponentially with Mach number. We specify to turbulence driven by MRI, convection, or spiral waves, and derive equivalent criteria in terms of Q and the cooling time. Cooling times >~50*t_dyn may be required to completely suppress fragmentation. These gravoturbulent events produce mass spectra peaked near ~M_disk*(Q*M_disk/M_star)^2 (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.