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In a turbulent proto-planetary disk, dust grains undergo large densityfluctuations and under the right circumstances, these grain overdensities canovercome shear, turbulent, and gas pressure support to collapse underself-gravity (forming a "pebble pile" planetesimal). Using a simple analyticmodel for the fluctuations predicted in simulations, we estimate therate-of-formation and mass function of self-gravitating, rapidly-collapsingplanetesimal-mass bodies formed by this mechanism. The statistics of thisprocess depend sensitively on the size/stopping time of the grains, disksurface density, and turbulent Mach numbers. However, when it occurs, wepredict that the resulting planetesimal mass function is broad andquasi-universal, with a slope dN/dM~1/M^(1-2), spanning a size/mass range~10-1e4 km (~1e-9-5.0 M_Earth). Collapse to planetesimal through super-Earthmasses is possible. The key condition is that grain density fluctuations reachlarge amplitudes on large scales, where gravitational instability proceeds mosteasily (collapse of small grains is strongly suppressed by turbulentvorticity). We show this leads to a new criterion for 'pebble-pile' formationin terms of the dimensionless particle stopping time (tau_stop > f(Q,Z,alpha)).In a MMSN, this requires grains larger than a=(50,1,0.1)cm at r=(1,30,100)au.At small radii, it would depend on the existence of large boulders. However,because density fluctuations depend super-exponentially on tau_stop (inverselyproportional to disk surface density), lower-density disks are more unstable.In fact, we predict that cm-sized grains at ~1au will form pebble piles in adisk with ~10% the MMSN density, so planet formation at ~au may genericallyoccur late, as disks are evaporating. We also predict that conditions becomeprogressively more favorable for pebble-pile formation around lower-mass,cooler stars.

Jumping the Gap: The Formation Conditions and Mass Function of Pebble-Pile Planetesimals