Jumping the Gap: The Formation Conditions and Mass Function of
  Pebble-Pile Planetesimals
  In a turbulent proto-planetary disk, dust grains undergo large density
fluctuations and under the right circumstances, these grain overdensities can
overcome shear, turbulent, and gas pressure support to collapse under
self-gravity (forming a "pebble pile" planetesimal). Using a simple analytic
model for the fluctuations predicted in simulations, we estimate the
rate-of-formation and mass function of self-gravitating, rapidly-collapsing
planetesimal-mass bodies formed by this mechanism. The statistics of this
process depend sensitively on the size/stopping time of the grains, disk
surface density, and turbulent Mach numbers. However, when it occurs, we
predict that the resulting planetesimal mass function is broad and
quasi-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-Earth
masses is possible. The key condition is that grain density fluctuations reach
large amplitudes on large scales, where gravitational instability proceeds most
easily (collapse of small grains is strongly suppressed by turbulent
vorticity). We show this leads to a new criterion for 'pebble-pile' formation
in 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 (inversely
proportional 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 a
disk with ~10% the MMSN density, so planet formation at ~au may generically
occur late, as disks are evaporating. We also predict that conditions become
progressively more favorable for pebble-pile formation around lower-mass,
cooler stars.
