http://arxiv.org/abs/1401.2458

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 insights from simulations and a new analytic model for the fluctuations, we calculate the rate-of-formation and mass function of self-gravitating, collapsing planetesimal-mass bodies formed by this mechanism. The statistics of this process depend sensitively on the size/stopping time of the largest 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, 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. So at large radii, this can easily occur and seed core accretion. 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.

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Tue, 14 Jan 14
2/72