Forming 'Pebble-pile' Planetesimals

Jumping the gap: the formation conditions and mass function of ‘pebble-pile’ planetesimals

Author:

Hopkins

Abstract:

In a turbulent proto-planetary disc, dust grains undergo large-density fluctuations and under the right circumstances, grain overdensities can collapse under self-gravity (forming a ‘pebble-pile’ planetesimal). Using a simple model for fluctuations predicted in simulations, we estimate the rate of formation and mass function of self-gravitating planetesimal-mass bodies formed by this mechanism. This depends sensitively on the grain size, disc surface density, and turbulent Mach numbers. However, when it occurs, the resulting planetesimal mass function is broad and quasi-universal, with a slope dN/dM ∝ M−(1−2), spanning size/mass range ∼10–104 km (∼10−9–5 M⊕). 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 suppressed by turbulence). This leads to a new criterion for ‘pebble-pile’ formation: τs ≳ 0.05 ln (Q1/2/Zd)/ln (1 + 10 α1/4) ∼ 0.3 ψ(Q, Z, α) where τs = ts Ω is the dimensionless particle stopping time. In a minimum-mass solar nebula, this requires grains larger than a = (50, 1, 0.1) cm at r=(1, 30, 100)aur=(1, 30, 100)au. This may easily occur beyond the ice line, but at small radii would depend on the existence of large boulders. Because density fluctuations depend strongly on τs (inversely proportional to disc surface density), lower density discs are more unstable. Conditions for pebble-pile formation also become more favourable around lower mass, cooler stars.