The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. I. The Role of Self-Gravity

Abstract

We study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over-densities generated via the streaming instability. To carry out these studies, we implement and test a particle-mesh self-gravity module for the Athena code that enables the simulation of aerodynamically coupled systems of gas and collisionless self-gravitating solid particles. Upon employment of our algorithm to planetesimal formation simulations, we find that (when a direct comparison is possible) the Athena simulations yield predicted planetesimal properties that agree well with those found in prior work using different numerical techniques. In particular, the gravitational collapse of streaming-initiated clumps leads to an initial planetesimal mass function that is well-represented by a power-law, dN/dM p ∝ M −p p , with p ≃ 1.6 ± 0.1, which equates to a differential size distribution dN/dR p ∝ R −q p , with q ≃ 2.8 ± 0.1. We find no significant trends with resolution from a convergence study of up to 512 3 grid zones and N par ≈ 1.5 × 10 8 particles. Likewise, the power-law slope appears indifferent to changes in the relative strength of self-gravity and tidal shear, and to the time when (for reasons of numerical economy) self-gravity is turned on, though the strength of these claims is limited by small number statistics. For a typically assumed radial distribution of minimum mass solar nebula solids (assumed here to have dimensionless stopping time τ = 0.3), our results support the hypothesis that bodies on the scale of large asteroids or Kuiper Belt Objects could have formed as the high-mass tail of a primordial planetesimal population.

Rocky Planet Formation: Quick and Neat

“…Unless planetesimal formation mechanisms assemble Mars-mass oligarchs directly, leaving behind 10% of the initial mass in debris is inevitable (e.g., Kenyon & Bromley 2016). By generating smaller planetesimals, current formation paths appear to preclude this possibility (Johansen et al 2015;Simon et al 2016). All popular models for the formation of Earth-mass planets include a giant impact phase which also generates significant amounts of debris.…”

“…In the pebble accretion scenario, dynamical processes within the gaseous disk concentrate cm-sized pebbles into large planetesimals with radii of 100-1000 km (e.g., Youdin & Goodman 2005;Johansen et al 2007;Youdin 2010;Johansen et al 2015;Simon et al 2016). Continued accretion of pebbles and mergers of planetesimals eventually produce a set of stable planets (e.g., Johansen et al 2015;Levison et al 2015;Chambers 2016).…”

“…Collisional and arXiv:1608.05410v1 [astro-ph.EP] 18 Aug 2016 -2 -collective processes then convert pebbles into km-sized or larger planetesimals (Youdin & Goodman 2005;Johansen et al 2007;Youdin 2011a;Johansen et al 2015;Simon et al 2016). …”

Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants

“…Pebbles can become concentrated in pressure bumps and through the streaming instability (see Johansen et al 2014 for a review), leading to planetesimal formation by gravitational collapse of the filaments. Planetesimals formed by the streaming instability have characteristic sizes of 100 km Simon et al 2015).…”

The Emerging Paradigm of Pebble Accretion

“…Clearly, geometric and Safronov accretion are not effective in growing planetesimals large; and the initiation of pebble accretion relies on the presence of a massive-enough seed that is produced by a process other than sweep up of small particles. Such a seed may result from classical self-coagulation mechanisms (i.e., runaway growth of planetesimals) or, more directly, from the high-mass tail of the planetesimal formation mechanism, e.g., by streaming or gravitational instabilities (Cuzzi et al 2010;Johansen et al 2015;Simon et al 2016;Schäfer et al 2017).…”