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

TL;DR

This study models planetesimal formation via streaming instability and self-gravity, revealing a power-law mass distribution consistent with observed asteroid and Kuiper Belt Object sizes, with results robust across various simulation parameters.

Contribution

Introduces a particle-mesh self-gravity module for Athena, enabling detailed simulations of planetesimal formation and confirming a power-law mass distribution consistent with prior studies.

Findings

Planetesimal mass function follows a power-law with p ≈ 1.6.

Size distribution slope q ≈ 2.8, matching observed small body populations.

Results are consistent across different resolutions and physical parameters.

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 ~ M^{-p}, with p = 1.6 +/- 0.1, which equates to a differential size distribution dN/dR ~ R^{-q}, 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 Npar = 1.5x10^8 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 \tau = 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.