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 , { d } N / { d } M _ { p } \propto M _ { p } ^ { - p } , with p \simeq 1.6 \pm 0.1 , which equates to a differential size distribution { d } N / { d } R _ { p } \propto R _ { p } ^ { - q } , with q \simeq 2.8 \pm 0.1 .
We find no significant trends with resolution from a convergence study of up to 512 ^ { 3 } grid zones and N _ { par } \approx 1.5 \times 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 \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 .