THE MASS AND SIZE DISTRIBUTION OF PLANETESIMALS FORMED BY THE STREAMING INSTABILITY. I. THE ROLE OF SELF-GRAVITY

<jats:title>ABSTRACT</jats:title> <jats:p>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 <jats:sc>Athena</jats:sc> 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 <jats:sc>Athena</jats:sc> 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, <jats:inline-formula> <jats:tex-math> <?CDATA ${dN}/{{dM}}_{p}\propto {M}_{p}^{-p}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj523488ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, with <jats:inline-formula> <jats:tex-math> <?CDATA $p\simeq 1.6\pm 0.1$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj523488ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, which equates to a differential size distribution of <jats:inline-formula> <jats:tex-math> <?CDATA ${dN}/{{dR}}_{p}\propto {R}_{p}^{-q}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj523488ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>, with <jats:inline-formula> <jats:tex-math> <?CDATA $q\simeq 2.8\pm 0.1$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj523488ieqn4.gif" xlink:type="simple" /> </jats:inline-formula>. We find no significant trends with resolution from a convergence study of up to 512<jats:sup>3</jats:sup> grid zones and <jats:inline-formula> <jats:tex-math> <?CDATA ${N}_{{\rm{par}}}\approx 1.5\times {10}^{8}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj523488ieqn5.gif" xlink:type="simple" /> </jats:inline-formula> 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 <jats:inline-formula> <jats:tex-math> <?CDATA $\tau =0.3$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj523488ieqn6.gif" xlink:type="simple" /> </jats:inline-formula>), 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.</jats:p>