Dynamics of solids in the midplane of protoplanetary disks: Implications for planetesimal formation

Xue Ning Bai, James M. Stone

Research output: Contribution to journalArticlepeer-review

249 Scopus citations


We present local two-dimensional and three-dimensional hybrid numerical simulations of particles and gas in the midplane of protoplanetary disks (PPDs) using the Athena code. The particles are coupled to gas aerodynamically, with particle-to-gas feedback included. Magnetorotational turbulence is ignored as an approximation for the dead zone of PPDs, and we ignore particle self-gravity to study the precursor of planetesimal formation. Our simulations include a wide size distribution of particles, ranging from strongly coupled particles with dimensionless stopping time τs = Ωtstop = 10-4 (where Ω is the orbital frequency, tstop is the particle friction time) to marginally coupled ones with τs = 1, and a wide range of solid abundances. Our main results are as follows. (1) Particles with τs ≳ 10-2 actively participate in the streaming instability (SI), generate turbulence, and maintain the height of the particle layer before Kelvin-Helmholtz instability is triggered. (2) Strong particle clumping as a consequence of the SI occurs when a substantial fraction of the solids are large (τs ≳ 10-2) and when height-integrated solid-to-gas mass ratio Z is super-solar. We construct a toy model to offer an explanation. (3) The radial drift velocity is reduced relative to the conventional Nakagawa-Sekiya-Hayashi (NSH) model, especially at high Z. Small particles may drift outward. We derive a generalized NSH equilibrium solution for multiple particle species which fits our results very well. (4) Collision velocity between particles with τs ≳ 10 -2 is dominated by differential radial drift, and is strongly reduced at larger Z This is also captured by the multi-species NSH solution. Various implications for planetesimal formation are discussed. In particular, we show that there exist two positive feedback loops with respect to the enrichment of local disk solid abundance and grain growth. All these effects promote planetesimal formation.

Original languageEnglish (US)
Pages (from-to)1437-1459
Number of pages23
JournalAstrophysical Journal
Issue number2
StatePublished - Oct 20 2010

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Diffusion
  • Hydrodynamics
  • Instabilities
  • Planets and satellites: formation
  • Protoplanetary disks
  • Turbulence


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