Dynamics of Solids in the Midplane of Protoplanetary Disks: Implications for Planetesimal Formation

Abstract

We present local two-dimensional (2D) and three-dimensional (3D) 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 τ s ≡ Ωt stop = 10 −4 to marginally coupled ones with τ s = 1 (where Ω is the orbital frequency, t stop is the particle friction time), and a wide range of solid abundances. Our main results are: 1. Particles with τ s 10 −2 actively participate in the streaming instability, 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 streaming instability occurs when a substantial fraction of the solids are large (τ s 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 τ s 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 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.

Dust and gas density evolution at a radial pressure bump in protoplanetary disks

“…Bai & Stone (2010) and Johansen et al (2012) included them and confirmed that gravitationally bound clumps are formed by SI at the midplane dust layer. This may also be applied to the pressure bump.…”

“…The essential physics of the dust-enriched region can be learned from these simple simulation results. and Bai & Stone (2010) found that SI dominantes the KHIs. In general, small-scale instability can be damped by other perturbations.…”

Comet formation in collapsing pebble clouds

“…On the other hand, in stratified simulations, pebbles with St ∼ 0.3 show a strong clustering behaviour (Johansen et al 2007. However, Bai & Stone (2010) reported clustering of pebbles via the streaming instability for St > ∼ 0.01, if Z was significantly higher than the nominal value of the minimum mass solar nebula, Z MMSN = 0.01 (Hayashi 1981).…”

“…The SI avoids the growth barriers by jumping directly from pebbles with Stokes number St ∼ 0.01−1 (corresponding to a grain size of mm to dm, depending on the radial location in the disk) to Ceres-sized planetesimals (Johansen et al 2007;Bai & Stone 2010;Drażkowska & Dullemond 2014). The SI is triggered once the local dust-to-gas ratio in the protoplanetary disk exceeds unity.…”

Hiding in the Shadows. Ii. Collisional Dust as Exoplanet Markers

“…The well known centimeter and meter barriers (Weidenschilling 1977;Morbidelli et al 2008) along with the fragility of 1 km planetesimals (Leinhardt et al 2009;Nelson & Gressel 2010) will perturb this power law, especially in the case of the centimeter barrier, which can result in mass "piling up" in smaller sizes. Also, if planetesimals are not constructed via dust coagulation, then pathways for the formation of gravitational instability, such as turbulent concentration and streaming instability (e.g., Johansen et al 2006;Cuzzi et al 2008;Bai & Stone 2010;Gressel et al 2011), can circumvent the growth of intermediate-sized objects completely such that Equation (7) no longer holds, even as an approximation.…”