From Dust to Planetesimals: An Improved Model for Collisional Growth in Protoplanetary Disks

Abstract

Planet formation occurs within the gas-and dust-rich environments of protoplanetary disks. Observations of these objects show that the growth of primordial submicronsized particles into larger aggregates occurs at the earliest evolutionary stages of the disks. However, theoretical models of particle growth that use the Smoluchowski equation to describe collisional coagulation and fragmentation have so far failed to produce large particles while maintaining a significant population of small grains. This has been generally attributed to the existence of two barriers impeding growth due to bouncing and fragmentation of colliding particles. In this paper, we demonstrate that the importance of these barriers has been artificially inflated through the use of simplified models that do not take into account the stochastic nature of the particle motions within the gas disk. We present a new approach in which the relative velocities between two particles is described by a probability distribution function that models both deterministic motion (from the vertical settling, radial drift and azimuthal drift) and stochastic motion (from Brownian motion and turbulence). Taking both into account can give quite different results to what has been considered recently in other studies. We demonstrate the vital effect of two "ingredients" for particle growth: the proper implementation of a velocity distribution function that overcomes the bouncing barrier and, in combination with mass transfer in high-mass-ratio collisions, boosts the growth of larger particles beyond the fragmentation barrier. A robust result of our simulations is the emergence of two particle populations (small and large), potentially explaining simultaneously a arXiv:1209.0013v3 [astro-ph.EP] 15 Dec 2012 number of long-standing problems in protoplanetary disks, including planetesimal formation close to the central star, the presence of mm-to cm-size particles far out in the disk, and the persistence of micron-size grains for millions of years.

Dust and gas mixtures with multiple grain species – a one-fluid approach

“…When grains are initially growing, most of the dust mass is concentrated in the largest particles (Blum & Wurm 2008;Windmark et al 2012;Garaud et al 2013). This implies φ 1 < 0.5 and would support the outward migration mechanism detailed above.…”

Vertical settling and radial segregation of large dust grains in the circumstellar disk of the Butterfly Star

“…Circumstellar disks are a natural outcome of the star formation process and are known to dissipate over time (∼10 6 -10 7 yr; Haisch et al 2001) by means of stellar winds or by photoevaporation caused by either the radiation of the central star or by an external source of radiation (e.g., Hollenbach et al 2000;Clarke et al 2001;Alexander & Armitage 2007), by accretion onto the central star (Hartmann et al 1998), by grain growth and fragmentation (e.g., Dullemond & Dominik 2005;Dominik et al 2007;Natta et al 2007;Birnstiel et al 2011;Garaud et al 2013;Ubach et al 2012), and by the formation of planets (e.g., Pollack et al 1996;Boss 2002;Armitage 2007Armitage , 2010Fortier et al 2013). The way in which the disk material dissipates has important implications for the possibility of planet formation.…”

The Emerging Paradigm of Pebble Accretion

“…However, it is especially below the ballistic:settling line where the change is the largest. Windmark et al (2012) and Garaud et al (2013) have hypothesized that some particles could cross the fragmentation/bouncing barriers that operate around s D 1, because of fortuitously colliding with particles at low collision energies. To grow into planetesimals, these "lucky" particles, however, still need to grow fast.…”