Planetesimal formation around the snow line

I. Monte Carlo simulations of silicate dust pile-up in a turbulent disk

¹ Earth-Life Science Institute, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan
e-mail: ida@elsi.jp
² Laboratoire J.-L. Lagrange, Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, 06304 Nice, France
³ ISAS/JAXA, Sagamihara, Kanagawa, Japan
⁴ Department of Eartha and Planetary Sciences, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan
⁵ Steward Observatory/The Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona 85721, USA

Received: 17 October 2020
Accepted: 24 November 2020

Abstract

Context. The formation of rocky planetesimals is a long-standing problem in planet formation theory. One of the possibilities is that it results from gravitational instability as a result of the pile-up of small silicate dust particles released from sublimating icy pebbles that pass the snow line.

Aims. We want to understand and quantify the role of the water snow line for the formation of rock-rich and ice-rich planetesimals. In this paper, we focus on the formation of rock-rich planetesimals. A companion paper examines the combined formation of both rock-rich and ice-rich planetesimals.

Methods. We developed a new Monte Carlo code to calculate the radial evolution of silicate particles in a turbulent accretion disk, accounting for the back reaction (i.e., inertia) of the particles on their radial drift velocity and diffusion. Results depend in particular on the particle injection width (determined from the radial sublimation width of icy pebbles), the pebble scale height, and the pebble mass flux through the disk. The scale height evolution of the silicate particles, which is the most important factor for the runaway pile-up, is calculated automatically in this Lagrange method.

Results. From the numerical results, we derive semi-analytical relations for the scale height of the silicate dust particles and the particle-to-gas density ratio at the midplane, as functions of a pebble-to-gas mass flux ratio and the α parameters for disk gas accretion and vertical/radial diffusion We find that the runaway pile-up of the silicate particles (formation of rocky planetesimals) occurs if the pebble-to-gas mass flux ratio is ≳ [(α_Dz/α_acc)/3 × 10⁻²]^1/2, where α_Dz and α_acc are the α parameters for vertical turbulent diffusion and disk gas accretion.