An Analytical Theory for the Growth from Planetesimals to Planets by Polydisperse Pebble Accretion

TL;DR

This paper develops a comprehensive polydisperse pebble accretion theory, revealing significantly higher accretion rates in the Bondi regime and demonstrating its potential to accelerate planet formation within disk lifetimes.

Contribution

It introduces the first analytical polydisperse pebble accretion model, extending previous monodisperse formulas to more realistic pebble size distributions and providing new insights into planetary growth.

Findings

Polydisperse accretion rates are 1-2 orders of magnitude higher than monodisperse in the Bondi regime.

Accretion timescales of Myr are achievable for planetary seeds within the disk lifetime.

Pebble accretion can occur immediately after planetesimal formation, reducing the need for collisions.

Abstract

Pebble accretion is recognized as a significant accelerator of planet formation. Yet, only formulae for single-sized (monodisperse) distribution have been derived in the literature. These can lead to significant underestimates for Bondi accretion, for which the best accreted pebble size may not be the one that dominates the mass distribution. We derive in this paper the polydisperse theory of pebble accretion. We consider a power-law distribution in pebble radius, and we find the resulting surface and volume number density distribution functions. We derive also the exact monodisperse analytical pebble accretion rate for which 3D and 2D accretion are limits. In addition, we find analytical solutions to the polydisperse 2D Hill and 3D Bondi limits. We integrate the polydisperse pebble accretion numerically for the MRN distribution, finding a slight decrease (by an exact factor 3/7) in the Hill regime compared to the monodisperse case. In contrast, in the Bondi regime, we find 1-2 orders of magnitude higher accretion rates compared to monodisperse, also extending the onset of pebble accretion to 1-2 order of magnitude lower in mass. We find Myr-timescales, within the disk lifetime, for Bondi accretion on top of planetary seeds of masses $10^{-6}-10^{-4} M_\oplus$, over a significant range of the parameter space. This mass range overlaps with the high mass end of the planetesimal initial mass function, and thus pebble accretion is possible directly following formation by streaming instability. This alleviates the need for mutual planetesimal collisions as a major contribution to planetary growth.