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

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.

17 pages, 12 figures. Accepted to ApJ

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Cited by in corpus (10)

• Planet formation throughout the Milky Way: Planet populations in the context of Galactic chemical evolution
• Formation of wide-orbit giant planets in protoplanetary disks with a decreasing pebble flux
• Filling in the Gaps: Can Gravitationally Unstable Discs Form the Seeds of Gas Giant Planets?
• Planetesimal and planet formation in transient dust traps
• From Planetesimals to Dwarf Planets by Pebble Accretion
• Planetesimal Growth in Evolving Protoplanetary Disks: Constraints from the Pebble Supply
• Exploring the conditions for forming planetesimals by the streaming instability and planetary systems by pebble accretion
• How stellar mass and disc size shape the formation and migration of super-Earths
• Forming Earth-like and Low-Mass Rocky Exoplanets Through Pebble and Planetesimal Accretion
• A multi-fluid approach for polydisperse pebble accretion: From particles to fluids, establishing the multifluid framework