Planet formation by pebble accretion in ringed disks

A Morbidelli

doi:10.1051/0004-6361/202037983

Abstract

Context.Pebble accretion is expected to be the dominant process for the formation of massive solid planets, such as the cores of giant planets and super-Earths. So far, this process has been studied under the assumption that dust coagulates and drifts throughout the full protoplanetary disk. However, observations show that many disks are structured in rings that may be due to pressure maxima, preventing the global radial drift of the dust.Aims.We aim to study how the pebble-accretion paradigm changes if the dust is confined in a ring.Methods.Our approach is mostly analytic. We derived a formula that provides an upper bound to the growth of a planet as a function of time. We also numerically implemented the analytic formulæ to compute the growth of a planet located in a typical ring observed in the DSHARP survey, as well as in a putative ring rescaled at 5 AU.Results.Planet Type I migration is stopped in a ring, but not necessarily at its center. If the entropy-driven corotation torque is desaturated, the planet is located in a region with low dust density, which severely limits its accretion rate. If the planet is instead near the ring’s center, its accretion rate can be similar to the one it would have in a classic (ringless) disk of equivalent dust density. However, the growth rate of the planet is limited by the diffusion of dust in the ring, and the final planet mass is bounded by the total ring mass. The DSHARP rings are too far from the star to allow the formation of massive planets within the disk’s lifetime. However, a similar ring rescaled to 5 AU could lead to the formation of a planet incorporating the full ring mass in less than 1/2 My.Conclusions.The existence of rings may not be an obstacle to planet formation by pebble-accretion. However, for accretion to be effective, the resting position of the planet has to be relatively near the ring’s center, and the ring needs to be not too far from the central star. The formation of planets in rings can explain the existence of giant planets with core masses smaller than the so-called pebble isolation mass.

Highlights

The formation of massive planets is not yet fully elucidated
Pierre-Simon de Laplace is recognized to have been the first scientist to theorize -back in 1796- the formation of a circumstellar disk due to angular momentum conservation during the contraction of gas towards the central star (Emmanuel Kant had envisioned the formation of a disk, but his reasoning was not scientifically correct)
Modern resolved observations of protoplanetary disks (Andrews et al 2018) show that most of them are structured in rings

Summary

Introduction

The formation of massive planets (cores of giant planets, superEarths) is not yet fully elucidated. Oligarchic growth in planetesimal disks is inefficient if the initial planetesimals are mostly ∼100 km in size (Fortier et al 2013), as predicted by the streaming instability model (Johansen et al 2015; Simon et al 2017) and suggested by observations of the size-frequency distribution of the remaining solar system planetesimals (for asteroids see e.g., Morbidelli et al 2009, Delbo’ et al 2017; for Kuiper-belt objects see e.g., Morbidelli & Nesvorný 2020) For these reasons, a new paradigm for planet formation has been developed in the last decade, dubbed pebble accretion (Ormel & Klahr 2010; Lambrechts & Johansen 2012, 2014; Lambrechts et al 2014; Levison et al 2015; Ida et al 2016; Ormel 2017, to quote just a few).

Dust dynamics in a ring and its accretion by a planet

Morbidelli

An application: growth of a planet in a DSHARP ring

Findings

Conclusions