How planets grow by pebble accretion

Abstract

Context. In the theory of pebble accretion, planets form by the subsequent accretion of solids (micron-sized dust and larger pebbles) and gas. The amount of nebular gas that a planet can bind is limited by its cooling rate, which is set by the opacity of its envelope. Accreting dust and pebbles contribute to the envelope opacity and, thus, influence the outcome of planet formation. Aims. Our aim is to model the size evolution and opacity contribution of solids inside planetary envelopes. We then use the resultant opacity relations to study emergent trends in planet formation. Methods. We design a model for the opacity of solids in planetary envelopes that accounts for the growth, fragmentation, and erosion of pebbles during their sedimentation. It also includes a separate dust component, which can be both replenished and swept up by encounters with pebbles, depending on the relative velocities. We formulate analytical expressions for the opacity of pebbles and dust and map out their trends as a function of depth, planet mass, distance, and accretion rate. Results. The accretion of pebbles rather than planetesimals can produce fully convective envelopes, but only in lower-mass planets that reside in the outer disk or in those that are accreting pebbles at a high rate. In these conditions, pebble sizes are limited by fragmentation and erosion, allowing them to pile up in the envelope. At higher planetary masses or reduced accretion rates, a different regime applies, where the sizes of sedimenting pebbles are only limited by their rate of growth. The opacity in this growth-limited regime is much lower and declines steeply with depth and planet mass but is invariant with the pebble mass flux. Our results imply that the opacity of a forming planet’s envelope cannot be approximated by a value that is constant with either depth or planet mass. Applying these results to the Solar System, we argue that Uranus and Neptune could not have maintained a sufficiently high opacity to avoid runaway gas accretion unless they both experienced sufficiently rapid accretion of solids and formed late.

Early planet formation in embedded protostellar disks

“…The delayed formation of Saturn with respect to Jupiter would be in line with the assumptions of the Grand Tack model (Walsh et al 2011), while the further delay in the formation of Uranus and Neptune would explain their lower masses in the pebble accretion paradigm (see e.g. Helled et al 2020;Brouwers et al 2021).…”

Possible In Situ Formation of Uranus and Neptune via Pebble Accretion

“…The dust opacity derived by Valencia et al (2013) is significantly higher than suggested by other studies (Mordasini et al 2014;Ormel 2014;Brouwers et al 2021). However, the grain opacity is expected to be high at early phases of the planetary growth when the protoplanet accretes pebbles due to efficient pebble fragmentation (Brouwers et al 2021;Chachan et al 2021), pebble ablation (e.g., Valletta & Helled 2020), and bouncing collisions between accreted pebbles (Ormel et al 2021).…”

“…As shown in previous studies, the envelope's opacity significantly affects the H-He accretion rate (e.g., Movshovitz & Podolak 2008;Mordasini et al 2014;Brouwers et al 2017Brouwers et al , 2021. The opacity that we used in this study corresponds to the sum of the gas and dust opacity.…”

Solid Accretion onto Neptune-Mass Planets I: In-Situ Accretion and Constraints from the metallicity of Uranus and Neptune

“…However, it would be ideal to self-consistently compute the atmospheric metallicity, the resulting gas accretion rate, and the accompanying accretion luminosity, by taking into account the complicated interplay among solid accretion, the resulting metal enrichment of the atmosphere, the subsequent metal sedimentation, and the eventually accelerated/slowed down gas accretion. In fact, detailed calculations show that the value of f grain can be much smaller and larger than that constrained from the gas ac-10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Size of Solid Particles s (cm) cretion timescale (Figure 9, e.g., Movshovitz et al 2010;Ormel 2014;Ali-Dib & Thompson 2020;Brouwers et al 2021). This complexity is beyond the scope of this work and remains to be the future work.…”