How planets grow by pebble accretion

Abstract

Context. Proto-planets embedded in their natal disks acquire hot envelopes as they grow and accrete solids. This ensures that the material they accrete – pebbles, as well as (small) planetesimals – will vaporize to enrich their atmospheres. Enrichment modifies an envelope’s structure and significantly alters its further evolution. Aims. Our aim is to describe the formation of planets with polluted envelopes from the moment that impactors begin to sublimate to beyond the disk’s eventual dissipation. Methods. We constructed an analytical interior structure model, characterized by a hot and uniformly mixed high-Z vapor layer surrounding the core, located below the usual unpolluted radiative-convective regions. Our model assumes an ideal equation of state and focuses on identifying trends rather than precise calculations. The expressions we derived are applicable to all single-species pollutants, but we used SiO2 to visualize our results. Results. The evolution of planets with uniformly mixed polluted envelopes follows four potential phases. Initially, the central core grows directly through impacts and rainout until the envelope becomes hot enough to vaporize and absorb all incoming solids. We find that a planet reaches runaway accretion when the sum of its core and vapor mass exceeds a value that we refer to as the critical metal mass – a criterion that supersedes the traditional critical core mass. The critical metal mass scales positively with both the pollutant’s evaporation temperature and with the planet’s core mass. Hence, planets at shorter orbital separations require the accretion of more solids to reach runaway as they accrete less volatile materials. If the solids accretion rate dries up, we identify the decline of the mean molecular weight – dilution – as a mechanism to limit gas accretion during a polluted planet’s embedded cooling phase. When the disk ultimately dissipates, the envelope’s inner temperature declines and its vapor eventually rains out, augmenting the mass of the core. The energy release that accompanies this does not result in significant mass-loss, as it only occurs after the planet has substantially contracted.

Jupiter’s heavy-element enrichment expected from formation models

“…Therefore, only for the naive scenario in which all the accreted heavy elements are assumed to go to the center the heavy-element mass in the planet is comparable to the core's mass. This is clearly not a realistic scenario as shown by various previous studies (Helled & Stevenson 2017;Brouwers & Ormel 2020;Brouwers et al 2018;Venturini & Helled 2017;Bodenheimer et al…”

“…We use the tables from Chen & Rogers 2016 to determine the core's radius at a given mass. The infalling planetesimals typically reach the core only at the very early stages of the formation process when the envelope's mass is negligible (Valletta & Helled 2019;Brouwers & Ormel 2020).…”

How drifting and evaporating pebbles shape giant planets

“…First, the planet accretes pebbles (e.g., Johansen & Lambrechts 2017) until it reaches the pebble isolation mass (e.g., Lambrechts & Johansen 2014;Bitsch et al 2018), where pebble accretion stops. During the solid accretion phase, we attributed 90% of the solids to the core and 10% of the solids to a primordial planetary atmosphere during core buildup, following the idea that pebbles evaporate during accretion (Hori & Ikoma 2011;Brouwers & Ormel 2020). The pebble isolation mass is smaller in the inner regions of the disk, due to the flaring disk structure (e.g., Chiang & Goldreich 1997;Bitsch et al 2015a), resulting in smaller core masses of inner forming planets.…”

Unified Simulations of Planetary Formation and Atmospheric Evolution: Effects of Pebble Accretion, Giant Impacts, and Stellar Irradiation on Super-Earth Formation

“…Lee et al 2014), the continual recycling of the accreting gas around the planet (e.g. Ormel et al 2015;Cimerman et al 2017;Kurokawa & Tanigawa 2018;Kuwahara et al 2019), the delay of gas accretion by polluted envelopes (Brouwers & Ormel 2020), and disk dissipation (Ikoma & Hori 2012;Hori & Ogihara 2020). We have recently proposed the possibility of suppressing envelope accretion via a limit due to the disk accretion rate (Ogihara & Hori 2018), and similar solutions have been discussed in other studies (e.g.…”

“…The polluted envelope layer above the core would delays the envelope cooling (Hori & Ikoma 2011;Venturini et al 2015). Recently, Brouwers & Ormel (2020) derived an analytical expression for the critical core mass for a polluted envelope in the pebble accretion scenario. Since silicate pebbles can grow via collisions in the envelope, they should settle down in a deep interior and then evaporate.…”