How planets grow by pebble accretion

Abstract

During their formation, planets form large, hot atmospheres due to the ongoing accretion of solids. It has been customary to assume that all solids end up at the center, constituting a “core” of refractory materials, whereas the envelope remains metal-free. However, recent work, as well as observations by the Juno mission, indicate that the distinction may not be so clear cut. Indeed, small silicate, pebble-sized particles will sublimate in the atmosphere when they hit the sublimation temperature (T ~ 2000 K). In this paper we extend previous analytical work to compute the properties of planets within such a pebble accretion scenario. We conduct 1D numerical calculations of the atmosphere of an accreting planet, solving the stellar structure equations, augmented by a nonideal equation of state that describes a hydrogen and helium-silicate vapor mixture. Calculations terminate at the point where the total mass in metal is equal to that of the H+He gas, which we numerically confirm as the onset of runaway gas accretion. When pebbles sublimate before reaching the core, insufficient (accretion) energy is available to mix dense, vapor-rich lower layers with the higher layers of lower metallicity. A gradual structure in which Z decreases with radius is therefore a natural outcome of planet formation by pebble accretion. We highlight, furthermore, that (small) pebbles can act as the dominant source of opacity, preventing rapid cooling and presenting a channel for (mini-)Neptunes to survive in gas-rich disks. Nevertheless, once pebble accretion subsides, the atmosphere rapidly clears followed by runaway gas accretion. We consider atmospheric recycling to be the most probable mechanism to have stalled the growth of the envelopes of these planets.

How drifting and evaporating pebbles shape giant planets

“…During the buildup of the core, we set the fraction of matter that is accreted to the core (with mass M c ) at M < M iso to 90% of the total accreted matter (10% of accreted pebbles contribute to the primary envelope). This approach is supposed to account for pebble evaporation into the planetary envelope during core buildup in a simplified way compared to more sophisticated models (e.g., Brouwers & Ormel 2020;Ormel et al 2021), who actually show that even less than 50% of the solids accreted via pebbles make up the core and the evaporated pebbles make up most of the heavy element content of these forming planets (Ormel et al 2021). The initial growth during the core buildup in our model is thus simply described via Ṁcore = 0.9 Ṁpeb ; Ṁgas = 0.1 Ṁpeb ,…”

“…We have assumed that during pebble accretion 90% of the accreted pebbles are attributed to the core and 10% are attributed to the heavy-element-rich atmosphere during core buildup. However, more detailed models have revealed that less than 50% of the accreted solids contribute to the core, while the remaining pebbles contribute to the high metallicity envelope (e.g., Brouwers & Ormel 2020;Ormel et al 2021). Taking a larger fraction of heavy elements to be accreted into the early atmosphere rather than the core will not influence the total heavy element content of the planet, because the accreted mass is the same.…”

“…Venturini et al (2015) shows that already for Z env > 0.45 a significant reduction of the critical core mass for gas accretion can be achieved. However, in the models of Brouwers & Ormel (2020) the pebbles evaporating in the planetary atmosphere do not allow such a fast transition into runaway gas accretion, while the study of Ormel et al (2021) shows that envelope pollution significantly reduces the time at which the planet reaches the cross over mass for runaway gas accretion in line with Venturini et al (2015). Furthermore, Johansen et al (2021) shows that water-rich pebbles entering the planetary Hill sphere can evaporate high up in the planetary atmosphere, where recycling flows (Lambrechts & Lega 2017;Cimerman et al 2017) could transport the water vapor away from the planet, preventing the buildup of a high Z envelope.…”

Hidden water in magma ocean exoplanets

“…As volatile partitioning in the deep interior has been neglected for inference studies of exoplanets, previous interior predictions have thus far generally underestimated the amount of water and hydrogen for sub-Neptunes. Sub-Neptune envelopes may possess compositional gradients (Ormel et al 2021;Helled & Stevenson 2017), e.g., water might only be mixed within a hydrogen layer up to heights where water condenses. This effect itself influences the calculated radii and should ideally be considered in parallel with the partitioning of volatiles in the deeper planetary parts.…”

How the planetary eccentricity influences the pebble isolation mass

“…This is in contrast to circular planets, for which a well-defined pebble isolation mass is found even at large turbulent viscosities. This may have interesting implications for the formation of the cores of massive planets in highly turbulent protoplanetary discs, with the possibility of a eccentricity influences the pebble isolation mass 9 reduced efficiency of accretion for eccentric planets (Liu & Ormel 2018;Ormel et al 2021). It would be interesting to examine whether such planets could still accrete gas with their envelope contraction not being hindered by the accretion of solids.…”