A radius valley between migrated steam worlds and evaporated rocky cores

Abstract

The radius valley (or gap) in the observed distribution of exoplanet radii, which separates smaller super-Earths from larger sub-Neptunes, is a key feature that theoretical models must explain. Conventionally, it is interpreted as the result of the loss of primordial hydrogen and helium (H/He) envelopes atop rocky cores. However, planet formation models predict that water-rich planets migrate from cold regions outside the snowline towards the star. Assuming water to be in the form of solid ice in their interior, many of these planets would be located in the radius gap contradicting observations. Here we use an advanced coupled formation and evolution model that describes the planets’ growth and evolution starting from solid, moon-sized bodies in the protoplanetary disk to mature Gyr-old planetary systems. Employing new equations of state and interior structure models to treat water as vapour mixed with H/He, we naturally reproduce the valley at the observed location. The model results demonstrate that the observed radius valley can be interpreted as the separation of less massive, rocky super-Earths formed in situ from more massive, ex situ, water-rich sub-Neptunes. Furthermore, the occurrence drop at larger radii, the so-called radius cliff, is matched by planets with water-dominated envelopes. Our statistical approach shows that the synthetic distribution of radii quantitatively agrees with observations for close-in planets, but only if low-mass planets initially containing H/He lose their atmosphere due to photoevaporation, which populates the super-Earth peak with evaporated rocky cores. Therefore, we provide a hybrid theoretical explanation of the radius gap and cliff caused by both planet formation (orbital migration) as well as evolution (atmospheric escape).

Peas-in-a-pod across the Radius Valley: Rocky Systems Are Less Uniform in Mass but More Uniform in Size and Spacing

“…From these revised samples, we find that, compared to their volatile-rich counterparts, rocky systems are more uniform in size, less uniform in mass, and more uniform in spacing at respective significance levels of 1.76σ, 2.41σ, and 2.88σ. We note that the relatively large drop in significance for our size uniformity result may be intuitively attributed to the high degree of compositional and physical diversity exhibited by volatile-rich planets lying close to the R cut = 1.6 R ⊕ boundary, as such worlds may harbor their volatile component predominantly in the form of an extremely tenuous H/He atmosphere (Misener & Schlichting 2021), a high-pressure H 2 O layer (Kite & Schaefer 2021), or ice sequestered in the planetary core (Izidoro et al 2022;Burn et al 2024), in contrast to the massive H/He envelopes commensurate with larger worlds (Owen & Wu 2013;Fulton et al 2017).…”

“…Conversely, planetary size may be modulated to order unity by the growth or removal of a gaseous envelope that accounts for only a few percent of the total planetary mass (e.g., Owen & Wu 2013), and while the removal of such atmospheres may indeed correlate strongly with prior interplanetary interactions (Ghosh et al 2023), their presence and appearance are strongly governed by planet-dependent processes that lie distinct from system-level evolution. Examples of such phenomena include, but are not limited to, atmospheric erosion via core-powered processes (e.g., Ginzburg et al 2018;Berger et al 2023) or photoevaporation (e.g., Owen & Wu 2017;Mordasini 2020), inflation from tidal heating (Millholland 2019), surface-atmosphere chemical reactions , secondary outgassing (Kite & Barnett 2020), partial retention of a hydrogen envelope (Misener & Schlichting 2021), and mixing of an extended H/He envelope with steam (Burn et al 2024). Each of these processes, or any combination thereof, may thereby generate significant variations in individual planetary size while operating independently from the global formation mechanisms that promote mass uniformity for volatile-rich systems.…”

“…Alternatively, their rocky counterparts may experience more extreme collisional mass modulation, which may itself augment the available debris from which sub-Earth worlds may be born. Finally, a divergent evolutionary scheme may exist for which rocky planets interior to the snow line are formed in situ with their mass scale determined by a series of giant impacts (Goldreich et al 2004;Emsenhuber et al 2023), while ex situ worlds with surrounding vaporized hydrospheres experience substantial inward drift and a reduced propensity for collision, as well as a resistance to water loss from early giant impacts (Burn et al 2024).…”

“…The volatile component of the latter subpopulation may exist primarily in the form of massive H/He envelopes that are either selectively accreted within gas-poor protoplanetary disks (Lee et al 2022) or shed at later epochs via photoevaporative processes (e.g., Owen & Wu 2017;Mordasini 2020) or core-powered mass loss (e.g., Ginzburg et al 2018;Berger et al 2023). Alternatively, these volatile-rich worlds may instead owe their nature to the bolstered accretion of water beyond the snow line (Luque & Pallé 2022), where size augmentation is the result of ice sequestered in the core (Izidoro et al 2022) or a vaporized hydrosphere surrounding the planet (Burn et al 2024).…”

A Unified Treatment of Kepler Occurrence to Trace Planet Evolution. II. The Radius Cliff Formed by Atmospheric Escape

“…These models make the assumption that sub-Neptunes form in situ with an Earth-like rocky core and H/He primordial envelope. Theory predicts a large fraction of water-rich cores interior to 1 au (Aguichine et al 2021;Chakrabarty & Mulders 2024;Burn et al 2024), which could impact the evolved sub-Neptune population.…”