Water-rich sub-Neptunes and rocky super Earths around different Stars: Radii shaped by Volatile Partitioning, Formation, and Evolution

TL;DR

The paper tests how water-rich interiors and different volatile partitioning schemes influence the mass–radius relation of sub-Neptunes and rocky super-Earths by coupling planet formation with long-term evolution under photoevaporation. It compares four interior-structure scenarios—Mixed, Fractionation, Layered, and Water Sequestration—using population synthesis outputs and a 1D interior–atmosphere model with hydrodynamic mass loss, calibrated to observations and Kepler biases. The main finding is that envelopes where water is mixed with H/He reproduce the observed radius valley and mass–radius trends reasonably well, while layered envelopes diverge from observations; fractionation has little impact for the chosen initial conditions, and interior water sequestration can match the high-mass sub-Neptunes but struggles at $M<3M_igoplus$. The study highlights the need for homogeneous, well-characterized samples and more advanced atmosphere–interior coupling, including magma-ocean solidification and multi-species sequestration, to robustly constrain planetary interiors and formation histories.

Abstract

The nature of sub-Neptunes remains unknown due to degeneracies in interior structure solutions. However, a statistical set of small planets with measured masses and radii can be used to test the planet formation theory prediction of large water reservoirs on sub-Neptunes. Here, we investigate whether water is included in photoevaporative mass loss and how much can partition into the rocky and metallic interior. We couple the result of a planetary formation model to evolution models which assume perfect mixing of water with H/He in the envelope or a layered structure. For the mixed envelopes, we also include fractionation during photoevaporative mass-loss. Further, the effect of equilibrium dissolution of water into an assumed magma ocean and into the metallic core is studied for the first time in coupled formation-evolution models. Out of the four tested scenarios, the mass-radius relation of exoplanets is relatively well matched by all scenarios except the one with layered H/He above water. The agreement depends on mass, with better consistency for the model without dissolution below 3 Earth masses and hints of the opposite at higher masses. In contrast to the significant effect of water dissolution, fractionation is not found to alter the properties of the planets for our initial conditions due to initially massive envelopes on all planets. For all scenarios, we quantify the radius valley location and scaling with stellar mass and conclude that water-rich sub-Neptunes mass-radius relations are broadly consistent with observations. Statistical surveys in mass and radius are required for distinction of the scenarios. The dissolution of different volatiles into the planetary interior and solidification of the magma ocean are natural next steps toward a comprehensive treatment of atmosphere-interior interaction in planet evolution models. (abridged)

Figures (17)

• Figure 1: Schematic visualization of the four considered different structure models. Considered layers (inside-out) are a metallic core (gray), a silicate mantle (green) expected to be in molten form as a magma ocean, in the Layered model an ice layer, and at the top a gaseous envelope (orange). Its metallicity $Z_{\rm env}$ is in the Mixed and initially in the Fractionation case set to $Z_{\rm homo}$ -- the metallicity resulting from mixing all volatiles with H/He uniformly in the gaseous envelope of the planet. For the Water Sequestration model (bottom), $Z_{\rm env}$ is lower since a part of the accreted volatiles are distributed to the magma ocean and metallic core (indicated by blue coloring of those two layers). The Layered model does not consider volatiles in the envelope. The arrows indicate mass loss and are colored in the Fractionation model to indicate varying metallicities in the lost gas (equal to or smaller than the envelope metallicity).
• Figure 2: Water mass fractions in core and mantle relative to total mass of the planet. These values provide an upper limit and are used in the Water Sequestration model. The three different colors indicate cases with 1, 10, and 30 % of total planetary volatile mass content (including the gaseous envelope) $M_{\rm vol}/M$ while the different linestyles show the two interior reservoirs (dotted for core, dashed for mantle), respectively the total water mass fraction sequestered in the interior (solid).
• Figure 3: Time evolution of planets using the different models. Top and middle panel show radii and radius difference to the Mixed model; the bottom plot envelope metallicities $Z_{\rm env}$. Time is measured relative to the start of the evolution, here fixed to 3 Myr. The dashed lines show a more massive sub-Neptune with an initial mass of 9.35, the solid ones that of an intermediate case (initial mass 4.96), and the dotted lines represent the evolution of a lighter planet 2.54. All planets are placed at 0.01 au around a 0.5 M$_\odot$ star (see text for further initial conditions). Note that the Fractionation model results overlap with the Mixed model result in the top panel. For this reason, the middle plot shows the relative radius difference to the equal-initial mass Mixed model case.
• Figure 4: Mass versus radius diagram of observed and synthetic planets. The four panels show the resulting planets using different model variations contrasted against the observational data from Parc2024. The synthetic data for all models is sampled according to the stellar mass distribution of the observations and an estimate of the detection and transit probability is applied. More saturated dots imply that the planet was sampled multiple times due to being more likely to be detected and their color is given by the planets' water mass fraction.
• Figure 5: Orbital period against planetary radii of observed and synthetic planets. The samples and coloring are the same as in Fig. \ref{['fig:m_R_all']}.