The uncertainty in water mass fraction of wet planets

TL;DR

This paper addresses the uncertainty in the water mass fraction (WMF) of water-rich sub-Neptune exoplanets by modeling interiors under rock–water miscibility concepts and a second critical point (SCP). Using the MAGRATHEA internal structure code, it compares two end-member distributions—a fully separated rock–water structure and a mixed mantle with an outer pure-water shell—while solving for hydrostatic equilibrium with a mixture EOS and an adiabatic temperature gradient, and defining the outer radius at $P=100$ mbar. A key result is that WMF inferred from radii spans from $0.002$ to $0.273$, with radii and the thickness of the outer water layer strongly dependent on $T_{ ext{eq}}$ and whether rock–water remains mixed or segregates, as captured by $1/ ho_{ ext{mix}} = X_w/ ho_w + X_r/ ho_r$ and the SCP criterion $[log(T),log(P)]$ values. The work highlights degeneracies in M–R inferences for water-rich planets, emphasizes the need for improved rock–water EOSs and gradual transition modeling, and discusses implications for interpreting exoplanet radii and potential steam atmospheres under realistic formation and evolution scenarios.

Abstract

Planets with masses between Earth and Neptune often have radii that imply the presence of volatiles, suggesting that water may be abundant in their interiors. However, directly observing the precise water mass fraction and water distribution remains unfeasible. In our study, we employ an internal structure code MAGRATHEA to model planets with high water content and explore potential interior distributions. Departing from traditional assumptions of a layered structure, we determine water and rock distribution based on water-rock miscibility criteria. We model {wet planets} with an iron core and a homogeneous mixture of rock and water above it. At the outer regions of the planet, the pressure and temperature are below the rock-water miscibility point (the second critical point), causing the segregation of water and rock. Consequently, a shell of water is formed in the outermost layers. By considering the water-rock miscibility and the vapor state of water, our approach highlights the uncertainty in estimating the water mass fraction of detected exoplanets.

Figures (10)

• Figure 1: Planets composed of iron, rock, and water. Illustrations not to scale. The planet model on the left-hand side develops a shallow layer of pure water, while the majority of the water is locked in the rock ("mixed"). The model on the right-hand side is assumed to have a three-layer structure ("separated"). The physical properties of the structures are shown in Figure \ref{['fig:RhoR5M500K']}.
• Figure 2: Representation of the internal structure of planets with a mass of 5M$_\oplus$ and a WMF of 0.5 (left panel) and 0.1 (right panel). The left columns depict planets with a sharp separation between rock and water, while the right columns represent models featuring fully mixed rock/water interiors. The percents above each pair of columns show the relative difference in the planetary radius between "separated" and "mixed". In the right-column models ("mixed"), a pure water layer develops on top of the planets, following the separation of water from rock under the pressure and temperature conditions (SCP) described by Melekhova2007. Note some non-monotonic behavior of the differences in high temperature and WMF of 0.1: this is a result of larger fraction of water mass mixed in the rock. An example of detailed interiors are shown in Figure \ref{['fig:RhoR5M500K']}.
• Figure 3: Internal structure of planets with 5 M$_\oplus$ and equilibrium temperature of 500K, with separated and mixed mantles. Both of the models have the same bulk composition of WMF=0.5 (2.5 M$_\oplus$ of water, 1.67 M$_\oplus$ of rock and 0.83 M$_\oplus$ of iron). The darker colors mark the iron core, and the dashed lines indicate outer water shells. Note the jumps in the density: jumps inside the iron core correspond the phase transitions Smith2018Dorogokupets2017 . The jump from solid lines to dotted lines indicates transition from regions of the mantle to pure water layers.
• Figure 4: Mass-Radius-Temperature diagram showing a sample of detected exoplanets with the selection of exoplanets highlighted. The selected sub-subsample can be identified as having WMF close to 0.5, based on M-R relations form Zeng2019 (brown solid curve). The dashed, dotted and dash-dotted curves are to show typical M-R relation for "mixed" scenario for different WMF and T, the solid curves are for "separated" scenario. For wider picture of M-R relations see figure \ref{['fig:MRTWMF300_500']}.
• Figure 5: Internal structure of five exoplanets modeled in this study (Table \ref{['Tbl:Pies']}). The left pies show the bulk composition of planets with "mixed" models. The right pies show the bulk composition for "separated" models. The right panels show density versus radius.