arXiv subjects

Caroline Dorn

Publications and source records attributed to Caroline Dorn.

At least 19 recordsLinked to original sources

arXiv2026

A Stellar-Type Dependence in the Rocky and Volatile Composition of Small Exoplanets

We investigate the rocky and volatile composition of small exoplanets by modeling the population-level distribution of densities using a mixture framework that links interior structure models to observable quantities. We analyze three complementary samples spanning different stellar environments: the Luque \& Pall\'e M-dwarf sample, the DACE M-dwarf sample, and the DACE FGK sample. We consider a log-normal parameterization, which captures a characteristic core mass fraction (CMF) and the intrinsic dispersion to describe a single rocky population. The single rocky population inference suggests a higher CMF for small planets around FGK stars than those around M stars by $\sim$16\% (7-11 $\sigma$ depending on sample selection). We also consider a power-law parameterization, which probes clustering near compositional boundaries at CMF=0.32. The power-law parameterization provides an alternative interpretation: 89.9\% to 97.0\% of the planets around FGK stars are rocky whereas up to 61.6\% (ranging from 4.1\% to 61.6\%) of planets around M stars are rocky. In addition, we find that volatile mass fractions are highly concentrated. For example, to describe the DACE M-dwarf sample using a mixture of rocky, water-rich, and gas-rich planets, we find that more than 99.5\% gaseous planets have an atmospheric mass fraction (AMF) $\lesssim 0.01\%$, and more than 55.4\% (82.7\%) gaseous planets have a water mass fraction (WMF) $\lesssim 0.1\%$ ($\lesssim 1\%$). These results suggest that while volatile-bearing planets are common, their composition and prevalence depend strongly on stellar environment, and their volatile inventories are tightly constrained by formation and evolutionary processes.

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arXiv2026

Atmospheric diversity of sub-Neptunes from formation with rock, water, and soot

Recent JWST detections of CH4 and CO2 in sub-Neptune atmospheres point to a link between atmospheric composition and the nature of planetary building blocks - rock, water, or refractory carbon ("soot") - yet this connection remains poorly understood. Here we investigate how different formation environments shape the coupled interior and atmospheric compositions of sub-Neptunes. We model planets assembled from varying proportions of rock, water, and soot and compute the global chemical equilibrium and the overlying atmospheric structure. We find that planets formed from water-poor material produce atmospheres strongly depleted in carbon-bearing species, with log(CH4) and log(CO2) below -4. In contrast, planets assembled from water-rich building blocks naturally develop methane- and carbon-dioxide-rich atmospheres with elevated metal mass fractions and C/O ratios. The presence of refractory carbon (soot) further enhances methane production and can lead to methane-dominated atmospheres. Comparison with JWST observations suggests that water-rich formation is sufficient to explain K2-18b and TOI-270d with no soot component required, while TOI-421b and GJ3470b are consistent with water-poor formation inside the water ice line. The ratio H2O/CH4 combined with the mean molecular weight (MMW) provides a powerful two-dimensional diagnostic linking atmospheric composition to formation environment, with departures from the predicted trends explained by water condensation in temperate atmospheres or fractionated atmospheric mass loss.

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arXiv2026

The Role of Formation Location in Shaping Sulfur-, Nitrogen-, and Carbon-Bearing Species in Super-Earth and Sub-Neptune Atmospheres

Atmospheric compositions of sub-Neptunes and super-Earths are often interpreted as tracers of formation location relative to volatile ice lines. However, prolonged magma oceans can chemically equilibrate with primordial atmospheres and modify accreted volatile signatures. In this study, we couple a synthetic planet population from the Bern Generation III formation model to an extended global chemical equilibrium framework including sulfur and nitrogen chemistry, and compare accreted and equilibrated compositions for $\sim$ 1200 young planets shortly after formation ($\sim$ 4 Myr) formed inside and outside the water ice line. We find that interior-atmosphere equilibration systematically alters elemental ratios and molecular abundances. The atmospheric C/O ratio shifts relative to the accreted state and remains systematically higher for planets formed outside the ice line. Nitrogen-bearing species NH$_3$, N$_2$ are strongly depleted through dissolution into the silicate melt, while minor amounts of HCN are produced, leading to low atmospheric nitrogen abundances. Sulfur-bearing species remain more abundant than nitrogen-bearing species; during equilibration, accreted H$_2$S partitions into the interior and small amounts of SO$_2$ form, but overall sulfur abundances depend only weakly on formation location. Silicon-bearing gases (SiH$_4$, SiO) are generated in substantial amounts, with narrower distributions for planets formed outside the ice line. We identify atmospheric C/O, SiH$_4$, and H$_2$O as potential indicators of formation location, while nitrogen depletion emerges as a generic outcome of magma ocean equilibration. Comparison with characterized sub-Neptunes such as TOI-270 d, K2-18 b, and GJ 3470 b shows broad consistency with oxygen-dominated, metal-rich atmospheres shaped by interior-atmosphere exchange.

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arXiv2026

A New Global Chemical Equilibrium Code: Refractory Element Signatures in Super-Earths and Sub-Neptunes

The atmospheres of super-Earths and sub-Neptunes can be strongly modified by chemical exchange with their molten interiors during long-lived magma ocean phases. Interpreting atmospheric observations requires fast models that self-consistently couple atmospheric chemistry to the composition of the planetary interior. We present an updated implementation of the global chemical equilibrium (GCE) framework from (Schlichting & Young 2022), which computes the equilibrium composition of a coupled metal-silicate-gas system. The numerical solver has been improved using a gradient-based optimizer, reducing the computational cost of solving the chemical network by more than two orders of magnitude and enabling large parameter studies. We apply the framework to a large synthetic population of planets and explore the imprint of bulk refractory composition of Mg, Si, and Fe on atmospheric properties. We consider planets with different masses, thermal states, and volatile inventories. We find that the atmospheric mass fraction and atmospheric metal mass fraction are primarily controlled by the temperature at the atmosphere-magma ocean interface and the planetary water budget, while the accreted hydrogen mass fraction plays a minor role because most hydrogen dissolves into the interior. For planets that accreted water, the refractory ratios Mg/Si and Fe/Si strongly influence carbon partitioning between the gas, silicate, and metal phases, producing large variations in atmospheric atmospheric metal mass fraction and C/O ratios. These results demonstrate that atmospheric compositions of sub-Neptunes depend sensitively on both the volatile inventory and the bulk composition of rocky material, providing new constraints for interpreting atmospheric observations. The new GCE code is open-source.

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arXiv2026

Origin and characterization of super-Earths and sub-Neptunes

Super-Earths and sub-Neptunes represent the most common class of exoplanets discovered to date in our galaxy, yet they have no direct analogues in the Solar System. Since 2014, researchers within the NCCR PlanetS have made significant contributions to understanding the origin and nature of these small planets. This chapter provides an overview of the progress made in their detection, characterization, and theoretical interpretation during the 2014-2025 period. The combined data from space-based photometric missions such as Kepler and TESS, together with ground-based radial velocity campaigns using state-of-the-art spectrographs (e.g., HARPS, ESPRESSO, NIRPS), have enabled detailed demographic analyses of these planets. These observational efforts are complemented by theoretical work exploring their internal structures, bulk compositions, formation and evolution, shedding light on the physical processes responsible for the observed diversity. As high-precision observations from facilities like JWST begin to probe the atmospheric composition of individual planets, a more complete picture of super-Earth and sub-Neptune origins is emerging, one that continues to challenge and refine current planet formation theories.

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arXiv2026

Super-Earth masses and stellar abundances from NIRPS reveal tentative evidence for water-rich formation around M dwarfs

Tracing the compositional link between terrestrial super-Earths and their host stars provides clues to their dominant formation pathway. By constraining the stellar abundances of refractory elements, we can predict the core mass fractions (CMFs) of their super-Earths. The level of agreement between this prediction and the planetary CMF derived from their masses and radii can reveal past formation processes, like mantle stripping and water-rich formation plus sequestration in the planet's core. Here, we present the first results from the Near Infrared Planet Searcher (NIRPS) GTO CMF subprogram: an intensive radial velocity campaign to refine masses and compute host stellar abundances of three hot super- Earths around M dwarfs (GJ 1132 b, GJ 1252 b, and LTT 3780 b), calculating masses of $1.69 \pm 0.15M_\oplus$, $1.54 \pm 0.18M_\oplus$, and $2.34 \pm 0.10M_\oplus$ respectively. We measure the CMFs of these and six further hot super-Earths with precise masses already available in the literature to 10-15% precision. We compare these to CMF predictions made from measuring the Fe, Mg, and Si abundances of their host stars measured from the NIRPS spectra. We find that the CMFs of these planets are smaller than expected from their host stellar abundances, to a statistically significant degree. This discrepancy is suggestive of significant reservoirs of water, and while these planets are too hot to harbor surface water, they likely have interior water mass fractions of $\sim$1%.

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arXiv2026

Weighing the mass of LHS 3844 b

Context: LHS 3844 b (TOI-136 b) is a ultra short-period, Earth-size exoplanet detected by TESS. It is one of the most favourable object for atmospheric characterisation and the study of its surface with the James Webb Space Telescope. However, the dynamical mass of this planet has not been measured yet. Aims: We aim to determine the mass of LHS 3844 b using high-precision radial velocity (RV) measurements and assess the robustness of the inferred signal across different noise and orbital modelling assumptions. Methods: We analyse 25 ESPRESSO RV observations within a fully Bayesian framework. We explore 15 competing RV models that differ in their treatment of correlated stellar variability (through different Gaussian Process kernels) and long-term drifts. Marginal likelihoods are computed for all models and used for Bayesian model comparison and evidence-weighted parameter estimation. Results: The RV planetary signal is robustly detected across all models, and the inferred semi-amplitude remains stable under all tested noise and drift prescriptions. From the evidence-weighted posterior samples we derive a planetary mass of $2.27 \pm 0.23$ M$_\oplus$ and a bulk density of $5.67 \pm 0.65$ gcm$^{-3}$, consistent with a predominantly rocky composition. Model comparison favours GP kernels including periodic or quasi-periodic components associated with stellar rotation and disfavors models with additional long-term drifts. Using interior-structure inference, we find that the core mass fraction is comparable to (or slightly smaller than) Earth's and only trace amounts of water are permitted, supporting a dry, terrestrial interior. We also investigate a tentative additional signal near $\sim 6.9$ days, but Bayesian model comparison does not provide conclusive support for its planetary interpretation.

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arXiv2026

Oxygen left behind: Atmospheric Enrichment due to Fractionation in Sub-Neptunes using BOREAS

The evolution of exoplanetary atmospheres is strongly influenced by atmospheric escape, particularly for close-in planets. Fractionation during atmospheric loss can preferentially remove lighter elements such as hydrogen, while retaining heavier species like oxygen. In this study, we investigate how and under what conditions hydrodynamic escape and chemical fractionation jointly shape the mass and composition of exoplanet atmospheres, especially for mixed H2 + H2O atmospheres. We develop BOREAS, a self-consistent mass loss model coupling a 1D Parker wind formulation with a mass-dependent fractionation scheme, which we apply across a range of planet masses, radii, equilibrium temperatures, and incident XUV fluxes, allowing us to track hydrogen and oxygen escape rates at different snapshots in time. We find that oxygen is efficiently retained over most of the parameter space. Significant oxygen loss occurs under high incident XUV fluxes, while at intermediate fluxes oxygen loss is largely confined to low-gravity planets. Where oxygen is retained, irradiation is too weak to drive significant escape of hydrogen and thus limiting atmospheric enrichment. By contrast, our model predicts that sub-Neptunes undergo substantial atmospheric enrichment over approx. 200 Myr when hydrogen escape is efficient and accompanied by partial oxygen entrainment. Notably, our results imply that sub-Neptunes near the radius valley can evolve into water-rich planets, in agreement with GJ 9827 d. Present-day water-rich atmospheres may have originated from water-poor envelopes under some conditions, highlighting the need to include chemical fractionation in evolution models. BOREAS is publicly available.

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arXiv2026

The Effects of Non-ideal Mixing in Planetary Magma Oceans and Atmospheres

Sub-Neptunes with hydrogen-rich envelopes are expected to sustain long-lived magma oceans that continuously exchange volatiles with their overlying atmospheres. Capturing these interactions is key to understanding the chemical evolution and present-day diversity of sub-Neptunes, super-Earths, and terrestrial planets, particularly in light of new JWST observations and upcoming missions. Recent advances in both geochemistry and astrophysics now allow the integration of experimental constraints and thermodynamic models across melt, metal, and gas phases. Here we extend a global chemical equilibrium model to include non-ideal behavior in all three phases. Our framework combines fugacity corrections for gas species with activity coefficients for silicate and metal species, enabling a fully coupled description of volatile partitioning. We show that for planetary embryos (0.5 M$_\oplus$ at 2350 K), non-ideality introduces only modest corrections to atmosphere-magma ocean interface (AMOI) pressures, volatile inventories, and interior compositions. In contrast, for sub-Neptunes with higher temperatures ($\approx$ 3000 K) and pressures, non-ideal effects are more pronounced, though still modest in absolute terms$-$typically within 20% and at most a factor of two. Including activity and fugacity coefficients simultaneously increases the AMOI pressure, enhances water retention in the mantle and the envelope. Our results demonstrate that non-ideality must be treated globally: applying corrections to only one phase leads to incomplete or even misleading trends. These findings highlight the importance of self-consistent global thermodynamic treatments for interpreting atmospheric spectra and interior structures of sub-Neptunes and super-Earths.

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arXiv2026

Densities of small planets around the M dwarfs TOI-4336 A and TOI-4342 with ESPRESSO: Three sub-Neptunes, one super-Earth, and a Neptune-mass candidate

We present the characterization of two planetary systems orbiting the M dwarfs TOI-4336 A (M3.5V) and TOI-4342 (M0V), each hosting two transiting planets previously validated with TESS and ground-based observations. We refined the photometry of the TOI-4342 system using TESS and LCOGT data, and characterized the host stars with NIRPS and ESPRESSO spectroscopy. High-precision ESPRESSO radial velocities allowed us to constrain the planetary masses and investigate their potential compositions. The TOI-4336 A system is composed of a sub-Neptune with a period of 16.34 days, a radius of $2.14 \pm 0.08$ Re, and a mass of $3.33 \pm 0.36$ Me, along with an inner super-Earth on a 7.59-day orbit with a radius of $1.25 \pm 0.07$ Re and a mass of $1.55 \pm 0.13$ Me. The TOI-4342 system hosts two sub-Neptunes of similar sizes ($2.33 \pm 0.09$ Re and $2.35 \pm 0.09$ Re), with periods of 5.54 and 10.69 days. Their masses are measured to be $7.3 \pm 1.3$ Me and $4.8 \pm 1.4$ Me, respectively. The RVs also reveal a planet candidate around TOI-4342, likely non-transiting, with a period of 47.5 days and a minimum mass of $17.8 \pm 3.0$ Me. With precise radii and masses, we derived bulk densities and explored possible compositions. The TOI-4336 A sub-Neptune and super-Earth have densities of $1.87 \pm 0.30$ and $4.35 \pm 0.79$ g cm$^{-3}$, while the two similar-sized sub-Neptunes in TOI-4342 show distinct densities of $3.18 \pm 0.67$ and $2.01 \pm 0.63$ g cm$^{-3}$. All four planets are excellent targets for future atmospheric characterization with JWST, and their multi-planet nature makes them especially interesting for comparative planetology. Notably, TOI-4336 A b stands out as one of the best-known targets in its size and temperature regime, with a TSM of 138, comparable to benchmark planets such as K2-18 b and LHS 1140 b.

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arXiv2026

Coupled Thermal-Chemical Evolution Models of Sub-Neptunes Reveal Atmospheric Signatures of Their Formation Location

The observed masses and radii of sub-Neptunes are typically explained by the gas dwarf and the water world scenarios. While their evolutionary history on a population level has been proposed as a method to distinguish between these compositions, previous evolutionary models, neglected the crucial role of atmosphere-interior chemical interaction. We present a novel evolution framework for sub-Neptunes that combines the thermal evolution with the chemical coupling of the atmosphere and interior. Using this model, we examine how planets formed inside and outside the water-ice line can be observationally distinguished, with an emphasis on their atmospheric properties. Young sub-Neptunes store the majority of their volatile budget in the interior, regardless of formation location. Nevertheless, the atmospheric metallicity is a factor 4 higher for the planet formed outside the water-ice line. During cooling, hydrogen and oxygen exsolve from the interior, increasing the atmospheric mass fraction and counteracting the thermal contraction. Consequently, radius evolution alone cannot distinguish between the two formation scenarios. Instead, the primary discriminators are the abundance of carbon-bearing species and the resulting atmospheric C/O ratio. For sub-Neptunes formed beyond the water-ice line, nearly all carbon resides in the gaseous phase. We find that high molar fractions of CH$_4$ ($>10^{-2}$) and H$_2$O ($> 5\times10^{-2}$), and a high C/O ratio $(> 5\times10^{-1})$ are indicative of formation outside the water-ice line. In contrast, sub-Neptunes formed inside the water-ice line exhibit strongly suppressed CH$_4$ abundances, yielding C/O ratios ranging from $10^{-7}$ to $10^{-1}$.

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arXiv2025

Surrogate-Accelerated Bayesian Inversion for Exoplanet Interior Characterization

Characterizing the interior structure of exoplanets is an inverse problem often solved using Bayesian inference, but this approach is hampered by the high computational cost of planetary structure models. To overcome this barrier, we present a robust framework that accelerates inference by replacing the computationally expensive physics-based forward model with a fast polynomial chaos-Kriging (PCK) surrogate directly within a Markov chain Monte Carlo (MCMC) sampling loop. We rigorously validate our approach using a suite of tests, including a direct comparison against a benchmark MCMC inference using the full forward model, and a large-scale coverage study with 1000 synthetic test cases to demonstrate the statistical reliability of our inferred credible intervals. Our surrogate-assisted framework achieves a computational speedup of over 2 orders of magnitude (factor of $\sim$320), reducing single-CPU inference times from days to minutes. This efficiency is achieved with a surrogate that requires only a few hundred forward model evaluations for training \rev{for a single planet}. This data efficiency provides significant flexibility for model developments and a clear advantage over common machine learning approaches, which typically demand vast training sets ($>10^6$ model runs) and intensive pre-computation. The PCK surrogate maintains high fidelity with $R^2 > 0.99$ for most scenarios, and root-mean-square errors typically an order of magnitude smaller than observational uncertainties. This efficiency enables large scale population studies while preserving statistical robustness, which is computationally impractical with traditional methods.

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arXiv2025

Fundamentals of interior modelling and challenges in the interpretation of observed rocky exoplanets

Most our knowledge about rocky exoplanets is based on their measure of mass and radius. These two parameters are routinely measured and are used to categorise different populations of observed exoplanets. They are also tightly linked to the planet's properties, in particular those of the interior. As such they offer the unique opportunity to interpret the observations and potentially infer the planet's chemistry and structure. Required for the interpretation are models of planetary interiors, calculated a priori, constrained using other available data, and based on the physiochemical properties of mineralogical phases. This article offers an overview of the current knowledge about exoplanet interiors, the fundamental aspects and tools for interior modelling and how to improve the contraints on the models, along with a discussion on the sources of uncertainty. The origin and fate of volatiles, and their role in planetary evolution is discussed. The chemistry and structure of planetary interiors have a pivotal role in the thermal evolution of planets and the development of large scale properties that might become observables with future space missions and ground-based surveys. As such, having reliable and well constrained interior models is of the utmost importance for the advancement of the field.

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arXiv2025

Limits on forming coreless terrestrial worlds in the TRAPPIST-1 system

With seven temperate Earth-sized planets revolving around an ultracool red dwarf, the nearby TRAPPIST-1 system offers a unique opportunity to verify models of exoplanet composition, differentiation, and interior structure. In particular, the low bulk densities of the TRAPPIST-1 planets, compared to terrestrial planets in our solar system, require either substantial amount of volatiles to be present or a corefree scenario where the metallic core is fully oxidised. Here, using an updated metal-silicate partitioning model, we show that during core-mantle differentiation oxygen becomes more siderophile (iron-loving) implying larger planet radii. For the seven TRAPPIST-1 planets, however, we find that they are not sufficiently large to oxidise all the iron in the core, if they differentiate from an Earth-like composition. Oxygen partitioning in rocky worlds precludes coreless planets up to about 4 Earth masses. The observed density deficit in the TRAPPIST-1 planets, and more generally in M dwarf systems if confirmed by future observations, may be explained by system-dependent element budgets during planet formation, which are intrinsically linked to their stellar metallicity.

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arXiv2025

The cosmochemistry of planetary systems

Planets form and obtain their compositions from the leftover material present in protoplanetary disks of dust and gas surrounding young stars. The chemical make-up of a disk influences every aspect of planetary composition including their overall chemical properties, volatile content, atmospheric composition, and potential for habitability. This Review discusses our knowledge of the chemical and isotopic composition of Solar System materials and how this information can be used to place constraints on the formation pathways of terrestrial planets. We conclude that planetesimal formation by the streaming instability followed by rapid accretion of drifting pebbles within the protoplanetary disk lifetime reproduces most of the chemical and isotopic observables in Solar System. This finding has important implications for planetary habitability beyond the Solar System because in pebble accretion, volatiles important for life are accreted during the main growth phase of rocky planets as opposed to the late-stage. Finally, we explore how bulk chemical inventories and masses of planetary bodies control the composition of their primordial atmospheres and their potential to develop habitable conditions.

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arXiv2025

Mineral cloud formation above magma oceans in sub-Neptune atmospheres

The potential presence of a magma surface below a thick atmosphere primarily composed of hydrogen in some sub-Neptune exoplanets suggests a strong link between the interior composition and atmosphere through chemical coupling of volatile and refractory species. In this study, we aim to model the possibility for mineral cloud formation in the atmosphere of sub-Neptunes from outgassing of refractory species at the magma surface. In our specific cases, we find that mineral clouds easily form near the magma-atmosphere boundary, but also higher in the atmosphere once vapour is mixed to the cooler atmospheric regions. We find that the vertical cloud structure depends on the mixing profile of the atmosphere, with stronger mixing allowing particles to remain lofted in the atmosphere, while weak to moderate mixing produces larger, more sedimented cloud particle profiles. We suggest that due to the strong thermal feedback from cloud opacity, clouds may play an important role in the overall structure of the interior-surface-atmosphere coupled system in sub-Neptunes, as well as affect their observed spectral properties, especially at near-infrared wavelengths.

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arXiv2025

Sub-Neptunes Are Drier Than They Seem: Rethinking the Origins of Water-Rich Worlds

Recent claims of biosignature gases in sub-Neptune atmospheres have renewed interest in water-rich sub-Neptunes with surface oceans, often referred to as Hycean planets. These planets are hypothesized to form beyond the snow line, accreting large amounts of H$_2$O (>10 wt%) before migrating inward. However, current interior models often neglect chemical equilibration between primordial atmospheres and molten interiors. Here, we compute global chemical equilibrium states for a synthetic population of sub-Neptunes with magma oceans. Although many initially accrete 5-30 wt% water, interior-atmosphere interactions destroy most of it, reducing final H$_2$O mass fractions to below 1.5 wt%. As a result, none meet the threshold for Hycean planets. Despite that, we find H$_2$O-dominated atmospheres exclusively on planets that accreted the least ice. These planets form inside the snow line, are depleted in carbon and hydrogen, and develop small envelopes with envelope mass fractions below 1%, dominated by endogenic water. In contrast, planets formed beyond the snow line accrete more volatiles, but their water is largely converted to H$_2$ gas or sequestered into the interior, resulting in low atmospheric H$_2$O mass fractions. Most H$_2$O-rich envelopes are also fully miscible with H$_2$, making a separate water layer unlikely. Our results topple the conventional link between ice accretion and water-rich atmospheres, showing instead that H$_2$O-dominated envelopes emerge through chemical equilibration in hydrogen-poor planets formed inside the snow line.

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arXiv2025

Atmospheric C/O Ratios of Sub-Neptunes with Magma Oceans: Homemade rather than Inherited

Recently, the James Webb Space Telescope has enabled detailed spectroscopic characterization of sub-Neptune atmospheres. With detections of carbon- and oxygen-bearing species such as CO, CO$_2$, CH$_4$, and H$_2$O, a central question is whether the atmospheric C/O ratio, commonly used to trace formation location in giant planets, can serve a similar diagnostic role for sub-Neptunes. We use the global chemical equilibrium framework of Schlichting & Young (2022) to quantify how magma ocean-atmosphere interactions affect the atmospheric C/O ratio. We find that the resulting C/O ratios range from several orders of magnitude below solar to a few times solar. The atmospheric C/O ratio in sub-Neptunes is therefore not inherited from the protoplanetary disk, but instead emerges from chemical equilibrium between the atmosphere and the underlying magma ocean. Planetary mass, atmospheric mass fraction, and thermal state all strongly influence the atmospheric C/O ratio. In addition, carbon partitioning into the metal phase typically reduces the atmospheric C/O ratio substantially, particularly for atmospheric mass fractions less than a few percent. Finally, we couple the deep equilibrium compositions to 1D atmospheric models that self-consistently solve for the pressure-temperature structure and chemical composition, including photochemistry. We find that the C/O ratio varies with altitude under low vertical mixing conditions (K$_\text{zz}=10^4$ cm$^2$s$^{-1}$), but remains constant under strong mixing (K$_\text{zz}=10^7$ cm$^2$s$^{-1}$). Our results imply that observed C/O ratios of sub-Neptunes can be used to probe their interiors. Specifically, C/O ratios much lower than host star values would imply an underlying magma ocean with iron metal having sequestered significant amounts of carbon.

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