arxiv: 2601.21377 · v2 · submitted 2026-01-29 · 🌌 astro-ph.EP

Recognition: no theorem link

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

Marie-Luise Steinmeyer , Caroline Dorn , Aaron Werlen , Simon L. Grimm

Authors on Pith no claims yet

Pith reviewed 2026-05-16 10:02 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords sub-Neptunesformation locationwater-ice lineatmospheric compositionC/O ratiochemical evolutionthermal evolutionvolatile exsolution

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The pith

Sub-Neptunes formed outside the water-ice line develop high atmospheric methane and water fractions with C/O ratios above 0.5, while those formed inside show suppressed methane and C/O ratios from 10^{-7} to 0.1.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a model that couples a sub-Neptune's thermal cooling history to the chemical exchange of volatiles between its atmosphere and interior. This coupling shows that formation location imprints on the final atmospheric composition even though both inside- and outside-formed planets initially hold most volatiles in the interior. A reader cares because mass and radius data alone cannot separate the two formation scenarios, but the new model identifies specific atmospheric tracers that future observations could measure. During cooling, hydrogen and oxygen exsolve from the interior, raising atmospheric mass and slowing radius contraction in both cases. The clearest distinctions appear in carbon-bearing species, with nearly all carbon staying in the gas phase for outer-formed planets.

Core claim

Young sub-Neptunes store the majority of their volatile budget in the interior regardless of formation location, yet the atmospheric metallicity is a factor of four higher for planets formed outside the water-ice line. During cooling, hydrogen and oxygen exsolve from the interior, increasing the atmospheric mass fraction and counteracting thermal contraction. Radius evolution therefore cannot distinguish the scenarios. The primary discriminators are instead the abundance of carbon-bearing species and the resulting atmospheric C/O ratio, with high molar fractions of CH4 above 10^{-2} and H2O above 5 times 10^{-2} plus C/O above 0.5 indicating formation outside the ice line.

What carries the argument

The coupled thermal-chemical evolution framework that tracks volatile exsolution from the interior into the atmosphere as the planet cools and reaches chemical equilibrium.

If this is right

Radius contraction is slowed equally in both formation scenarios by exsolved gases, so size alone cannot reveal birth location.
Atmospheric C/O ratio becomes a direct observable tracer of whether the planet formed inside or outside the water-ice line.
Nearly all carbon remains in the gas phase for planets born beyond the ice line, producing elevated CH4 and H2O abundances.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Atmospheric spectra from future telescopes could map the fraction of sub-Neptunes born inside versus outside the water-ice line across a population.
Models that omit chemical coupling between interior and atmosphere will systematically underestimate final atmospheric masses for outer-formed planets.
Population-level trends in measured C/O ratios could test whether migration or in-situ formation dominates for the sub-Neptune class.

Load-bearing premise

The model assumes initial volatile budgets are stored mostly in the interior and that chemical equilibrium plus exsolution rates during cooling are captured accurately by the framework.

What would settle it

A spectroscopic measurement of a sub-Neptune showing CH4 molar fraction below 10^{-3} together with C/O ratio above 0.5 would contradict the predicted separation between inside- and outside-formation signatures.

Figures

Figures reproduced from arXiv: 2601.21377 by Aaron Werlen, Caroline Dorn, Marie-Luise Steinmeyer, Simon L. Grimm.

**Figure 1.** Figure 1: Comparison of the evolution of a 4 M⊕ planet with atmosphere–interior coupling (solid lines) and in the uncoupled case (dashed lines). The orange lines represent a sub-Neptune formed inside the water-ice line, while the blue lines correspond to a planet formed outside the water-ice line. Both planets have a total mass of 4 M⊕ and an equilibrium temperature of Teq = 800 K. The top row shows the evolution of… view at source ↗

**Figure 2.** Figure 2: Partitioning of H (left), C (middle), and O (right) into metallic (dotted lines), silicate (dashed lines), and gaseous phases (solid lines) over time. The gas phase refers to the atmosphere of the planet, while the metallic and silicate phases refer to the deep planet interior. It is important to note that the fractions are normalized to the total abundance of each element and that only oxygen in non-silic… view at source ↗

**Figure 3.** Figure 3: Evolution of the atmospheric C/O ratio for the planet formed dry (orange line) and the planet formed outside the water-ice line (blue line). The atmospheric C/O ratio differs by almost 4 orders of magnitude between the two formation locations at the end of the evolution. sphere of the planet formed outside the water-ice line is dominated by mass in H2O both in the chemically coupled and uncoupled case. Co… view at source ↗

**Figure 4.** Figure 4: Evolution of the molar fractions of major atmospheric species over time. The left plot shows the atmosphere composition for a planet formed inside the water-ice line, and the right plot is for a planet formed outside the water-ice line. The planet mass is 4 M⊕ in both cases. For both planets, H2 and H2O are the major atmospheric species. However, the mole fractions of CH4, CO2, and CO2 in the atmosphere of… view at source ↗

**Figure 5.** Figure 5: Molar gas fraction of H2O versus CH4 (left plot) and molar gas fraction of CH4 versus atmospheric C/O ratio (right plot) for a synthetic population of planets (see [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

**Figure 6.** Figure 6: Structure of the upper atmosphere at 5 Gyr. Top: pressure–temperature profiles (blue: formed outside the water-ice line; orange: formed inside). Bottom: vertical mixing ratios of dominant C- and O-bearing species, assuming Kzz = 108 , cm2 s −1 . Solid lines show the planet formed dry; dotted lines show the planet formed water-rich. The C/O ratio remains constant in the upper atmosphere. chemical equilibr… view at source ↗

read the original abstract

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 $10^{-1}$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Coupled thermal-chemical models give CH4/H2O/C/O thresholds to distinguish sub-Neptune formation inside versus outside the ice line, but the results need sensitivity tests on initial conditions.

read the letter

The paper's key takeaway is that a new coupled thermal-chemical model for sub-Neptunes produces distinct atmospheric CH4, H2O, and C/O values depending on whether the planet formed inside or outside the water ice line. High CH4 (>10^{-2}), H2O (>5x10^{-2}), and C/O (>0.5) point to outside formation, while inside formation suppresses CH4 and drops C/O to 10^{-7}-0.1. What is new here is the explicit coupling of the planet's cooling history with atmosphere-interior chemistry. Earlier work treated thermal evolution and chemistry separately, so this integrated framework tracks how hydrogen and oxygen exsolve from the interior as the planet cools, boosting the atmospheric mass fraction and slowing contraction. The result is that radius evolution looks similar in both cases, but the gas-phase abundances differ because carbon stays mostly in the atmosphere for outside-ice-line planets. The model does well at explaining why population-level radius trends alone won't separate the gas-dwarf and water-world scenarios. It gives concrete numerical thresholds that observers could check with transmission spectroscopy. The main soft spot is the lack of robustness checks. The thresholds depend on the initial volatile budgets being mostly locked in the interior and on the specific partition coefficients and equilibrium constants used. If those starting conditions or reaction rates are off by even a modest factor, the CH4 and C/O ranges could overlap between the two formation locations. The paper does not appear to include sensitivity tests or alternative chemical networks to show how stable the discriminator remains. This work is aimed at researchers modeling sub-Neptune interiors and atmospheres, especially those trying to connect formation location to current observables. A reader focused on JWST data interpretation or disk chemistry would find the framework useful for generating testable predictions. It deserves a serious referee because the coupling is a genuine step forward and the claims are specific enough to be checked against data, even though the parameter space needs more exploration. I would recommend sending it to peer review.

Referee Report

2 major / 1 minor

Summary. The paper presents a novel coupled thermal-chemical evolution framework for sub-Neptunes that incorporates atmosphere-interior chemical interactions. It claims that young sub-Neptunes store most volatiles in the interior regardless of formation location, that radius evolution cannot distinguish inside versus outside the water-ice line due to exsolution counteracting contraction, and that atmospheric chemistry provides the key discriminator: high CH4 (>10^{-2}), H2O (>5×10^{-2}), and C/O (>0.5) indicate formation outside the ice line, while inside-ice-line planets show suppressed CH4 and C/O ratios between 10^{-7} and 0.1.

Significance. If the central thresholds prove robust, the work offers a concrete observational pathway to link sub-Neptune atmospheric spectra to formation location, addressing a gap left by prior models that omitted chemical coupling. The demonstration that radius evolution alone is degenerate while C/O and molecular abundances are not is a useful advance for the field.

major comments (2)

[Abstract] Abstract: the reported thresholds (CH4 >10^{-2}, H2O >5×10^{-2}, C/O >0.5 outside; C/O 10^{-7}–0.1 inside) are stated without derivation, error propagation, or sensitivity tests to the free parameters (initial interior volatile budget and chemical partition coefficients). If these parameters vary by even a factor of ~2, the claimed separation can overlap, undermining the discriminator.
[Model Description] Model framework: the assumption that chemical equilibrium and exsolution rates during cooling are accurately captured lacks any cross-validation against independent chemical networks or tests showing that the C/O cutoffs survive reasonable variations in equilibrium constants or timescales.

minor comments (1)

[Abstract] Abstract: the statement that atmospheric metallicity is 'a factor 4 higher' for outside-ice-line planets is given without the reference value or the exact epoch at which it is measured.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. We have carefully considered each point and provide detailed responses below, including revisions to address the concerns raised.

read point-by-point responses

Referee: [Abstract] Abstract: the reported thresholds (CH4 >10^{-2}, H2O >5×10^{-2}, C/O >0.5 outside; C/O 10^{-7}–0.1 inside) are stated without derivation, error propagation, or sensitivity tests to the free parameters (initial interior volatile budget and chemical partition coefficients). If these parameters vary by even a factor of ~2, the claimed separation can overlap, undermining the discriminator.

Authors: The thresholds presented in the abstract are based on the results of our coupled thermal-chemical evolution simulations for planets formed inside and outside the water-ice line. In the revised manuscript, we have expanded the abstract to briefly note the model basis and added a dedicated subsection in the methods and results sections explaining the derivation of these specific values, including how they arise from the chemical partitioning and exsolution processes. We have also conducted additional sensitivity tests by varying the initial interior volatile budget and chemical partition coefficients by factors of up to 2. These tests show that while the exact numerical thresholds shift slightly, the qualitative separation (high CH4, H2O, C/O outside vs. suppressed inside) remains robust without overlap in the key regimes. Error propagation is now included based on the parameter ranges. A new figure illustrates these sensitivity results. revision: yes
Referee: [Model Description] Model framework: the assumption that chemical equilibrium and exsolution rates during cooling are accurately captured lacks any cross-validation against independent chemical networks or tests showing that the C/O cutoffs survive reasonable variations in equilibrium constants or timescales.

Authors: We acknowledge that our model relies on standard chemical equilibrium assumptions for the H-C-O system during cooling and exsolution. To address this, we have added in the revised version a comparison of our equilibrium constants with those from independent sources in the literature, and performed tests varying the constants within 20% and exsolution timescales by factors of 10. The C/O cutoffs and abundance thresholds are shown to be insensitive to these variations, supporting the robustness of our conclusions. Full cross-validation with comprehensive atmospheric chemistry codes is planned for future work but is outside the current scope. revision: partial

Circularity Check

0 steps flagged

Atmospheric CH4/H2O/C/O signatures emerge from distinct initial volatile budgets and coupled evolution without reduction to inputs by construction

full rationale

The paper's central claim rests on running a coupled thermal-chemical evolution model with different initial volatile budgets (majority sequestered in interior) for planets formed inside versus outside the water-ice line. The reported thresholds (CH4 >10^{-2}, H2O >5e-2, C/O >0.5 outside; suppressed CH4 and C/O 10^{-7} to 0.1 inside) are computed outputs of the exsolution and equilibrium chemistry during cooling, not inputs or self-definitions. No equations or steps in the abstract reduce the discriminators to fitted parameters renamed as predictions, nor do they rely on self-citations for uniqueness or ansatzes. The framework is self-contained against the stated assumptions about initial budgets and equilibrium rates; the differences arise from the model's propagation of formation-location-dependent starting conditions rather than circular re-labeling of those conditions.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on an assumed initial partitioning of volatiles between interior and atmosphere plus a specific chemical network for H, O, and C species; these are not derived from first principles within the paper.

free parameters (2)

initial interior volatile budget
The fraction of total H, O, C stored in the interior at formation is set by hand for each formation-location scenario.
chemical partition coefficients
Rates at which H and O exsolve during cooling are governed by parameters that are not shown to be independently measured.

axioms (1)

domain assumption chemical equilibrium holds between atmosphere and interior at each time step
Invoked to compute exsolution and atmospheric enrichment during cooling.

pith-pipeline@v0.9.0 · 5619 in / 1382 out tokens · 47740 ms · 2026-05-16T10:02:40.471706+00:00 · methodology

discussion (0)

Reference graph

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