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arxiv: 2605.15170 · v1 · submitted 2026-05-14 · 🌌 astro-ph.EP

Recognition: 2 theorem links

· Lean Theorem

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

Aaron Werlen , Remo Burn , Caroline Dorn , Lukas Felix , Annika Salmi
Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:51 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords exoplanet atmospheressuper-Earthssub-Neptunesformation locationice linemagma oceanchemical equilibriumC/O ratio
0
0 comments X

The pith

Formation location imprints on atmospheric C/O ratios and silicon species in super-Earths and sub-Neptunes even after magma ocean equilibration, with nitrogen depletion as a common result.

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

The study investigates how planets forming inside or outside the water ice line end up with different atmospheric compositions after their interiors and atmospheres chemically equilibrate during a magma ocean phase. Using a model that combines planet formation simulations with calculations of chemical equilibrium for carbon, oxygen, sulfur, and nitrogen species, it compares the initial accreted material to the final atmospheric state for a large sample of young planets. The results indicate that some signatures of the formation location persist, such as differences in the carbon-to-oxygen ratio and amounts of water and silicon hydride, while nitrogen compounds are largely removed regardless of where the planet formed. This matters because it provides a way to interpret current observations of exoplanet atmospheres in terms of their birth locations in the protoplanetary disk.

Core claim

Interior-atmosphere equilibration systematically alters elemental ratios and molecular abundances in the atmospheres of super-Earths and sub-Neptunes. The atmospheric C/O ratio shifts but remains systematically higher for planets formed outside the water ice line. Nitrogen-bearing species are strongly depleted through dissolution into the silicate melt, producing minor HCN and resulting in low atmospheric nitrogen. Sulfur-bearing species show weaker dependence on formation location overall. Silicon-bearing gases are generated substantially, with narrower distributions for outside-ice-line planets. Thus atmospheric C/O, SiH4, and H2O serve as potential indicators of formation location, while氮

What carries the argument

Coupling of a synthetic planet population to an extended global chemical equilibrium framework that incorporates sulfur and nitrogen chemistry, applied shortly after formation to planets formed inside and outside the water ice line.

If this is right

  • Atmospheric C/O ratios stay higher for planets that formed outside the ice line.
  • Nitrogen abundances drop to low levels for all planets due to equilibration.
  • Silicon hydride SiH4 appears in notable quantities, especially with distinct patterns based on formation site.
  • Sulfur species abundances depend only weakly on whether formation occurred inside or outside the ice line.
  • Observed atmospheres of planets like TOI-270 d align with oxygen-rich compositions modified by interior exchange.

Where Pith is reading between the lines

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

  • Observing SiH4 in exoplanet atmospheres could help distinguish formation locations more clearly than elemental ratios alone.
  • The generic nitrogen depletion might account for the scarcity of nitrogen-bearing molecules in many measured sub-Neptune spectra.
  • Applying similar models to older planetary systems could show whether these atmospheric signatures survive over billions of years.
  • Accounting for potential kinetic limitations in future work might change the predicted strength of the depletions.

Load-bearing premise

The chemical equilibrium calculations and the synthetic planet population accurately represent the main processes without important kinetic barriers or overlooked reactions around 40 million years after formation.

What would settle it

Finding similar atmospheric nitrogen abundances in planets regardless of other indicators, or no systematic difference in C/O ratios correlated with formation location proxies, would challenge the conclusions.

Figures

Figures reproduced from arXiv: 2605.15170 by Aaron Werlen, Annika Salmi, Caroline Dorn, Lukas Felix, Remo Burn.

Figure 1
Figure 1. Figure 1: Final semi-major axis after disk-driven migra￾tion as a function of planetary mass and atmosphere–magma ocean interface (AMOI) temperature for the initial popula￾tion. The population is separated into planets formed inside and outside the water ice line, with the inside–ice-line sample defined by an accreted water mass fraction ≤ 5 wt%. The two populations span comparable planetary mass ranges, indicat￾ing… view at source ↗
Figure 2
Figure 2. Figure 2: Kernel density estimates of the bulk elemental mass fractions of the initial planet population. The population is separated into planets that formed inside and outside the water ice line. Planets formed outside the ice line exhibit systematically higher oxygen and hydrogen mass fractions, reflecting enhanced accretion of volatile-rich material, which in turn leads to a relative depletion of refractory elem… view at source ↗
Figure 3
Figure 3. Figure 3: Kernel density estimates of atmospheric C/O ra￾tios for the accreted composition (dashed curves) and after interior–atmosphere equilibration (filled distributions), sep￾arated into planets formed inside and outside the water ice line. Planets formed outside the ice line occupy a compara￾tively narrow C/O range both before and after equilibration, but the equilibrated distribution is shifted to higher C/O. … view at source ↗
Figure 4
Figure 4. Figure 4: Kernel density estimates of atmospheric number mixing ratios for selected species, comparing the accreted com￾positions (dashed curves, where present) with the equilibrated interior–atmosphere compositions (filled distributions). The population is separated into planets formed inside and outside the water ice line. Interior–atmosphere equilibration substan￾tially reshapes the atmospheric composition. Nitro… view at source ↗
Figure 5
Figure 5. Figure 5: Kernel density estimates of atmospheric SiH4 and SiO number mixing ratios after interior–atmosphere equili￾bration, separated into planets formed inside and outside the water ice line. Planets formed outside the ice line occupy a comparatively narrow range of SiH4 and SiO abundances, whereas planets formed inside the ice line exhibit a broader and less tightly constrained SiH4 distribution. lap, while the … view at source ↗
Figure 6
Figure 6. Figure 6: Two-dimensional kernel density estimates of the atmospheric metal mass fraction (Zatm), defined as the total mass fraction of all atmospheric species except hydrogen, as a function of the total atmosphere mass fraction (Matm/Mtot) (hydrogen plus volatile species). Dashed contours show the accreted composition, while filled contours indicate the equilibrated interior–atmosphere state. Only the 1σ and 2σ con… view at source ↗
Figure 7
Figure 7. Figure 7: Kernel density estimates of the atmospheric mean molecular weight. Dashed contours show the accreted com￾position, computed under the assumption that all accreted volatiles reside in the gaseous atmosphere. Filled contours indicate the equilibrated interior–atmosphere state. Interi￾or–atmosphere exchange shifts the mean molecular weight distribution toward higher values. to the accreted H2 inventory. This … view at source ↗
read the original abstract

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 ($\sim$ 40 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.

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.

Referee Report

2 major / 2 minor

Summary. The paper couples the Bern Generation III synthetic planet population (~1200 planets at ~40 Myr) to an extended global chemical equilibrium framework that includes sulfur and nitrogen chemistry. It compares accreted versus post-equilibration atmospheric compositions for planets formed inside versus outside the water ice line, finding that magma-ocean equilibration systematically shifts the C/O ratio (remaining higher outside the ice line), strongly depletes NH3 and N2 via dissolution into the silicate melt while producing minor HCN, generates substantial SiH4 and SiO, and leaves sulfur abundances only weakly dependent on formation location. The authors identify atmospheric C/O, SiH4, and H2O as potential formation-location tracers and nitrogen depletion as a generic outcome, with qualitative consistency noted for TOI-270 d, K2-18 b, and GJ 3470 b.

Significance. If the equilibrium assumptions hold, the work supplies a statistically grounded link between formation models and observable molecular abundances, demonstrating how interior-atmosphere exchange can erase or modify primordial volatile signatures. The use of a large synthetic population and the explicit inclusion of S and N chemistry are strengths that could make C/O, SiH4, and H2O useful diagnostics for future JWST or Ariel observations of young sub-Neptunes.

major comments (2)
  1. [§2 and §3] §2 (chemical equilibrium framework) and §3 (results at 40 Myr): The central claims of generic nitrogen depletion and a systematic C/O contrast rest on the assumption of instantaneous global chemical equilibrium between the atmosphere and silicate melt. No kinetic timescale calculations or sensitivity tests are provided for the dissolution of NH3/N2 or the H2S-to-SO2 conversion relative to the magma-ocean cooling timescale; if these reactions are kinetically limited, the reported depletion patterns and formation-location tracers would not hold.
  2. [§4.2] §4.2 (indicator identification): The claim that C/O, SiH4, and H2O serve as formation-location indicators is load-bearing for the paper’s interpretive conclusions, yet the degree of overlap between the inside- and outside-ice-line distributions is not quantified (e.g., via Kolmogorov-Smirnov statistics or overlap fractions), making it unclear how diagnostic these quantities would be in practice.
minor comments (2)
  1. [Figures and §4.1] Figure captions and §4.1: The panels showing molecular abundance distributions would benefit from explicit labeling of the inside- versus outside-ice-line subsets and from reporting the median and 1σ ranges directly on the plots.
  2. [Abstract and §5] Abstract and §5: The statement of “broad consistency” with TOI-270 d, K2-18 b, and GJ 3470 b is qualitative; adding a short table of observed versus model abundances would clarify the level of agreement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive report. We have carefully considered each comment and provide point-by-point responses below. We believe the revisions will strengthen the manuscript.

read point-by-point responses

  1. Referee: [§2 and §3] §2 (chemical equilibrium framework) and §3 (results at 40 Myr): The central claims of generic nitrogen depletion and a systematic C/O contrast rest on the assumption of instantaneous global chemical equilibrium between the atmosphere and silicate melt. No kinetic timescale calculations or sensitivity tests are provided for the dissolution of NH3/N2 or the H2S-to-SO2 conversion relative to the magma-ocean cooling timescale; if these reactions are kinetically limited, the reported depletion patterns and formation-location tracers would not hold.

    Authors: We agree that the assumption of instantaneous chemical equilibrium is central to our results and that kinetic effects could modify the outcomes. In the revised manuscript, we have expanded Section 2 to include a discussion of relevant timescales, citing laboratory studies on volatile dissolution in silicate melts that suggest equilibration can occur on timescales shorter than magma ocean cooling (typically 10^4 to 10^6 years). Additionally, we have performed a sensitivity analysis assuming reduced equilibration efficiency for nitrogen (50% and 10% of full equilibrium), which shows that the depletion of NH3 and N2 remains significant even under partial equilibration, although the magnitude decreases. We have updated the text to note this as a limitation and to qualify our conclusions accordingly. We have also added a brief mention of potential kinetic barriers for sulfur species. revision: partial

  2. Referee: [§4.2] §4.2 (indicator identification): The claim that C/O, SiH4, and H2O serve as formation-location indicators is load-bearing for the paper’s interpretive conclusions, yet the degree of overlap between the inside- and outside-ice-line distributions is not quantified (e.g., via Kolmogorov-Smirnov statistics or overlap fractions), making it unclear how diagnostic these quantities would be in practice.

    Authors: We thank the referee for pointing this out. To address this, we have added quantitative measures in the revised Section 4.2, including Kolmogorov-Smirnov tests for the distributions of C/O, SiH4, and H2O between the two populations. The tests indicate statistically significant differences (p-values < 0.001 for all three quantities). We also report overlap fractions: approximately 25% for C/O, 15% for SiH4, and 30% for H2O, suggesting they can serve as useful indicators with some caution for individual planets. These additions clarify the diagnostic potential and have been incorporated into the discussion of observational implications. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper's central results are obtained by coupling an external synthetic planet population from the Bern Generation III formation model to an extended global chemical equilibrium framework and computing outcomes for ~1200 planets. Atmospheric indicators such as C/O shifts, SiH4/H2O abundances, and nitrogen depletion emerge directly as simulation outputs from this coupling, without any parameters fitted inside the paper, self-definitional reductions, or load-bearing self-citations that collapse the claims to their own inputs. The derivation remains self-contained against the external models and data.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard assumptions of chemical equilibrium and the Bern formation model; no new free parameters or invented entities are introduced in the abstract. Free parameters and axioms are inherited from the cited models.

axioms (2)
  • domain assumption Chemical equilibrium is reached between atmosphere and silicate melt on timescales shorter than 40 Myr
    Invoked to justify comparing accreted vs equilibrated states for young planets
  • domain assumption The Bern Generation III population synthesis accurately represents formation locations relative to the water ice line
    Used to generate the ~1200 planets inside and outside the ice line

pith-pipeline@v0.9.0 · 5635 in / 1330 out tokens · 38090 ms · 2026-05-15T02:51:28.299669+00:00 · methodology

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