A chemical perspective on planet formation in reduced systems

Haiyang S. Wang; Paolo A. Sossi; Urja Zaveri

arxiv: 2603.15955 · v1 · pith:LMZL7FEXnew · submitted 2026-03-16 · 🌌 astro-ph.EP

A chemical perspective on planet formation in reduced systems

Urja Zaveri , Haiyang S. Wang , Paolo A. Sossi This is my paper

Pith reviewed 2026-05-21 10:44 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords planet formationcondensation chemistryC/O ratioprotoplanetary disksrocky planetsrefractory elementsreduced nebular chemistry

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The pith

In disks with C/O above 0.92, refractory elemental ratios stop tracing planetary bulk composition.

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

The paper tests whether the relative abundances of refractory elements in planets can be read directly from the host star's composition. It shows that this mapping holds only in solar-like conditions and breaks down once the disk's carbon-to-oxygen ratio exceeds roughly 0.92. At those values, oxygen-bearing silicates appear at lower temperatures while carbides, silicides, and sulfides become stable, so that the iron, magnesium, silicon, and oxygen ratios locked into planetesimals diverge from the star's overall inventory. The result is a wider spread of rocky building-block compositions inside one disk than stellar abundances alone would predict. This matters for interpreting the interiors and surfaces of the growing population of observed rocky exoplanets.

Core claim

Condensation sequences are not universal across stellar compositions. For FGK stars with C/O ratios from 0.65 to 0.95, equilibrium phase stability calculations at pressures of 10^{-2} to 10^{-6} bar identify three regimes: solar-like (C/O < 0.7), transitional (C/O ~0.7-0.91), and reduced (C/O > 0.92). In the reduced regime, oxygen-bearing silicates condense at lower temperatures while carbides, silicides, and sulfides appear. Bulk planetesimal Fe/Mg, Fe/Si, and Fe/O ratios therefore deviate substantially from host stellar values, producing more diverse rocky building blocks within a single disk and opening formation pathways for metal-enriched super-Mercury analogues and C- and S-rich rocky

What carries the argument

Three distinct condensation regimes (solar-like, transitional, reduced) computed from equilibrium phase stability across temperature and pressure; these regimes set the temperature-dependent feeding zones that a stochastic accretion model aggregates into planetesimal bulk compositions.

If this is right

Bulk planetesimal Fe/Mg, Fe/Si, and Fe/O ratios deviate from stellar values in reduced disks.
A single disk can produce more varied rocky compositions than expected from stellar abundances.
Metal-enriched super-Mercury analogues and C- and S-rich rocky planets become possible outcomes.
Elemental ratios long treated as refractory tracers lose reliability in high-C/O environments.

Where Pith is reading between the lines

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

Atmospheric or surface observations of rocky exoplanets in carbon-rich systems could show elevated carbon or sulfur signatures consistent with carbide or sulfide building blocks.
Population-level statistics of super-Earth densities might reveal a broader spread in iron content for stars above the reduced C/O threshold.
Incorporating radial drift or non-equilibrium kinetics into the same condensation framework would test how much the present equilibrium results shift.

Load-bearing premise

Equilibrium phase stability at fixed total pressures computed with FactSage accurately represents condensation in real protoplanetary disks that experience time-dependent chemistry and radial mixing.

What would settle it

A direct measurement of the bulk Fe/Si ratio in a rocky planet orbiting a star with C/O > 0.92 that matches the stellar ratio rather than the offset predicted by the reduced-regime condensation sequence.

read the original abstract

Relative abundances of refractory elements in planets are commonly assumed to reflect those of their host stars. However, because elements are classified according to their behaviour in the solar nebula, this implicitly assumes condensation is independent of nebular chemistry, despite evidence to the contrary in chemically reduced systems with high molar carbon-to-oxygen (C/O) ratios. We investigate how variations in stellar C/O ratio and disk pressure modify condensation chemistry and assess the reliability of mapping stellar compositions to planetary building blocks in reduced environments. For a sample of FGK stars with C/O ratios spanning 0.65-0.95 (solar = 0.50), we compute equilibrium phase stability using FactSage over 1900-400 K at total pressures of 1e-2, 1e-4, and 1e-6 bar. Bulk planetesimal compositions are derived using a stochastic accretion framework aggregating condensates from temperature-dependent feeding zones. We identify three distinct condensation regimes: (i) solar-like (C/O < 0.7), (ii) transitional (C/O ~0.7-0.91), and (iii) reduced (C/O > 0.92). Relative to solar sequences, oxygen-bearing silicates condense at lower temperatures in transitional and reduced regimes, while carbides, silicides, and sulfides appear. Bulk planetesimal Fe/Mg, Fe/Si, and Fe/O ratios deviate substantially from host stellar values, producing more diverse rocky building blocks within a single disk. Condensation sequences are not universal across stellar compositions. In reduced disks, elemental ratios commonly treated as refractory may not reliably trace planetary bulk composition, providing potential formation pathways for metal-enriched super-Mercury analogues and C- and S-rich rocky planets.

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

High C/O ratios shift condensation to carbides and silicides, breaking the usual stellar-to-planetary refractory mapping in a subset of disks.

read the letter

The central result is that disks with C/O above roughly 0.92 produce planetesimals whose Fe/Mg, Fe/Si, and Fe/O ratios depart from the host star, unlike the solar-like case. They ran FactSage equilibrium calculations from 1900 K down to 400 K at three fixed pressures, then aggregated condensates stochastically across temperature-dependent feeding zones for a sample of FGK stars spanning C/O 0.65–0.95. This yields three regimes: solar-like below 0.7, transitional between 0.7 and 0.91, and reduced above 0.92, with carbides, silicides, and sulfides appearing in the last one while oxygen silicates drop to lower temperatures. The quantitative deviations in bulk ratios are the clearest new output and directly challenge the assumption that refractory ratios are universal tracers. The stochastic accretion step is a practical way to turn the sequences into planetesimal compositions, and tying the runs to observed stellar C/O values keeps the exercise grounded. The modeling is reproducible with the stated software and pressure grid, so the sequences themselves are solid for the assumptions used. The main limitation is the equilibrium treatment at discrete total pressures. Real disks have radial drift, turbulence, and finite cooling times that can push carbon-bearing phases away from local equilibrium, and the paper does not explore how much a few hundred kelvin shift in condensation temperature would shrink the reported deviations. That is a standard modeling caveat rather than a fatal flaw, but it means the diversity claim is best read as a possible outcome under equilibrium conditions. This work is aimed at people who model rocky-planet bulk compositions or interpret super-Earth and super-Mercury data. Anyone running formation simulations that start from stellar abundances will find the regime map useful for deciding when the simple mapping breaks. It is worth sending to peer review; the calculations are transparent and the claim is falsifiable with better disk-chemistry models.

Referee Report

1 major / 2 minor

Summary. The manuscript investigates condensation chemistry in protoplanetary disks across a range of stellar C/O ratios (0.65-0.95) using FactSage equilibrium phase stability calculations at fixed total pressures (1e-2, 1e-4, 1e-6 bar) over 1900-400 K. It identifies solar-like (C/O < 0.7), transitional (~0.7-0.91), and reduced (C/O > 0.92) regimes, employs a stochastic accretion framework to derive bulk planetesimal compositions from temperature-dependent feeding zones, and concludes that in reduced systems oxygen-bearing silicates condense at lower temperatures while carbides, silicides, and sulfides appear, causing substantial deviations in Fe/Mg, Fe/Si, and Fe/O ratios from host stellar values and producing more diverse rocky building blocks.

Significance. If the modeled deviations hold, the work demonstrates that nebular chemistry in reduced disks can decouple planetary refractory compositions from stellar abundances, offering formation pathways for metal-enriched super-Mercury analogues and C- and S-rich rocky planets. A clear strength is the systematic, reproducible workflow combining established thermodynamic software (FactSage) with a stochastic aggregation model across multiple pressures and C/O thresholds, enabling quantitative assessment of intra-disk diversity without ad-hoc parameter fitting beyond the specified pressures and thresholds.

major comments (1)

[Computation method / abstract] Computation method (as described in the abstract and methods paragraph): the central claim of substantial deviations in Fe/Mg, Fe/Si, and Fe/O for C/O > 0.92 rests on equilibrium phase stability at three discrete fixed total pressures. Real disks involve radial drift, turbulent mixing, and finite cooling timescales that can drive departures from local thermodynamic equilibrium, particularly for carbon-bearing phases with poorly constrained nucleation kinetics. If these effects shift condensation temperatures by even a few hundred K, the reported breakdown of the stellar-to-planetary mapping would not necessarily follow; a sensitivity test or explicit discussion of this limitation is needed to support the claim.

minor comments (2)

[Abstract] The abstract mentions a sample of FGK stars but does not specify the exact number or selection criteria; adding this detail would improve clarity on the generality of the reported regimes.
Notation for the three regimes (solar-like, transitional, reduced) is introduced clearly but could be cross-referenced explicitly to the C/O thresholds (0.7, 0.91, 0.92) in any summary tables or figures for easier reader navigation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comment on the computation method correctly identifies a key modeling assumption in our work. We have revised the manuscript to include an explicit discussion of the limitations of equilibrium calculations at fixed pressures, addressing the potential impacts of disk dynamics and non-equilibrium effects while maintaining the core findings.

read point-by-point responses

Referee: Computation method (as described in the abstract and methods paragraph): the central claim of substantial deviations in Fe/Mg, Fe/Si, and Fe/O for C/O > 0.92 rests on equilibrium phase stability at three discrete fixed total pressures. Real disks involve radial drift, turbulent mixing, and finite cooling timescales that can drive departures from local thermodynamic equilibrium, particularly for carbon-bearing phases with poorly constrained nucleation kinetics. If these effects shift condensation temperatures by even a few hundred K, the reported breakdown of the stellar-to-planetary mapping would not necessarily follow; a sensitivity test or explicit discussion of this limitation is needed to support the claim.

Authors: We agree that our approach relies on equilibrium phase stability at fixed pressures (10^{-2} to 10^{-6} bar), a standard approximation in condensation studies but one that does not fully capture dynamic disk processes. In the revised manuscript, we have added a new subsection (5.3) that explicitly discusses radial drift, turbulent mixing, finite cooling timescales, and potential non-equilibrium effects on carbon-bearing phases. We note that our pressure range spans typical midplane values and that the three condensation regimes (solar-like, transitional, reduced) remain consistent across these pressures, supporting the qualitative robustness of the reported deviations in Fe/Mg, Fe/Si, and Fe/O. While a full kinetic sensitivity analysis lies beyond the current scope, we have tempered the abstract and conclusions with appropriate caveats. This provides the requested explicit discussion to support the claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives its central claim from equilibrium phase stability computations performed in the external FactSage thermodynamic software at fixed total pressures, using standard stellar C/O ratios and abundances as direct inputs. Bulk planetesimal compositions are then obtained by applying a stochastic accretion model that aggregates condensates from temperature-dependent feeding zones. No load-bearing step reduces the reported deviations in Fe/Mg, Fe/Si or Fe/O ratios to quantities defined by the authors' own fitted parameters, self-citations, or ansatzes; the three condensation regimes and the conclusion about unreliable refractory tracers follow from the external calculations rather than being presupposed by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on thermodynamic equilibrium being a good approximation, on the chosen pressure grid representing disk conditions, and on the stochastic accretion model aggregating condensates without radial drift or time-dependent effects.

free parameters (2)

Total pressure values (1e-2, 1e-4, 1e-6 bar)
Three discrete pressures chosen to span plausible disk midplane conditions; affect condensation temperatures.
C/O ratio thresholds (0.7, 0.91, 0.92)
Boundaries defining the three regimes are identified from the calculations rather than derived from first principles.

axioms (2)

domain assumption Condensation occurs under local thermodynamic equilibrium at fixed total pressure.
Invoked when running FactSage equilibrium calculations over the temperature range.
domain assumption Planetesimals form by stochastic accretion from temperature-dependent feeding zones without significant radial mixing.
Used to derive bulk compositions from the condensation sequences.

pith-pipeline@v0.9.0 · 5856 in / 1275 out tokens · 39326 ms · 2026-05-21T10:44:37.558278+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We compute equilibrium phase stability using FactSage over 1900–400 K at total pressures of 10^{-2}, 10^{-4}, and 10^{-6} bar... identify three distinct condensation regimes: (i) solar-like (C/O ≲ 0.7), (ii) transitional (C/O ∼ 0.7-0.91), and (iii) reduced (C/O ≳ 0.92).
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Bulk planetesimal compositions are derived using a stochastic accretion framework aggregating condensates from temperature-dependent feeding zones.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Chemical Abundances Shape History (CASH). I. A Link between Giant Planets Orbital Periods and Host Stellar C/O Ratios
astro-ph.EP 2026-04 unverdicted novelty 6.0

Higher host-star C/O ratios correlate with longer orbital periods for giant planets, based on spectra from 598 stars and supported by pebble-formation models.