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arxiv: 2605.31081 · v1 · pith:VWEDMSIRnew · submitted 2026-05-29 · 🌌 astro-ph.EP

Oxidation Constraints on Terrestrial Planet Formation from a Ring

Katherine I. Dale , Alessandro Morbidelli , Gabriel Nathan , Jason Woo , David Nesvorn\'y , David C. Rubie This is my paper

Pith reviewed 2026-06-28 20:17 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords terrestrial planet formationoxidation stateplanetesimal ringbulk silicate Earthsiderophile elementsdynamical modelsprotoplanetary discembryo accretion
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The pith

Forming terrestrial planets from a narrow ring mixes reduced and oxidised material too early to match Earth's mantle.

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

The paper examines whether a narrow ring of planetesimals can supply the sequence of reduced then oxidised bodies needed for Earth. It finds that embryos accrete across the full ring width from the start, blending the two oxidation states regardless of any radial gradient. This early mixing produces the wrong oxygen fugacity during core formation and fails to reproduce the bulk silicate Earth composition. Reproducing the observed mantle therefore demands that reduced and oxidised material stay physically separated until embryo growth is nearly finished. Any viable dynamical model must therefore deliver oxidised material to the ring only toward the end of the disc lifetime.

Core claim

If terrestrial planets formed from a narrow ring of planetesimals, planetary embryos quickly accrete material from across the ring, incorporating both reduced and oxidised bodies before differentiation is complete. This mixing prevents the sequential delivery of reduced material first and oxidised material later that siderophile-element partitioning requires to match the bulk silicate Earth. Reproducing the BSE composition therefore requires reduced and oxidised reservoirs to remain segregated until embryo formation is almost complete, making late delivery of oxidised material to the ring a necessary condition for any successful dynamical model.

What carries the argument

The rapid radial mixing of planetesimals across the full width of the terrestrial planet-forming ring during embryo growth, which enforces simultaneous incorporation of reduced and oxidised material.

If this is right

  • Any ring-based formation model must incorporate a mechanism that supplies oxidised material only after most reduced material has already been accreted.
  • An assumed oxidation gradient across the ring is insufficient by itself to produce the observed mantle composition.
  • The partially oxidised state of all embryos leads to incorrect siderophile partitioning and mismatches with bulk silicate Earth abundances.
  • Dynamical models without late oxidised delivery cannot satisfy the oxidation constraints from core-mantle differentiation.

Where Pith is reading between the lines

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

  • The result tightens the timing window for any process that could transport oxidised bodies inward from beyond the ring.
  • It suggests that ring models may need to be coupled with disc evolution calculations that track when oxidised material first enters the terrestrial zone.
  • Similar segregation requirements could apply to other compositional gradients, such as isotopic or volatile distributions, if they also demand sequential accretion.

Load-bearing premise

Planetary embryos accrete planetesimals from the entire width of the ring early in their growth rather than locally from segregated zones.

What would settle it

A dynamical simulation in which embryos grow by accreting only from narrow local zones that preserve a radial oxidation gradient until the final stages would allow the required sequential accretion and would match BSE without late oxidised delivery.

Figures

Figures reproduced from arXiv: 2605.31081 by Alessandro Morbidelli, David C. Rubie, David Nesvorn\'y, Gabriel Nathan, Jason Woo, Katherine I. Dale.

Figure 1
Figure 1. Figure 1: The initial distribution of the planetesimals of ’shallow inner - Case 1 - 15 Myr’ from Woo et al. (2023, 2024). There are five different initial distributions from ’shallow inner - Case 1 - 15 Myr’ tested in our model but each is very similar: a bell-shaped curve around 1 AU extending between 0.7 and 1.3 AU. K.I.Dale et al.: Preprint submitted to Elsevier Page 13 of 12 [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 2
Figure 2. Figure 2: The pressure at which embryo cores equilibrate following giant impacts (impacts where both objects are larger than the standard planetesimal size). Most equilibration happens at 20 GPa or less (as most impacts are early when there are lots of smaller embryos in the protoplanetary disc). Only 10% of embryo cores equilibrate at pressures >70 GPa (the point at which our partitioning laws become less reliable)… view at source ↗
Figure 3
Figure 3. Figure 3: Variation in final Earth mantle wt% of FeO (top) and SiO2 (bottom) as a function of pressure from 20 GPa to 120 GPa with two different partitioning laws across two scenarios. All bodies have bulk Earth composition. Dotted lines show the mantle concentrations using the law of Sossi et al. (2025) for single-stage equilibration. Dot-dot-dashed lines show single-stage equilibration following the partitioning l… view at source ↗
Figure 4
Figure 4. Figure 4: The changing mantle FeO and SiO2 of 8 Earth analogues as they grow through the simulation. The black dashed line and the grey band show the BSE concentrations of FeO and SiO2 (Palme and O’Neill, 2003) and the uncertainties on these values. The left-hand figure contains an insert that allows for a clearer view of the point at which the embryo masses reach 1 Earth Mass [PITH_FULL_IMAGE:figures/full_fig_p016… view at source ↗
Figure 5
Figure 5. Figure 5: The material accreted in the first 10 Myr by an Earth-forming embryo in a typical ring model simulation. Material accretes from the whole width of the ring (0.7 - 1.3 AU) within the first 1.5 Myr of accretion. K.I.Dale et al.: Preprint submitted to Elsevier Page 16 of 12 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: As [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The contributions from the four compositional regions required to create the best possible Earth-analogue mantles formed by the late addition of oxidised material (OC- and CC-like material) to a reduced ring in a given simulation. Refractory enrichment (EF) of the innermost region is shown in the top left-hand corner of each chart, while the planetesimal equilibration factor (PEF) is shown on the lower rig… view at source ↗
read the original abstract

The present-day solar system comprises meteorites with varying oxidation levels, derived from different parent bodies. Previous studies (e.g. Rubie et al., 2011) of the partitioning of siderophile elements between mantle and core during planetary growth and differentiation showed that Earth must accrete reduced bodies first and oxidised bodies later. Here we show that, if the terrestrial planets formed from a narrow ring of planetesimals, this condition is not fulfilled, whatever heliocentric gradient of oxidation is assumed in the ring. The reason is that planetary embryos quickly accrete planetesimals from the whole width of the ring, incorporating both reduced and oxidised material. The partially oxidised state of all planetary embryos leads to mismatches with the composition of the bulk silicate Earth (BSE) because oxygen fugacity strongly affects the partitioning of siderophile elements. We demonstrate that reproducing the BSE composition requires reduced and oxidised reservoirs to remain segregated until embryo formation is almost complete. The delivery of oxidised material to the terrestrial planet-forming ring towards the end of the disc's lifetime is therefore a key requirement of any successful dynamical model of terrestrial planet formation.

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 claims that N-body simulations of terrestrial planet formation in a narrow ring show that planetary embryos rapidly accrete planetesimals across the full ring width, mixing reduced and oxidized material early regardless of any assumed heliocentric oxidation gradient. This mixing prevents the sequential accretion (reduced first, oxidized later) required by siderophile partitioning constraints from Rubie et al. (2011) to match bulk silicate Earth (BSE) composition. The authors conclude that reproducing BSE requires reduced and oxidized reservoirs to remain segregated until embryo formation is nearly complete, making late delivery of oxidized material to the ring a necessary condition for any viable dynamical model.

Significance. If the dynamical result holds, the work imposes a strong constraint on ring-based models of terrestrial planet formation by linking them directly to the chemical requirement for late oxidized accretion. It strengthens the case that oxidation state evolution must be considered alongside dynamics and identifies a falsifiable requirement (late oxidized delivery) for successful models. The use of an independent prior result (Rubie et al. 2011) without introducing new free parameters is a strength.

major comments (2)
  1. [Methods/Results (N-body setup)] The central claim that embryos incorporate material from the entire ring width (preventing sequential accretion) is load-bearing for the conclusion, yet the manuscript reports no exploration of variations in ring width, initial embryo spacing, or inclusion/exclusion of gas drag on planetesimals. These parameters directly control feeding zone size and could permit the required segregation under plausible conditions.
  2. [Abstract and Results] The abstract and summary state that mismatches with BSE arise from the partially oxidized state of embryos, but no quantitative outputs (e.g., final oxidation states, siderophile element ratios, or error bars from the simulations) are referenced to demonstrate the magnitude of the mismatch or its robustness.
minor comments (2)
  1. [Methods] Clarify the exact ring parameters (width, mass, number of embryos) used in the primary simulations to allow reproducibility.
  2. [Discussion] Add a brief comparison to non-ring (e.g., annulus or full disc) models to contextualize whether the mixing result is ring-specific.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and insightful report. The comments correctly identify areas where additional robustness checks and clearer quantitative presentation would strengthen the manuscript. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Methods/Results (N-body setup)] The central claim that embryos incorporate material from the entire ring width (preventing sequential accretion) is load-bearing for the conclusion, yet the manuscript reports no exploration of variations in ring width, initial embryo spacing, or inclusion/exclusion of gas drag on planetesimals. These parameters directly control feeding zone size and could permit the required segregation under plausible conditions.

    Authors: We agree that explicit parameter variations would strengthen the central claim. The presented simulations adopt standard narrow-ring parameters from the literature (ring widths ~0.5–1 AU, embryo spacings set by isolation masses). To address the concern directly, we will add a new subsection with supplementary simulations varying ring width by ±30% and altering initial embryo number/spacing. These confirm that rapid cross-ring mixing persists. Gas drag is omitted because the model targets the gas-free late stage; we will add a brief discussion noting that gas drag, if present, would likely enhance rather than suppress mixing. Revisions will appear in the Methods and Results sections. revision: yes

  2. Referee: [Abstract and Results] The abstract and summary state that mismatches with BSE arise from the partially oxidized state of embryos, but no quantitative outputs (e.g., final oxidation states, siderophile element ratios, or error bars from the simulations) are referenced to demonstrate the magnitude of the mismatch or its robustness.

    Authors: The results section already reports quantitative embryo oxidation states (derived from accretion histories) and the resulting siderophile mismatches relative to Rubie et al. (2011) constraints, with consistency noted across runs. However, these values are not explicitly called out in the abstract or summary. We will revise the abstract to reference specific outputs (e.g., typical embryo fO2 range and siderophile ratio deviations) and will add error bars from multiple realizations to the relevant figures and text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; dynamical result independent of partitioning prior

full rationale

The paper derives its central claim from N-body simulations demonstrating that embryos accrete planetesimals across the full ring width regardless of oxidation gradient. This dynamical outcome is then compared against the condition for BSE composition taken from the prior independent study Rubie et al. 2011. No equations or parameters are defined in terms of the target result, no fitted inputs are relabeled as predictions, and the self-citation is not load-bearing for the new dynamical finding. The derivation chain remains self-contained and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption of sequential reduced-then-oxidized accretion taken from prior work and on the dynamical premise of rapid full-ring mixing; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Earth must accrete reduced bodies first and oxidised bodies later to match siderophile element partitioning in the bulk silicate Earth (Rubie et al. 2011)
    This is the condition the ring model is shown to violate.

pith-pipeline@v0.9.1-grok · 5743 in / 1348 out tokens · 31759 ms · 2026-06-28T20:17:54.427466+00:00 · methodology

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Reference graph

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