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REVIEW 3 major objections 5 minor 58 references

Accretion of Uranus and Neptune: confronting different giant impact scenarios

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper argues that the two main giant-impact formation channels for Uranus and Neptune—collisions among roughly equal-mass embryos versus collisions with much smaller impactors—match the observed masses, obliquities, and rotation…

desk verdict Useful first N-body test of the high-mass-ratio impact scenario, but the 'within a factor of ~2' comparison is not supported by the small-number statistics. read the letter →

arxiv 2412.02785 v1 pith:BYMC4BQN submitted 2024-12-03 astro-ph.EP

Leandro Esteves , André Izidoro , Othon C. Winter This is my paper · ORCID
classification astro-ph.EP
keywords PlanetaryformationGiantimpactsUranusNeptuneObliquityRotationperiodN-bodysimulationsType-Imigration
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to decide whether Uranus and Neptune were more likely finished by impacts between bodies of roughly equal mass or by a large proto-planet absorbing a much smaller embryo. The authors run thousands of N-body simulations of migrating protoplanets in a gas disk and compare how often each scenario produces planets matching Uranus and Neptune's masses, mass ratio, obliquities, and rotation periods. They find that the two scenarios succeed at nearly the same low rate, with overall success probabilities of order 0.1–1% and within a factor of about 2 of each other. The reason for the tie is complementary: equal-mass collisions happen often but leave planets spinning too fast, while high-mass-ratio collisions give the right spins but are rare because small embryos are scattered rather than accreted. If correct, this means the formation of the ice giants was a lucky outcome of chaotic accretion, and formation models alone cannot tell the two impact channels apart.

What carries the argument

Two pieces of machinery carry the argument. First, the N-body model adds type-I migration, eccentricity damping, and inclination damping from a one-dimensional gas disk, and this determines whether small embryos are scattered away or actually collide with the proto-Uranus and proto-Neptune; this is why the two scenarios have different collision frequencies. Second, the rotation period of every post-impact planet is computed in post-processing from angular momentum conservation using a Maclaurin spheroid moment of inertia, a simplified treatment that the paper validates against smooth-particle hydrodynamics simulations. The paper's central product is the joint statistic: the fraction of simulations in which both proto-planets survive, each experience at least one giant impact, the outer Solar System architecture is preserved, and the final rotation periods fall within a chosen fraction of the observed averaged value. That joint fraction is the quantity that comes out nearly equal, within a factor of about 2, for the two competing scenarios.

What would settle it

Run smoothed-particle hydrodynamics impact simulations of the actual collision geometries recorded in the both-collide outcomes from each scenario, including fragmentation and hit-and-run physics, and compare the resulting rotation periods with the Maclaurin-spheroid estimates used here; if the two scenarios diverge by more than the assumed factor-of-2 grazing correction, the paper's equal-success-rate conclusion fails.

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Extended reading notes

Core claim

On the paper's own terms: in N-body simulations of the final accretion of Uranus and Neptune, the high-mass-ratio scenario—a proto-Uranus and proto-Neptune of roughly 13 and 16 Earth masses, each absorbing a single small embryo of 0.5–3 Earth masses—produces rotation periods that peak near the observed roughly 16.5-hour values, but the required collisions occur in only about 1.16% of simulations. The equal-mass-ratio scenario produces collisions about ten times more often, about 10.25%, but the resulting planets generally spin too fast. Combining collision frequency with rotation-period agreement, the paper reports overall success rates of roughly 0.1–1% for each scenario, differing by no more than a factor of about 2 across rotation-period tolerance intervals of ±15% to ±100%. The paper concludes that, from a planet-formation perspective, there is no clear statistical preference for either giant-impact channel, and that reproducing Uranus and Neptune is a fortuitous outcome of the chaotic accretion phase.

Load-bearing premise

Final rotation periods are computed assuming that collisions merge perfectly, with only a simplified correction for grazing impacts; if a substantial fraction of collisions instead fragment or involve hit-and-run, as suggested by the authors' own estimate of roughly 30% high-impact-parameter events, the resulting spins could shift by up to a factor of about 2 and change the success rates in Table 3.

Editorial extensions

If this is right

  • If the claim is right, the high-mass-ratio scenario's better spin match is offset by its rarer collisions, so neither the equal-mass nor the high-mass-ratio scenario can be rejected on dynamical grounds alone.
  • The low absolute success rates, of order 0.1–1%, imply that forming Uranus and Neptune is a rare, chance outcome of the giant-impact phase rather than a generic pathway of gas-disk accretion.
  • If some unknown mechanism removes angular momentum after accretion, such as interaction with the surrounding gas disk, the equal-mass scenario would become strongly preferred, with its success rate rising by up to an order of magnitude.
  • Starting with three or four protoplanets instead of two does not improve the success rate, so a five-giant-planet initial configuration offers no clear advantage for matching Uranus and Neptune.
  • Because roughly 30% of collisions have impact parameters above 0.8, fragmentation at those grazing impacts could lengthen rotation periods by up to a factor of 2 and shift the quantitative success rates by a factor of a few, though the authors argue the qualitative tie remains.
  • One concrete test: take the actual impact geometries recorded in the both-collide simulations from each scenario and run them in a smoothed-particle hydrodynamics impact code that allows fragmentation and hit-and-run. If the resulting spin periods differ systematically from the Maclaurin-spheroid estimate by more than the assumed factor for grazing impacts, the paper's equal-success-rate conclusio
  • The paper leaves untested whether varying the gas disk's lifetime or surface density would break the factor-of-2 tie and also whether the leftover embryos and co-orbital objects seen in many HMR simulations would survive the later Solar System instability, potentially adding an independent observational constraint on the scenario.
  • The simplified perfect-merging assumption may not bias the comparison symmetrically: fragmentation at high impact parameters tends to remove angular momentum from near-equal-mass collisions more effectively, so a fuller hydrodynamical treatment could widen, rather than narrow, the gap between the two scenarios.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper investigates whether the formation of Uranus and Neptune through giant impacts with high mass-ratio impactors (small embryos of 0.5–3 M⊕ hitting ~13–17 M⊕ protoplanets) is dynamically as likely as the previously studied equal-mass-ratio embryo scenario (I15). The authors run 12 sets of 1000 N-body simulations including gas disk migration and tidal damping, classify outcomes, compute rotation periods of collision products via a two-body angular momentum approximation, and then compare the fraction of simulations that produce both planets with plausible masses and rotation periods. They conclude that the two scenarios have broadly similar success rates, within a factor of ~2, with overall probabilities of order 0.1–1%. The paper also tests a simplified correction for grazing collisions and a scenario with more than two initial protoplanets.

Significance. If the central quantitative claim were fully supported, this paper would be a valuable contribution to the ice-giant formation literature: it is the first to test the high-mass-ratio impact scenario, motivated by SPH simulations, within a planet-formation N-body framework rather than assuming the impact happens. The authors provide a systematic parameter study with 1000 simulations per set, transparently describe their initial conditions and acknowledge their ad-hoc nature, and test the robustness of their rotation-period results to a simplified grazing-impact correction. The qualitative conclusion that both scenarios are rare (order 0.1–1%) appears robust and is itself a useful result. However, the more specific quantitative comparison between scenarios is not yet supported by the statistics reported, and the mass-matching component of the success criterion is partly imposed by the initial conditions rather than predicted.

major comments (3)
  1. [Section 4, Table 3] The central quantitative claim in the Abstract and Section 4 that the two scenarios have success rates "within a factor of ~2" is not supported by the reported statistics, because each percentage in Table 3 corresponds to only 0.2–15.4 successful simulations out of 1000. For example, the ±15% column gives 0.42% (≈4 events) for the Msmall = 0.5 M⊕ HMR set and 0.16% (≈1.6 events) for the I15 6 M⊕ set; the 95% Poisson confidence intervals for these counts are approximately 0.11%–1.07% and 0.02%–0.58%, respectively, which overlap substantially and permit true ratios ranging from well below 1 to over 10. The paper should report confidence intervals for every success rate and either soften the factor-of-2 wording to a qualitative statement or demonstrate that the ratio is robust to counting uncertainty.
  2. [Section 2 and Section 4] The statement in the Abstract that the simulations broadly match the masses, mass ratio, and rotation periods is partly by construction for the HMR scenario. The protoplanet initial masses are chosen (Table 1) so that a single collision with an embryo of mass Msmall yields exactly the present-day masses of Uranus and Neptune, and the success criterion in Section 4 for HMR runs only requires that both protoplanets experience at least one collision with a small embryo; final masses are not checked. For the I15 runs, a mass threshold larger than 12 M⊕ is imposed, so the two scenarios are not evaluated with the same mass-selection criterion. The authors should either verify final masses in the reported statistics or explicitly state that mass matching is imposed rather than predicted.
  3. [Section 5] The sensitivity of the central comparison to the perfect-merging assumption is underreported. The authors state that when grazing collisions (impact parameter greater than 0.8, about 30% of collisions) are assigned rotation periods a factor of 2 longer, the probabilities of Table 3 change "by up to a factor of a few," which is larger than the claimed factor-of-2 difference between scenarios. Because this uncertainty is comparable to or larger than the effect being measured, the recalculated probabilities should be presented explicitly, for example as an additional table or column, so that the reader can judge whether the factor-of-2 claim survives. The current qualitative statement that the conclusions remain broadly unchanged is not sufficient for the quantitative claim in the Abstract.
minor comments (5)
  1. [Abstract and Keywords] There are several typographical errors: "1 Merath" in the Abstract should be "1 M⊕", and "Planetary dinamics" in the keywords should be "Planetary dynamics".
  2. [Section 2] When comparing to the original I15 scenario, the paper should state more prominently that the I15-like runs in this work place Jupiter at 5.2 au, whereas most original I15 simulations placed Jupiter at 3.5 au; this difference may affect the collision statistics and thus the direct comparison to the earlier work.
  3. [Figure 2] The x-axis label says "see 1," which should read "see Table 1."
  4. [Section 4.1] The five-giant-planet scenario is described only qualitatively, stating that success fractions are "very similar" to those in Table 3, but no numbers are provided; a table or a quantitative sentence would allow the reader to assess this claim.
  5. [Section 6] In the sentence "this scenario is refereed to as the high-mass-ratio scenario," "refereed" should be "referred."

Circularity Check

1 steps flagged · score 4.0 of 10

Only the HMR mass/mass-ratio component is set by construction; the emergent collision-probability and rotation-period comparison is self-contained.

  1. self definitional [Section 2 (Simulations) and Section 4 (Statistics/Table 3); mirrored in the Abstract]
    "The initial masses of the protoplanets in our simulations is a free parameter and assumed to vary between 11 and 16.5 M⊕, depending on the initial masses of the small embryos. For instance, for a set of simulations where small embryos have initial masses set to Msmall, the proto-Uranus and proto-Neptune start the simulations with masses set to 14−Msmall and 17−Msmall, respectively. We choose these specific protoplanets masses such that only a single giant impact is needed to achieve Uranus/Neptune current masses."

    In the HMR sets, a collision of proto-Uranus (14−Msmall) with one embryo of mass Msmall yields exactly 14 M⊕, and proto-Neptune (17−Msmall) similarly yields 17 M⊕, so the final masses and the 14/17 mass ratio are fixed by the initial conditions whenever the Both Collide criterion is met. Since secondary collisions are rare (about 5% for Msmall below 1 M⊕ and roughly 15% at larger Msmall), the mass and mass-ratio part of the Abstract's 'probability of broadly matching the masses, mass ratio, and rotation periods' is true by construction for HMR. The paper explicitly calls the initial choice ad-hoc, which is honest, but the mass/mass-ratio 'match' in HMR is not an independent prediction; only the collision probability and rotation-period distribution are emergent.

full rationale

The central new results are the N-body collision statistics and the post-processed rotation periods, both of which emerge from the simulations rather than being fitted to Uranus and Neptune. The HMR initial masses are admittedly chosen so that one impact produces the current masses, so the mass-matching component of the stated success rate is self-definitional rather than a test; this is the only genuine circular element I find. The comparison between HMR and I15 scenarios does not reduce to a fitted parameter or to a self-citation chain: I15 initial conditions are taken from prior work by one author, but the present 1000-run-per-set statistics and rotation-period calculations are new simulations, and the cited SPH work is used as validation of the rotation-period approximation, not as a uniqueness theorem that forces the conclusion. The paper's own Section 5 caveat about perfect merging and the roughly 30% grazing collisions is a legitimate modeling robustness concern, not circularity. The small-number statistics criticism of Table 3 (success counts of order 1-15 per 1000 simulations, with overlapping Poisson confidence intervals) is a valid correctness/statistical-support issue, but it is not an instance of circular reasoning. Overall, the emergent parts of the claim—collisions are rare in HMR, and HMR rotations cluster near the ice-giant values—are self-contained, so the circularity score is moderate rather than high.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard planet-formation modeling assumptions and several ad hoc choices, chiefly the initial masses of the proto-planets and the simplified collision treatment. No new physical entities are introduced.

free parameters (6)
  • proto-Uranus initial mass = 13.5, 13, 12, 11 M⊕ depending on Msmall
    Chosen ad hoc so that a single impact with one small embryo yields the present mass; acknowledged as ad hoc in Section 2.
  • proto-Neptune initial mass = 16.5, 16, 14, 13 M⊕ depending on Msmall
    Chosen ad hoc to achieve the current Neptune mass after one small-embryo impact; not fitted to rotation data.
  • small embryo mass Msmall = 0.5, 1, 2, 3 M⊕
    A scanned parameter, not fitted to the target result; each value defines a separate simulation set.
  • number of small embryos Nsmall = 5, 10, 20
    A scanned parameter controlling the population of impactors; results vary with Nsmall.
  • Jupiter and Saturn damping timescales = e_j/e_dot ~ 1e4 yr, i_j/i_dot ~ 1e5 yr; Saturn ~1e3 and 1e4 yr
    Manual choices to mimic gas disk effects on the giant planets, following I15; not fitted to the outcomes.
  • Disk dissipation timescale = 3 Myr (simulation duration)
    The gas disk is assumed to dissipate after 3 Myr; this timescale is not derived from the model and affects migration and collision probabilities.
assumptions (5)
  • domain assumption Uranus and Neptune experienced at least one giant impact during their formation.
    This is the hypothesis being tested, motivated by their high obliquities and satellite properties (Section 1).
  • domain assumption The protoplanetary disk can be approximated by a 1D azimuthally averaged locally isothermal disk with type-I migration torques.
    Standard but approximate; the results depend on this disk model (Section 2, Figure 1).
  • domain assumption Jupiter and Saturn were fully formed at ~5.2 au during the ice giant formation phase.
    They are not grown in the simulations; this fixed architecture may differ from the original I15 setup where Jupiter started at 3.5 au (Section 2).
  • ad hoc to paper Collision outcomes in the N-body code can be modeled as perfect mergers, with a simplified correction for grazing impacts.
    Fragmentation and hit-and-run are neglected; the authors test a factor-of-2 spin-period correction for impact parameters >0.8 in Section 5.
  • ad hoc to paper Initial spins of protoplanets are negligible and aligned with orbital angular momentum.
    A subset of simulations with distributed spins shows qualitative results unchanged, but the baseline assumption is ad hoc (Section 3.2).

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Cite this review

Pith. "Pith review of Accretion of Uranus and Neptune: confronting different giant impact scenarios." pith.science (2026). https://pith.science/paper/BYMC4BQN

@misc{pith2026241202785,
  author       = {Pith},
  title        = {Pith review of: Accretion of Uranus and Neptune: confronting different giant impact scenarios},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BYMC4BQN}},
  note         = {Machine review of arXiv:2412.02785}
}
read the original abstract

The origins of Uranus and Neptune are not fully understood. Their inclined rotation axes -- obliquities -- suggest that they experienced giant impacts during their formation histories. Simulations modeling their accretion from giant impacts among ~5 Earth masses planetary embryos -- with roughly unity impactors' mass ratios -- have been able to broadly match their current masses, final mass ratio, and obliquity. However, due to angular momentum conservation, planets produced in these impacts tend to rotate too fast, compared to Uranus and Neptune. One potential solution for this problem consists of invoking instead collisions of objects with large mass ratios (e.g. a proto-Uranus with 13 Mearth and an embryo of 1 Mearth). Smooth-particle hydrodynamics simulations show that in this scenario final planets tend to have rotation periods more consistent with those of Uranus and Neptune. Here we performed a large suite of N-body numerical simulations modelling the formation of Uranus and Neptune to compare these different dynamical views. Our simulations start with a population of protoplanets and account for the effects of type-I migration, inclination and eccentricity tidal damping. Our results show that although scenarios allowing for large impactors' mass ratio favour slower rotating planets, the probability of occurring collisions in these specific simulations is significantly low. This is because gas tidal damping is relatively less efficient for low-mass embryos (<~1 Merath) and, consequently, such objects are mostly scattered by more massive objects (~13 Mearth) instead of colliding with them. Altogether, our results show that the probability of broadly matching the masses, mass ratio, and rotation periods of Uranus and Neptune in these two competing formation scenarios is broadly similar, within a factor of ~2, with overall probabilities of the order of ~0.1-1%.

Figures

Figures reproduced from arXiv: 2412.02785 by the authors.

Figure 1
Figure 1. Simulation initial conditions for the protoplanetary disk and the planets. Top panel: The gas surface density as a function of radial distance. The blue curve illustrates how the giant planets shape the disk. Coloured lines represent the approximate orbits of Jupiter, Saturn, and the range of distribution for embryos. Middle Panel: Normalized resultant torque. Negative values indicate a reduction in orbital angular … view at source ↗
Figure 2
Figure 2. Stacked bars illustrating the results of 1000 numerical simulations for each set. The set name indicates the small embryos mass in M⊕ on the right and the number of small embryos on the left. The bars colour-coding denotes the final classification of simulations. The number indicates how many simulations in the set have the given category. The last two bars are the sets from I15 scenario. inner Solar System (see our… view at source ↗
Figure 3
Figure 3. Final snapshot of simulations in which both protoplanets have experienced at least one collision. Each simulation is identified by #𝑖𝑖𝑖_𝑗𝑗, where 𝑖𝑖𝑖 is the simulation number, and 𝑗𝑗 is the number of small embryos that starts the simulation. The planets are sorted by their semi-major axis. The first planets are Jupiter and Saturn followed by proto-Uranus (light￾blue) or proto-Neptune (dark-blue) analogues. The small… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Fraction of planets analogues to Uranus/Neptune from Both Collide simulations by their rotation period in hours. The light-blue and dark-blue reference lines represent the rotation periods of Uranus and Neptune, respectively. The four upper panels show planets that col…
Figure 5
Figure 5. Figure 5: Obliquity and mass evolution of planets after collisions in HMR and I15 scenarios. Each marker represent the resulting planet after a collision. Square markers represent Neptune analogues and circle markers Uranus analogues. In the radial axis we plot the planet mass. …

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