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REVIEW 4 major objections 4 minor 1 cited by

Formation of super-Earths and mini-Neptunes from rings of planetesimals

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Super-Earths and mini-Neptunes form from two separated planetesimal rings: rocky super-Earths from an inner ring by planetesimal collisions, icy mini-Neptunes from an outer ring by pebble accretion.

desk verdict A plausible and honest two-ring planet formation model whose broad observational match is partly calibration and whose fixed ring locations are the main soft spot; deserves a serious referee, not a desk reject. read the letter →

arxiv 2501.03345 v1 pith:R3E36DQX submitted 2025-01-06 astro-ph.EP

Sho Shibata , Andre Izidoro This is my paper · ORCID
classification astro-ph.EP
keywords planetformationsuper-Earthsmini-NeptunesplanetesimalringspebbleaccretionradiusvalleyexoplanetsystemsN-bodysimulations
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

The paper tries to establish that super-Earths and mini-Neptunes, the common close-in planets with radii from about 1 to 4 Earth radii, can form from the same ring-based pathway proposed for the solar system. It simulates growth starting from an inner ring of rocky planetesimals (kilometre-scale building blocks) at about 0.5-1.5 au and an outer icy ring at about 8-15 au, tracking collisions, pebble accretion, gas-driven migration, and later orbital instabilities. The simulations broadly match the observed bimodal radius distribution with its valley, the period-ratio distribution, intra-system size uniformity, and planet multiplicity. The authors conclude that super-Earths grow mainly by planetesimal accretion in the inner disk, mini-Neptunes form by pebble accretion beyond the snowline and migrate inward, and the radius valley constrains the typical inner rocky reservoir to less than 3-6 Earth masses. If correct, most planets near 1 au in such systems should be water-rich, with about 1% of systems hosting rocky Earth-sized planets that went through late giant impacts akin to the Moon-forming event.

What carries the argument

The central mechanism is a pair of initial planetesimal rings, an inner rocky ring at 0.5-1.5 au and an outer icy ring at 8-15 au, embedded in a viscous gas disk with an inner cavity, combined with simultaneous treatment of planetesimal accretion, pebble accretion (growth by sweeping up small drifting icy grains), gas-driven migration, and orbital damping. The rings set where and how growth happens: the inner ring mass is the free parameter that controls where the radius valley sits, while the outer ring feeds inward-migrating icy planets that form the mini-Neptune peak. The comparison chain that carries the argument is the conversion of simulated masses and compositions into planet radii using mass-radius relations and atmospheric-loss prescriptions, followed by simulated transit observations that apply geometric and signal-to-noise biases before comparing with observed exoplanet distributions.

What would settle it

A transit and atmospheric survey of planets at orbital periods 100-400 days around Sun-like stars that found most to be rocky and dry, or found a substantial population of close-in planets below 1 Earth radius, would contradict the model; the paper reports that its simulations underproduce such small planets.

Watch

Extended reading notes

Core claim

The central discovery claimed is that the observed population of close-in super-Earths and mini-Neptunes around Sun-like stars is consistent with formation from two narrow rings of planetesimals rather than from a broad, continuous disk. In the inner ring, planetary seeds grow to super-Earth sizes mainly through mutual collisions, with pebble accretion inefficient because silicate pebbles are small; in the outer ring beyond the water snowline (where water condenses as ice), icy pebbles are larger and pebble accretion dominates, producing mini-Neptunes that migrate inward and stir the inner system. The resulting systems, after gas dispersal and dynamical instabilities, broadly match the observed radius distribution, period-ratio distribution, size-ratio distribution, and multiplicity, and the location of the radius valley implies that the typical inner rocky reservoir is between about 3 and 6 Earth masses. The paper also claims that most planets at 100-400 day periods in such systems are water-rich, and that roughly 1% of systems host rocky, Earth-mass planets at about 1 au that experienced a late giant impact analogous to the Moon-forming event.

Load-bearing premise

The load-bearing premise is that planetesimal formation concentrated solids into two narrow rings, an inner rocky one at 0.5-1.5 au and an outer icy one at 8-15 au, with inner-ring masses around 3-6 Earth masses, and the paper itself notes that the exact ring locations and masses are not well constrained.

Editorial extensions

If this is right

  • If the two-ring scenario is right, the exoplanet radius valley is set primarily by the mass of the inner rocky planetesimal ring, so systems whose inner rings exceed about 6 Earth masses should fill the valley with planets absent from the observed bimodality.
  • Super-Earths and mini-Neptunes then have distinct origins: rocky super-Earths grow by planetesimal collisions inside the snowline, while icy mini-Neptunes grow by pebble accretion beyond the snowline and migrate inward to short periods.
  • The model predicts that planets at 100-400 day periods in super-Earth and mini-Neptune systems are mostly water-rich, and that roughly 1% of such systems host rocky, Earth-sized planets at about 1 au that underwent a late giant impact like the Moon-forming event.
  • The agreement with the observed period-ratio, size-ratio, and multiplicity distributions implies that most close-in multi-planet systems form in resonant chains during disk migration and then become dynamically unstable within about 50 Myr, breaking the chains and shaping the final architectures.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A consequence the authors leave implicit is that if planetesimal rings form at condensation fronts generally, the same two-ring mechanism could unify solar-system and exoplanet formation: differences in ring mass and location, rather than differences in formation physics, would choose between a terrestrial-planet system and a super-Earth and mini-Neptune system.
  • The paper's self-identified mismatches, an underproduction of planets below about 1 Earth radius and an excess of planet pairs near the 4:3 and 5:4 resonances, point directly to a testable extension: simulating inner rings with masses below 3 Earth masses, which should populate the small-planet tail and smooth the resonant excess.
  • The model's dominance of impact-driven atmospheric stripping suggests an observational signature the paper does not spell out: among close-in planets, those with a collisional history involving giant impacts should show a stronger tendency to lack atmospheres than equally irradiated planets without such impacts.
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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

4 major / 4 minor

Summary. The paper presents N-body simulations, using the FLINSTONE/MERCURY code, of planet formation from two narrow planetesimal rings: an inner rocky ring at 0.5-1.5 au and an outer icy ring at 8-15 au. The authors vary the inner-ring mass (3, 6, 9, 15 Earth masses) and disk lifetime (2, 3 Myr), include planetesimal accretion, pebble accretion, gas migration, atmospheric loss, and simulated transit observations, and then mix the simulated scenarios with weights chosen by minimizing KS distances to CKS observations. They report that a mixture of 10% M3T2, 20% M3T3, and 70% M6T2 reproduces the observed radius, period-ratio, size-ratio, and multiplicity distributions, and conclude that super-Earths form from the inner ring by planetesimal accretion while mini-Neptunes form from the outer ring by pebble accretion, that the rocky reservoir is limited to 3-6 Earth masses, and that planets at 100-400 days should be predominantly water-rich, with a ~1% chance of an Earth-like rocky planet near 1 au.

Significance. If correct, the paper would unify solar-system ring formation with exoplanet architectures and provide falsifiable predictions for PLATO and other surveys. Strengths include the simultaneous treatment of pebble accretion and planetesimal accretion with composition tracking, the explicit modeling of observational bias, and the transparent reporting of KS p-values, including the borderline radius p-value and the period-ratio <1.5 discrepancy. The paper's central claim is, however, conditional on an admittedly unconstrained two-ring initial condition and on an in-sample calibration of mixing weights; these issues must be addressed before the broad-match conclusion can be accepted.

major comments (4)
  1. [Section 2.2] The two-ring initial condition is load-bearing for the central claim, yet the ring locations and widths are adopted rather than tested. The paper states that "the exact location where planetesimal rings form is not well constrained" and sets the inner and outer rings at 0.5-1.5 au and 8-15 au following Izidoro et al. (2021b); the only varied ring property is the inner-ring mass Mdisk. The ring radii set the planetesimal isolation mass, the migration history, the onset of pebble accretion, and the depletion of the 1-au region, so the predicted radius valley, the composition dichotomy, and the water-rich 100-400 day population all depend on this assumed geometry. Because no continuous-disk control or sensitivity runs with different ring locations and widths are presented, the comparison with observations tests this particular initial condition rather than the ring-formation scenario generally. I request control simulations with a continuous planetesimal disk and with shifted ring radii and widths.
  2. [Sections 3.3 and 4.1; Appendix E] The statistical support for the "broad match" claim is weakened by in-sample calibration. The mixing weights (10% M3T2, 20% M3T3, 70% M6T2) are obtained by minimizing the KS distance to the same four observed distributions that are later used to assert agreement, so the reported p-values (0.05, 0.42, 0.35, 0.88) are post-fit and do not account for the selection of weights. In addition, Eq. (E22) defines the KS statistic as δ = n max_i |Fsim(i)-Fobs(i)|, which is bin-dependent and nonstandard, and summing δ across radii, period ratios, size ratios, and multiplicities with different bin counts has no clear statistical justification. Please provide an out-of-sample or cross-validated evaluation, and either use the standard KS statistic or justify the binning-based objective.
  3. [Section 4.1] The paper's own KS tests show that the radius distribution is borderline (p=0.05) and that the period-ratio region below 1.5 is significantly discrepant (p=0.01); the radius comparison only becomes acceptable (p=0.26) after excluding planets smaller than 1 Earth radius. These are not merely cosmetic issues, because the central claim is that the simulations "broadly match" the observed distributions. The proposed explanations - late dynamical instabilities beyond 50 Myr and formation from lower-mass rings - are qualitative and untested. I ask for quantitative tests of these hypotheses, for example by explicitly adding a post-50 Myr instability prescription or by including Mdisk below 3 Earth masses in the simulations, before the broad-match claim is accepted.
  4. [Section 2.2] The initial seed masses and start time are an additional load-bearing assumption. The simulations begin at 0.3 Myr with Moon-mass seeds in the inner ring and Ceres-mass seeds in the outer ring, justified only as "broadly consistent" with expected growth; no sensitivity runs are shown. Because the paper's growth-mechanism dichotomy (planetesimal accretion inside, pebble accretion outside) is controlled by the seed-mass-dependent timescales in Fig. 1, the robustness of the results to seed mass and start time should be demonstrated before drawing conclusions about formation mechanisms.
minor comments (4)
  1. [Abstract] The abstract's "less than 3-6 Earth masses" is ambiguous; Section 3.2 says the inner ring mass must be "less than ~6 Earth masses", Section 3.3 says "lower than 6 Earth masses", and Section 4.2 says "up to 3-6 Earth masses". Please harmonize these statements.
  2. [Section 2.4] The sentence "Planets with water contents less/more than 10% are categorized as rocky/icy cores" should be rewritten as "below/above 10%" to avoid ambiguity.
  3. [Figure 3 caption] The caption's phrasing "In light blue, we show the radius distribution" and "The thin, dark blue, and red lines" is confusing because the legend uses "light-blue" for observations and "red" and "blue" for rocky and icy planets; please clarify the wording.
  4. [Appendix E.2] Please define \bar N_system and state the observed sample sizes used in the KS tests; as written, the effective sample size construction (e.g., nsim=74 for radius) is not fully motivated.

Circularity Check

2 steps flagged · score 4.0 of 10

Partially circular: the broad match to observed architectures is an in-sample fit of mixing weights, and the two-ring initial geometry is imported from a same-author model.

  1. fitted input called prediction [Section 3.3 ('Mixing formation scenarios') and Section 4.1 ('Statistical Comparison'); abstract]
    "We look for the best-fit mixing ratio using the Kolmogorov-Smirnov test (KS). We calculate the KS statistic δ for each distribution: planet radius (size), period ratio of adjacent planet-pairs, size-ratio of adjacent planet-pairs, and planet multiplicity distributions. Our best-fit mixing ratio is defined as that with which the sum of all δ (for the four distributions) takes the minimum value. We found that combining 10%, 20%, and 70% of systems from the M3T2, M3T3, and M6T2 scenarios provides the best fit to observations."

    The abstract and Section 4.1 present agreement with the period-ratio, radius-ratio, and multiplicity distributions as support for the model, but the mixing weights were explicitly chosen by minimizing the KS distance to those same observed distributions. The 'broadly match' statement is therefore an optimized in-sample calibration, not an independent test; the reported p-values (0.42, 0.35, 0.88) are computed after model selection on the same data and cannot independently validate the two-ring scenario. The N-body dynamics are not literally forced—the distribution shapes emerge from the simulations—but the claimed confirmation from these four distributions is partly self-fulfilling.

  2. self citation load bearing [Section 2.2 ('Two-ring disk of planetesimals')]
    "The exact location where planetesimal rings form is not well constrained because it depends on the disk's temperature evolution, the structure of potential pressure bumps, and the pebble flux. For simplicity, we set the inner and outer rings at 0.5 − 1.5 au and 8 − 15 au, respectively, following the model by Izidoro et al. (2021b)."

    The central scenario—inner rocky ring at 0.5–1.5 au producing super-Earths by planetesimal accretion and outer icy ring at 8–15 au producing mini-Neptunes by pebble accretion—rests on these initial ring radii. The radii are adopted from Izidoro et al. (2021b), a paper sharing a coauthor (Izidoro), and the text admits they are not well constrained. No sensitivity runs vary the ring locations, so the observed-match claims establish consistency with this particular same-author initial condition rather than an independent test of the ring-location hypothesis. The admission of uncertainty makes this a load-bearing self-citation rather than a hidden derivation.

full rationale

The paper is transparent that the two-ring initial conditions are assumptions and that mixing weights are fitted to the CKS sample, so this is not a case where a hidden derivation is equivalent to its inputs. Nevertheless, the headline claim that the simulations 'broadly match' the observed period-ratio, size-ratio, and multiplicity distributions is weakened because the mixture weights were optimized against exactly those distributions via KS minimization; the p-values are in-sample. In addition, the specific ring radii generating the inner-rocky/outer-icy dichotomy are imported from a prior model by the same author group and are explicitly unconstrained, so the central formation-pathway conclusion is conditional on a self-citation. The genuine N-body dynamics and the water-rich/1%-Earth-analog predictions are independent outputs, which prevents a higher score. Score 4 reflects the load-bearing self-cited initial condition and the in-sample fitting of the match claim, while acknowledging the model's independent dynamical content.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The model rests on a small number of hand-chosen initial conditions and standard sub-models. The main free parameters (inner ring mass, disk lifetime, and mixing weights) are calibrated to the Kepler observations, which is the main source of circularity burden. No new particles, forces, or other physical entities are introduced.

free parameters (8)
  • Inner ring mass Mdisk = 3, 6, 9, 15 M_Earth
    Scanned as a free parameter; the best fit to the observed radius valley excludes 9 and 15 Earth masses, producing the central <3-6 M_Earth constraint.
  • Disk lifetime tdisk = 2 and 3 Myr
    Chosen from the literature and included as a discrete parameter; the best-fit mixture contains both M3T2 and M3T3.
  • Mixing ratios wM3T2, wM3T3, wM6T2 = 0.10, 0.20, 0.70
    Fitted by minimizing the summed KS statistic across the observed radius, period ratio, size ratio, and multiplicity distributions.
  • Inner ring radial extent = 0.5-1.5 au
    Chosen following Izidoro et al. (2021b); the exact ring location is not well constrained and is load-bearing for the model.
  • Outer ring radial extent = 8-15 au
    Chosen following Izidoro et al. (2021b); the exact location depends on disk temperature history and pressure bump structure.
  • Silicate pebble radius inside snowline = 1 mm
    Chosen by hand to match dust evolution and chondrule sizes; this assumption controls the claim that inner-ring growth is dominated by planetesimal accretion.
  • Water mass fraction of icy material beyond snowline = 50%
    Assumed composition split used to classify rocky versus icy planets and to predict water-rich planets at 1 au.
  • Atmospheric mass fraction at gas disk dispersal = 0.003
    Assumed from prior studies; Appendix B shows the radius distribution is not highly sensitive to this choice.
assumptions (6)
  • domain assumption Planetesimals form in narrow rings at sublimation and condensation fronts rather than across a continuous disk.
    Invoked in Sections 1 and 2.2; the entire simulation setup starts from two rings at 0.5-1.5 au and 8-15 au.
  • domain assumption The gas disk evolution follows the 1D profiles of Bitsch et al. (2015b) with alpha=0.004 and metallicity=0.01.
    Appendix A.1; the paper explicitly does not explore other alpha or metallicity values.
  • domain assumption Pebble accretion follows the Lambrechts and Johansen (2014) model with epsilon_D=0.05 and epsilon_p=0.5.
    Appendix A.2; a standard model in the field but not derived in this paper.
  • ad hoc to paper Planetary seeds start at Moon mass in the inner ring and Ceres mass in the outer ring at 0.3 Myr.
    Section 2.2; chosen to make N-body simulations computationally feasible, not directly observed or derived from first principles.
  • domain assumption Complete atmospheric loss occurs for giant impacts with projectile-to-target mass ratio greater than 0.1.
    Section 2.4 and Appendix B; based on Biersteker and Schlichting (2019), with acknowledged uncertainty in impact geometry and core composition.
  • domain assumption Most resonant chains of super-Earths become dynamically unstable within 20-50 Myr after disk dispersal.
    Sections 3.1 and 4.1; motivates stopping simulations at 50 Myr and interpreting surviving resonant pairs as needing late instabilities.

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Pith. "Pith review of Formation of super-Earths and mini-Neptunes from rings of planetesimals." pith.science (2026). https://pith.science/paper/R3E36DQX

@misc{pith2026250103345,
  author       = {Pith},
  title        = {Pith review of: Formation of super-Earths and mini-Neptunes from rings of planetesimals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R3E36DQX}},
  note         = {Machine review of arXiv:2501.03345}
}
read the original abstract

The solar system planetary architecture has been proposed to be consistent with the terrestrial and giant planets forming from material rings at ~1 au and ~5 au, respectively. Here, we show that super-Earths and mini-Neptunes may share a similar formation pathway. In our simulations conducted with a disk alpha-viscosity of 4e-3, super-Earths accrete from rings of rocky material in the inner disk, growing predominantly via planetesimal accretion. Mini-Neptunes primarily originate from rings located beyond the water snowline, forming via pebble accretion. Our simulations broadly match the period-ratio distribution, the intra-system size uniformity, and the planet multiplicity distribution of exoplanets. The radius valley constrains the typical total mass available for rocky planet formation to be less than 3-6 Earth masses. Our results predict that planets at ~1 au in systems with close-in super-Earths and mini-Neptunes are predominantly water-rich. Though relatively uncommon, at ~1% level, such systems might also host rocky Earth-sized planets in the habitable zone that underwent late giant impacts, akin to the Moon-forming event.

Figures

Figures reproduced from arXiv: 2501.03345 by the authors.

Figure 1
Figure 1. shows the mass-doubling timescale of plan￾etary seeds at different disk locations. The location of the inner and outer rings are shown in red and blue, respectively. The solid lines show the planetesi￾mal accretion timescale in the runaway growth regime. The surface density of planetesimals is assumed to be three times heavier than minimum mass solar nebulae (Hayashi 1981). We use a statistical model to compute the … view at source ↗
Figure 2
Figure 2. Snapshots show planetary seeds’ growth and migration from two rings of material. This simulation comes from our M6T2 scenario. The top-left panel shows the starting time of the simulation. The time of each snapshot is shown on the bottom-left of each panel. The color of each dot corresponds to the water mass fraction of each planetary seed. We plot planetesimal and pebble isolation masses with dotted and dashed line… view at source ↗
Figure 3
Figure 3. Radius distribution of planets at orbital periods shorter than 100 days. The black line shows the results ob￾tained in our simulations, including observational bias, and the light-blue line shows the observed planets from the Cali￾fornia Kepler Survey. The red and blue lines show the rocky and icy planets, respectively. We define rocky planets as planets with a water mass fraction lower than 10%. In these simulation… view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Planet radius distribution grouping planets into different ranges of orbital period. From top to bottom, panels show the radius distribution of planets with 0 day < P < 10 day, 10 day < P < 30 day, 30 day < P < 100 day, and 100 day < P < 400 day. The dark-red and dark-…
Figure 6
Figure 6. Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Schematic view of where and how super-Earths and mini-Neptunes form. Planetesimal formation occurs at different locations in the disk, associated with sublimation and condensation lines of silicates and water. Planetesimals and pebbles in the inner and outer rings have…
Figure 9
Figure 9. Figure 9: The histogram of the radius of planets with the different atmospheric mass fraction fatm. We show the simula￾tions with tdisk = 3 Myrs. The planetesimal disk mass Mdisk is labeled in each panel. The blue, green, and orange lines show fatm = 0.01, 0.003, and 0.001, resp…
Figure 10
Figure 10. Figure 10: Representative example of the dynamical evolution of a planetary system during the gas disk phase. Left: time evolution of planetary seeds’ mass. Time is expressed relative to the start time of the simulation. Gray lines represent planetesimals accreted by other plane…
Figure 11
Figure 11. Figure 11: Upper panel: Distance between the radius distribution of our mixed simulations and observations as a faction of the mixing ratio wM3T3. We mix M3T2 and M3T3 simulations. Lower panel: Corresponding radius distributions of mixed simulations with different mixing ratios …
Figure 12
Figure 12. Figure 12: Radius distribution. The left and right columns show simulations with tdisk = 2 Myrs and 3 Myrs, respectively. The respective inner ring mass Mdisk is shown in each panel. The black line shows the outcome of our simulations, including observational bias. The thin red …
Figure 13
Figure 13. Figure 13: Period ratio of adjacent planets. The left and right columns show simulations with tdisk = 2 Myrs and 3 Myrs, respectively. The planetesimal disk mass Mdisk is labeled in each panel. The black line shows the planets obtained in our formation model with the observation…
Figure 14
Figure 14. Figure 14: Radius ratio of adjacent planets. The respective inner ring mass Mdisk is shown in each panel. The black line shows the outcome of our simulations, including observational bias. The thin red and blue solid lines show the distributions of planets grouped into rocky and…
Figure 15
Figure 15. Figure 15: Observed number of planets. The respective inner ring mass Mdisk is shown in each panel. The black line shows the outcome of our simulations, including observational bias. The thin red and blue solid lines show the distributions of planets grouped into rocky and icy c…
Figure 16
Figure 16. Figure 16: Final planetary systems produced in our M3T3 (left panel) and M6T2 (right panel) simulations. The point’s size scales with the planet’s radius, and the color corresponds to its water mass fraction. The green line connects planets in mean motion resonances. The vertica…

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