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arxiv: 2606.11330 · v1 · pith:UINPRQSJnew · submitted 2026-06-09 · 🌌 astro-ph.EP

Do Super-Puffs Defy Core Accretion? Population-Wide Interior Structure Constraints

Nicholas T. Marston , Juliette Becker , Alex R. Howe This is my paper

Pith reviewed 2026-06-27 11:32 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords super-puffscore accretionexoplanet interiorslow-density planetsplanet formationhydrostatic structure modelsexoplanet populations
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The pith

Most cold super-puffs fit core accretion once age is adjusted, but six planets do not.

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

The paper applies hydrostatic interior models to 34 cold super-puffs to test whether their extremely low densities can arise under standard core accretion. Twenty-eight planets match the expected structures after accounting for their ages. Six planets remain inconsistent even after that adjustment and point toward additional processes such as rings or late dynamical heating. The models also show that impacts can sustain super-puff densities for roughly a billion years while extra radiogenic heat cannot.

Core claim

Hydrostatic interior structures computed for 34 cold super-puffs show that 28 are reproducible by core-accretion models once planet age is varied. The six planets that remain inconsistent are HIP 41378 f, Kepler-30 d, Kepler-51 d, Kepler-177 c, TOI-1420 b, and WASP-107 b. All but TOI-1420 b become compatible if an extra heat source is allowed. Late impacts can produce the required inflation for up to 1 Gyr; radiogenic heating cannot.

What carries the argument

Population-wide hydrostatic interior structure calculations that match observed mass and radius while allowing age and composition to vary within core-accretion limits.

If this is right

  • 28 of the 34 cold super-puffs remain consistent with core accretion.
  • Late impacts can inflate sub-Neptunes to super-puff densities for up to 1 Gyr.
  • Radiogenic heating alone is insufficient to reach the observed densities.
  • Five of the six inconsistent planets could be reconciled with an added heat source.
  • A compiled index lists all currently known super-puffs.

Where Pith is reading between the lines

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

  • More precise mass and radius data on the six exceptions could separate ring explanations from impact heating.
  • Super-puff occurrence may trace rare dynamical events layered on top of standard formation.
  • Applying the same modeling approach to irradiated super-puffs could quantify how much of their low density is due to stellar heating versus formation history.

Load-bearing premise

The published masses, radii, and ages are accurate and the hydrostatic models capture the relevant physics without needing extra free parameters beyond age.

What would settle it

A new mass or radius measurement for any of the six listed planets that falls outside the range allowed by the models even when extra heating or rings are included.

Figures

Figures reproduced from arXiv: 2606.11330 by Alex R. Howe, Juliette Becker, Nicholas T. Marston.

Figure 1
Figure 1. Figure 1: Bulk densities for sub-giant planets with well– constrained reported mass and radius measurements. Plan￾ets in our sample are denoted as yellow stars. Data sourced from NASA Exoplanet Archive on 12/23/2025 (J. L. Chris￾tiansen et al. 2025). (The extreme high density outlier is Kepler-131c, based on the RV solution published by G. W. Marcy et al. 2014) In this work, we consider the possible interior struc￾t… view at source ↗
Figure 2
Figure 2. Figure 2: The hot-cold distribution of our sample. Shown on the horizontal axis is each planet’s insolation flux com￾pared to Earth (units of S⊕). Orbital period (in days) is shown on the vertical axis for comparison. The dashed line denotes the hot-cold boundary used in this work (160S⊕). For the circumbinary Kepler-47 system, we use the time-av￾eraged insolation flux reported in Section 6.4 of J. A. Orosz et al. (… view at source ↗
Figure 3
Figure 3. Figure 3: A set of modeled Mcore −Rp curves for TOI-1338 b, computed for a range of atmospheric specific entropies and metallicities. The inset shows the point where several of the curves achieve TOI-1338 b’s measured radius, shown as a solid line with the shaded region representing measurement uncertainty. tion of the HSE models described in A. R. Howe et al. (2014) and A. R. Howe & A. Burrows (2015). For each plan… view at source ↗
Figure 4
Figure 4. Figure 4: The interior structure solution that achieved the highest fcore for each planet in our sample with K = 7.0kB/baryon, shown with respect to the Core Mass Mcore (horizontal axis) and the Core (and Envelope) Mass Fraction fcore (fenv) (vertical axis). Note that we find the fcore for a given solution to be monotonically increasing with K ∈ [5.5, 7.0]kB/baryon. Results corresponding to each of the core composit… view at source ↗
Figure 5
Figure 5. Figure 5: The measured orbital period and densities for our modeled cold super-puffs, in the context of the broader ex￾oplanet sample as a whole (grey points). Super-puff points are color coded according to their classification in Section 3.2. Left-facing triangles, right-facing triangles, and dia￾monds denote planets whose adopted parameters are consis￾tent with TTV measurements, RV measurements, or both, respectiv… view at source ↗
Figure 6
Figure 6. Figure 6: Examples of the evolution of Radius (top left), Entropy (top right), Envelope Mass Fraction fenv (bottom left), and Mass (bottom right) for 20% envelope mass planet models with enhanced radionuclide abundances A = α × A⊕. Evolution tracks corresponding to log10 α = 0.5, 1.0, 1.5, and 2 are shown. We derive the effects of increased radiogenic heating by comparing each track to the 20% fenv control planet (d… view at source ↗
Figure 7
Figure 7. Figure 7: The maximum radius inflation, ∆R = R(t) − Rcontrol(t), achieved with 10%, 20%, 30% envelope mass fraction models for a range of enhanced ra￾diogenic abundances, where model abundance A = α × A⊕ for each of 40K, 232Th, 235U, and 238U. For context, the ∆R needed to reach 0.3 g/cm3 and become a super-puff is > 1 R⊕ for all models. These results suggest that radiogenic heating is not sufficient to produce plan… view at source ↗
Figure 8
Figure 8. Figure 8: Examples of the evolution of Radius (top left), Entropy (top right), Envelope Mass Fraction fenv (bottom left), and Mass (bottom right) after an impact event for our 10% initial envelope mass model. Impactor masses of Mimp/Mcore = 5×10−4 , and 1.0, 1.7, 2.3, 2.8 × 10−3 are shown. Note that the uneven steps are a consequence of the code’s use of entropy, rather than time, as the iterating variable. tion) ca… view at source ↗
Figure 9
Figure 9. Figure 9: The maximum radius inflation, ∆R = R(t) − Rcontrol(t), achieved with the 10%, 20%, 30% envelope mass fraction models described above with respect to the ratio of impact mass to core mass. The two dashed lines represent the approximate radius inflation required to lower the planet’s bulk density below 0.3g/cm3 for 20% (top) and 30% (middle) envelope mass models. The dot-dashed line denotes the point at whic… view at source ↗
read the original abstract

Sub-Saturn mass planets with extremely low bulk densities $(\rho\lesssim0.3)\mathrm{g/cm^3}$, or ``super-puffs'', are one of the most interesting and least understood populations of exoplanets. While many short-period super-puffs can be attributed to the effects of high irradiation and star-planet interactions, cold super-puffs appear to challenge the expectations of core accretion theory. We constrain the possible properties of 34 cold super-puffs by computing hydrostatic interior structures using PlanetSolver. We find that 28 planets in our sample can be reproduced by models consistent with core accretion based on their observed masses and radii and adjusting for planet age. We identify HIP 41378 f, Kepler-30 d, Kepler-51 d, Kepler-177 c, TOI-1420 b, and WASP-107 b as planets inconsistent with core accretion theory which necessitate a non-standard explanation (e.g. exo-rings). With the exception of TOI-1420 b, core accretion-compatible solutions are possible for these planets if an additional heat source is present. We modify planetary evolution models to determine whether enhanced radiogenic heating or late impacts with sub-planetary mass objects can plausibly inflate sub-Neptunes enough to achieve super-puff densities. We find that the effects of radiogenic heating are insufficient to produce super-puff densities, but that impacts can in many cases produce the necessary inflation for upwards of 1Gyr. We also compile and present here an index of all currently known super-puffs.

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

3 major / 2 minor

Summary. The manuscript claims that hydrostatic interior structure calculations with PlanetSolver for 34 cold super-puffs show that 28 can be reproduced by core-accretion models (rocky/icy core + H/He envelope) once planet age is adjusted as a free parameter, while six specific planets (HIP 41378 f, Kepler-30 d, Kepler-51 d, Kepler-177 c, TOI-1420 b, WASP-107 b) remain inconsistent even after age adjustment and require non-standard explanations such as exo-rings; the authors further modify evolution models to show that late impacts can sustain the necessary inflation for up to ~1 Gyr while radiogenic heating cannot, and they compile an index of all known super-puffs.

Significance. If robust, the work supplies a systematic, population-level test of whether cold super-puffs challenge core accretion, supporting the standard theory for the large majority while isolating a small set of outliers whose explanation may involve rings or impacts. The explicit comparison of radiogenic versus impact heating and the public index of super-puffs are concrete contributions that can be used by the community. The strength lies in the uniform application of a single structure code across the sample.

major comments (3)
  1. [§4] §4 (inconsistent planets subsection): the central claim that the six named planets cannot be reproduced by core-accretion models rests on the failure of PlanetSolver to match observed radii after age adjustment; however, the manuscript provides no tabulated or plotted sensitivity of the required ages to the observational uncertainties in mass, radius, and stellar age, so it is unclear whether the inconsistency survives within 1-σ error bars.
  2. [Methods] Methods (PlanetSolver description): the declaration of inconsistency for the six planets assumes that PlanetSolver includes all relevant physics at the relevant P-T conditions; the text does not report the specific EOS, opacity tables, or atmospheric boundary conditions used, nor does it test the effect of plausible additions such as composition gradients or enhanced envelope opacities that could alter the radius-age relation.
  3. [§5] §5 (impact-heating models): while impacts are stated to produce the necessary inflation for upwards of 1 Gyr, the manuscript does not quantify the minimum impactor mass or impact rate required for each of the six planets, nor does it compare those rates to expected dynamical environments, leaving the physical plausibility of the scenario untested.
minor comments (2)
  1. [Abstract] Abstract: the total sample of 34 planets is stated without a forward reference to the table or section that lists all objects and their adopted M, R, and age values.
  2. [Super-puff index] Super-puff index: the selection criteria (density threshold, orbital-period cut, etc.) used to compile the index should be stated explicitly so that the catalog can be reproduced or extended.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive report and positive evaluation of the manuscript's contributions. We address each major comment below, agreeing where revisions are warranted to improve clarity and robustness.

read point-by-point responses

  1. Referee: [§4] the central claim that the six named planets cannot be reproduced by core-accretion models rests on the failure of PlanetSolver to match observed radii after age adjustment; however, the manuscript provides no tabulated or plotted sensitivity of the required ages to the observational uncertainties in mass, radius, and stellar age, so it is unclear whether the inconsistency survives within 1-σ error bars.

    Authors: We agree that an explicit sensitivity analysis to observational uncertainties would strengthen the claim of inconsistency. In the revised manuscript we will add a new subsection (or appendix) that tabulates and plots the range of required ages for the six planets when mass, radius, and stellar age are varied within their 1-σ uncertainties. This will directly show whether any of the six planets become consistent with core accretion within errors. revision: yes

  2. Referee: [Methods] the declaration of inconsistency for the six planets assumes that PlanetSolver includes all relevant physics at the relevant P-T conditions; the text does not report the specific EOS, opacity tables, or atmospheric boundary conditions used, nor does it test the effect of plausible additions such as composition gradients or enhanced envelope opacities that could alter the radius-age relation.

    Authors: The methods section references the PlanetSolver implementation but does not list the exact EOS, opacity tables, or boundary conditions. We will expand the methods to explicitly state the EOS (e.g., the specific H/He and rock/ice tables), opacity sources, and atmospheric boundary conditions employed. We will also add a short discussion of why composition gradients and enhanced opacities were not included in the baseline runs, together with a qualitative assessment of how they might affect the radius-age relation for the outlier planets. revision: yes

  3. Referee: [§5] while impacts are stated to produce the necessary inflation for upwards of 1 Gyr, the manuscript does not quantify the minimum impactor mass or impact rate required for each of the six planets, nor does it compare those rates to expected dynamical environments, leaving the physical plausibility of the scenario untested.

    Authors: The impact-heating calculations demonstrate that sub-planetary impacts can maintain the required radii for ~1 Gyr, which is the central result. A full per-planet calculation of minimum impactor mass and rate, including comparison to each system's dynamical environment, would require additional assumptions about orbital architectures and is outside the scope of the present study. We will nevertheless add a brief paragraph that reports the minimum impactor masses implied by our models for the six planets and notes that such rates are within the range seen in some young systems, while acknowledging that system-specific N-body work would be needed for a definitive test. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is a direct model-data comparison

full rationale

The paper runs PlanetSolver hydrostatic models on observed M, R, and age values to test whether standard core-accretion structures can reproduce the radii. The 28/6 split is an output of that comparison, not a re-expression of any fitted parameter or self-citation. Age is treated as an external observational input rather than a free parameter tuned to force agreement. No equations or claims reduce a prediction to its own inputs by construction, and the central claim remains falsifiable against independent M/R/age measurements and model physics.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The analysis rests on standard assumptions of hydrostatic equilibrium and core-accretion growth tracks plus the ability to add an ad-hoc heat source or impact heating. No new entities are postulated beyond the suggestion of exo-rings for a subset of cases.

free parameters (2)
  • planet age adjustment
    Age is adjusted to find core-accretion consistent solutions; exact fitting procedure and priors not visible in abstract.
  • additional heat source magnitude
    Introduced to reconcile the six outliers with core accretion; magnitude chosen to match observed radii.
axioms (2)
  • standard math Planetary interiors obey hydrostatic equilibrium
    Invoked by the use of PlanetSolver for structure calculations.
  • domain assumption Observed mass and radius are accurate inputs for interior modeling
    Central to all consistency checks.
invented entities (1)
  • exo-rings no independent evidence
    purpose: To explain anomalously low densities for the six outliers
    Suggested as a non-standard explanation; no independent evidence provided in abstract.

pith-pipeline@v0.9.1-grok · 5820 in / 1482 out tokens · 19715 ms · 2026-06-27T11:32:59.496730+00:00 · methodology

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