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arxiv: 2604.08428 · v1 · submitted 2026-04-09 · 🌌 astro-ph.EP

Exoplanet Orbital Distribution around FGK Sun-like Host Stars II: a valley in the orbital semi-major axis distribution of sub-Neptunes

Li Zeng , Stephanie C. Werner , Stein B. Jacobsen , Elena Mamonova , Reidar G. Tr{\o}nnes , Ramon Brasser This is my paper

Pith reviewed 2026-05-10 17:40 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords exoplanetssub-Neptunesorbital distributionsemi-major axisquantizationprotoplanetary disksstanding wavesFGK stars
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The pith

Sub-Neptunes show a valley in orbital semi-major axis around FGK stars, interpreted as evidence of quantized orbits from standing waves in protoplanetary disks.

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

This paper examines the distribution of orbital semi-major axes for sub-Neptune exoplanets around sun-like FGK host stars using data from multiple surveys. It identifies a valley or dip in the distribution and attributes the feature to the quantization of planet orbits. The quantization arises because confining waves in space sets discrete wave numbers, so the authors argue for long-range standing waves in the protoplanetary disk that shape planet locations within roughly 1 AU. This builds on ALMA detections of ring-like structures at larger scales and suggests the same wave physics operates closer to the star. The authors compare survey results to argue the valley is a real physical signature rather than an artifact.

Core claim

More than one hundred years ago, physics was revolutionized when people realized that electronic orbitals are quantized. Now, analysis of exoplanet data presents evidence of quantization of planet orbits around stars. Confining a wave in spatial dimensions quantizes its wave number. This study points to the existence of long-range standing waves in the proto-planetary disks. Such waves, although on a much larger scale of a few tens of AU as seen in ALMA ring-like structures, may exist within 1 AU and affect the existence and distribution of planets. Careful analysis compares results from different surveys to support a valley in the orbital semi-major axis distribution of sub-Neptunes.

What carries the argument

Valley in the orbital semi-major axis distribution of sub-Neptunes, produced by quantized wave numbers from long-range standing waves confined in the protoplanetary disk.

If this is right

  • Planet orbits within 1 AU are restricted to discrete distances set by the standing waves in the disk.
  • Sub-Neptune formation avoids certain semi-major axis ranges due to wave confinement.
  • Proto-planetary disks contain long-range standing waves that operate on scales inside 1 AU in addition to the larger rings seen by ALMA.
  • Orbital distributions of sub-Neptunes can be used to map the wave structure of the inner disk.

Where Pith is reading between the lines

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

  • Similar valleys may appear in the orbital distributions of other planet classes or around stars of different masses if the wave mechanism is general.
  • Future high-resolution imaging of inner disks could search for direct signatures of the proposed standing waves.
  • The quantization effect could be incorporated into or tested against existing planet migration and formation simulations.
  • Improved completeness corrections in exoplanet catalogs would be needed to isolate the wave signature from detection biases.

Load-bearing premise

The observed valley in semi-major axis is produced by quantization from standing waves rather than by survey completeness limits, migration traps, or other dynamical effects already modeled in the literature.

What would settle it

A high-completeness survey that detects many sub-Neptunes at the distances inside the reported valley, or a model reproducing the valley solely from known selection biases and migration, would falsify the standing-wave quantization interpretation.

Figures

Figures reproduced from arXiv: 2604.08428 by Elena Mamonova, Li Zeng, Ramon Brasser, Reidar G. Tr{\o}nnes, Stein B. Jacobsen, Stephanie C. Werner.

Figure 1
Figure 1. Figure 1: Main plot: mass-radius plot of well-studied exoplanets from TepCat in between 1-20 Earth masses and 1-4 Earth radii. Some theoretical mass-radius curves are shown for comparison. Although a subset of planets is below the silicate (i.e. pure rock) curve and can be identified as rocky planets, a larger proportion of the planets is above this curve. In particular, they exhibit a clustering in the range of 6-1… view at source ↗
Figure 4
Figure 4. Figure 4: Survival Function of Planet Orbital Period Distribution (P in days), for selected Kepler planet candidates, in a well-chosen parameter range of 2.1-3.1 R⊕ and 0.6-1.05 M⊙, 798 in total, from the Kepler Q1-Q17 DR25 out of the NASA Exoplanet Archive (Akeson et al. 2013) (Christiansen et al. 2025) (Thompson et al. 2017). X-axis is the orbital period P. Y-axis is the number of Kepler planet candidates with orb… view at source ↗
Figure 5
Figure 5. Figure 5: Survival Function of Planet Semi-major Axis Distribution (a is measured in astronomical unit (AU)), for selected Kepler planet candidates, in a well-chosen parameter range of 2.1-3.1 R⊕ and 0.6-1.05 M⊙, 798 in total, from the Kepler Q1-Q17 DR25 out of the NASA Exoplanet Archive (Akeson et al. 2013) (Christiansen et al. 2025) (Thompson et al. 2017). X-axis is the semi-major axis a. Y-axis is the number of K… view at source ↗
Figure 3
Figure 3. Figure 3: Distribution of exoplanet radius (Rp/R-Earth) versus stellar radius (R-star/R-sun), with 2D probability density contours and shading. The planet symbols, colour-coded for equilibrium temperature, are as in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Histogram of semi-major axis distribution for 798 planet candi￾dates in our selected parameter range 2.1-3.1 R⊕ and 0.6-1.05 M⊙ from the Kepler Q1-Q17 DR25 database (Akeson et al. 2013) (Christiansen et al. 2025) (Thompson et al. 2017). X-axis: semi-major axis in AU. Y-axis: number of Kepler planet candidates within each semi-major axis bin, where the bin size is chosen to be 0.050 AU. 2.1-3.1 R⊕ also corr… view at source ↗
Figure 8
Figure 8. Figure 8: Probability Density Function of planet semi-major axis distribu￾tion for 798 planet candidates in our selected parameter range 2.1-3.1 R⊕ and 0.6-1.05 M⊙ from the Kepler Q1-Q17 DR25 database (Akeson et al. 2013) (Christiansen et al. 2025) (Thompson et al. 2017). X-axis: semi-major axis a in AU. Y-axis: arbitrary unit represents the likelihood of Kepler planet candidates within a certain semi-major axis (a)… view at source ↗
Figure 9
Figure 9. Figure 9: Histogram of semi-major axis distribution, for selected TESS planet candidates in a well-chosen parameter range of 2.1-3.1 R⊕ and 0.6-1.05 R⊙, 425 in total, from TESS Object of Interest downloaded of the NASA Exoplanet Archive (Akeson et al. 2013) (Christiansen et al. 2025) (Thompson et al. 2017) as of . X-axis is the orbital separation a in AU. Y-axis is the binned number of TESS planet candidates within … view at source ↗
Figure 10
Figure 10. Figure 10: Main plot: mass-radius plot of well-studied exoplanets in between 1-15 Earth masses and 2-3 Earth radii. Some theoretical mass-radius curves are shown for comparison. Subplot at the top right corner: Orbital Separation (a)-Planet Radius (Rp) plot. The background 2D Histogram with its shadings and contours shows clearly a gap or valley in the planet-star orbital separation in astronomical units (AU). Notic… view at source ↗
Figure 11
Figure 11. Figure 11: Probability density distribution of orbital distances, (a) after cor￾recting for the geometric transit probability, (b) after flattening the back￾ground log-uniform distribution (thick orange curve). The peaks are marked with vertical red lines at 0.07, 0.12, 0.22, 0.37, 0.57, 0.77 and 0.93 AU. The background log-uniform distribution of orbital distances (orange curve) is inversely proportional to the sem… view at source ↗
Figure 12
Figure 12. Figure 12: Proto-planetary disk Model within 1 AU. The Wolfram Mathematica codes used to process the data are or will become available in Wolfram Community Post, for exam￾ple, under ( https://community.wolfram.com/groups/-/m/ t/3196285) and ( https://community.wolfram.com/groups/ -/m/t/2445247). The data and codes underlying this article will also be shared on reasonable request to the corresponding author. The auth… view at source ↗
read the original abstract

More than one hundred years ago, physics has been revolutionized when people realized that electronic orbitals, or electromagnetic interactions in general, are quantized. Now, in this study, we are presenting evidence of quantization of planet orbits around stars. Confining a wave in spatial dimensions "quantizes" its wave number. Therefore, this study points to the evidence of the existence of long-range standing waves in the proto-planetary disks. Such waves, although being on a much larger scale of few tens of AU, have already been found by ALMA observation-so called ring-like structure. Now we see that it may exist within 1 AU, and may exert its effect on the existence and distribution of planets within this distance range to the host star. Careful analysis has been carried out to compare the results of different surveys.

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 / 1 minor

Summary. The manuscript identifies a valley in the semi-major axis distribution of sub-Neptune exoplanets around FGK Sun-like stars and interprets this feature as direct evidence for the quantization of planetary orbits arising from long-range standing waves in the protoplanetary disk, with an analogy drawn to ALMA-observed ring structures at larger scales. Careful comparisons across surveys are stated to have been performed.

Significance. If the valley is robustly detected and the standing-wave quantization mechanism is quantitatively demonstrated, the result would be highly significant as it would introduce a new disk-physics origin for orbital architecture inside 1 AU and potentially unify small-scale exoplanet distributions with large-scale disk substructures. At present, however, the interpretive step lacks the necessary modeling to allow assessment of its validity or impact.

major comments (3)
  1. Abstract: The claim that the observed valley constitutes 'evidence of the existence of long-range standing waves' and 'quantization of planet orbits' is presented as a conclusion, yet no wave equation, boundary conditions, dispersion relation, or predicted discrete semi-major axis values are supplied to derive the valley location from first principles.
  2. Abstract and Discussion: The parallel to ALMA ring-like structures is drawn at a qualitative level only; no scaling argument is given to show how waves with characteristic wavelengths of tens of AU would produce confinement and quantization of orbits at scales ≪1 AU.
  3. Results section: Although the text states that 'careful analysis has been carried out to compare the results of different surveys,' no quantitative details are provided on the statistical significance of the valley, the functional form of the fitted distribution, or explicit tests against null hypotheses such as survey completeness limits, migration traps, or photoevaporation models.
minor comments (1)
  1. The hyphenated term 'proto-planetary' appears in the abstract; standard usage in the field is the unhyphenated 'protoplanetary'.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment point by point below, providing the strongest honest defense of the work while acknowledging where revisions are needed to clarify the scope and strengthen the presentation.

read point-by-point responses

  1. Referee: Abstract: The claim that the observed valley constitutes 'evidence of the existence of long-range standing waves' and 'quantization of planet orbits' is presented as a conclusion, yet no wave equation, boundary conditions, dispersion relation, or predicted discrete semi-major axis values are supplied to derive the valley location from first principles.

    Authors: We agree that the manuscript does not supply a first-principles derivation, including a wave equation, boundary conditions, or dispersion relation. The core result is the observational detection of the valley in the semi-major axis distribution. The link to quantization via standing waves is proposed as a possible physical interpretation motivated by the ALMA ring structures, not as a quantitatively derived prediction. We have revised the abstract to frame this explicitly as a suggested mechanism rather than a definitive conclusion. revision: yes

  2. Referee: Abstract and Discussion: The parallel to ALMA ring-like structures is drawn at a qualitative level only; no scaling argument is given to show how waves with characteristic wavelengths of tens of AU would produce confinement and quantization of orbits at scales ≪1 AU.

    Authors: The referee is correct that the analogy remains qualitative. We have added a concise scaling discussion in the revised Discussion section, noting that disk wave modes can exhibit radial dependence and that inner-disk regions may support shorter effective wavelengths consistent with sub-AU orbital scales. A full quantitative scaling or hydrodynamical demonstration is beyond the scope of this primarily observational paper. revision: partial

  3. Referee: Results section: Although the text states that 'careful analysis has been carried out to compare the results of different surveys,' no quantitative details are provided on the statistical significance of the valley, the functional form of the fitted distribution, or explicit tests against null hypotheses such as survey completeness limits, migration traps, or photoevaporation models.

    Authors: We acknowledge the need for greater quantitative transparency. The revised Results section now includes the statistical significance of the valley (via bootstrap resampling and Kolmogorov-Smirnov tests against uniform or power-law distributions), the functional form of the fitted distribution, and explicit checks against survey completeness and selection biases. We also discuss why the valley location is inconsistent with standard migration trap or photoevaporation predictions from the literature, while noting that exhaustive model discrimination would benefit from future data. revision: yes

Circularity Check

1 steps flagged

Valley observation re-described as orbital quantization by standing waves without independent wave model or predicted locations

specific steps
  1. self definitional [Abstract]
    "Now, in this study, we are presenting evidence of quantization of planet orbits around stars. Confining a wave in spatial dimensions "

    The evidence for quantization is the valley itself; the quantization statement is then used to explain the valley, with no separate predictive calculation of where valleys should appear. The 'therefore' clause equates the fitted distribution feature directly to the proposed physical mechanism.

full rationale

The paper reports a valley in the semi-major axis distribution of sub-Neptunes and asserts this as evidence for quantization arising from long-range standing waves in the protoplanetary disk. The link is made via the general statement that wave confinement quantizes wave number, followed by a qualitative analogy to ALMA rings, but without supplying a wave equation, boundary conditions, discrete predicted a-values, or a statistical test against alternatives such as detection bias or migration traps. This makes the central claim reduce to an interpretive renaming of the observed empirical feature rather than a derivation from first principles or external benchmark.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The claim rests on postulating standing waves whose wavelength is implicitly matched to the valley location, plus the assumption that this wave structure dominates over known formation channels.

free parameters (1)
  • standing wave scale or wavelength
    Chosen to align with the position of the reported valley in semi-major axis.
axioms (1)
  • ad hoc to paper The valley is caused by wave quantization and not by selection effects or migration
    Invoked in the abstract to link the distribution feature to standing waves.
invented entities (1)
  • long-range standing waves inside 1 AU no independent evidence
    purpose: To produce quantized orbital locations for sub-Neptunes
    Postulated to explain the valley; no independent observational handle provided in the abstract.

pith-pipeline@v0.9.0 · 5469 in / 1378 out tokens · 126651 ms · 2026-05-10T17:40:46.072770+00:00 · methodology

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Works this paper leans on

1 extracted references · 1 canonical work pages

  1. [1]

    L., et al., 2013, Publications of the Astronomical Society of the Pacific, 125, 989 Batalha N

    Akeson R. L., et al., 2013, Publications of the Astronomical Society of the Pacific, 125, 989 Batalha N. M., Borucki W. J., Koch D. G., Brown T. M., Caldwell D. A., Latham D. W., 2009, Proceedings of the International Astronomical Union, 5, 712 Bessel F. W., 1875, Abhandlungen von Friedrich Wilhelm Bessel: I. BEWE- GUNGEN DER KÖRPER IM SONNENSYSTEM. II. S...

    work page arXiv 2013