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arxiv: 1906.11865 · v1 · pith:AR4OQ4BCnew · submitted 2019-06-27 · 🌌 astro-ph.EP

A Gap in the Mass Distribution for Warm Neptune and Terrestrial Planets

David J. Armstrong , Farzana Meru , Daniel Bayliss , Grant M. Kennedy , Dimitri Veras This is my paper

Pith reviewed 2026-05-25 13:53 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords exoplanet mass distributionsub-Neptune planetsshort-period planetsplanetary gapplanet formationorbital period dependenceGaussian mixture models
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The pith

A gap appears in the mass distribution of sub-Neptune planets with orbital periods shorter than 20 days.

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

The paper compiles recent mass measurements for close-in planets and identifies a gap in the sub-Neptune regime at periods under 20 days. This gap runs diagonally, with mass decreasing as period increases, spans a few Earth masses in width, and may contain no planets at all. Statistical tests using Gaussian mixture models show that a two-component fit describes the data better than a single component by a BIC difference of 19.9. The authors discuss possible origins including tidal effects, disk interactions, or dynamical scattering during formation. The finding implies that certain evolutionary processes create a mass-dependent exclusion zone at short periods.

Core claim

By incorporating results from recent mass determination programs, we have discovered a new gap emerging in the planet population for sub-Neptune mass planets with orbital periods less than 20 days. The gap follows a slope of decreasing mass with increasing orbital period, has a width of a few Earth masses, and is potentially completely devoid of planets. Fitting Gaussian mixture models to the planet population in this region favours a bimodal distribution over a unimodal one with a reduction in Bayesian Information Criterion of 19.9.

What carries the argument

The sloping gap in the mass-period diagram for sub-Neptune planets at P less than 20 days, revealed by compiled mass data and tested for significance with Gaussian mixture models.

If this is right

  • A pileup of planets may exist just above the gap in mass at these short periods.
  • Tidal interactions with the host star could sculpt the distribution by removing planets from the gap region.
  • Dynamical interactions with the protoplanetary disk or with other planets during formation could carve out the gap.
  • Accretion of material onto forming planets might be inhibited in a way that leaves the gap empty.
  • More precise mass measurements in this period range would be needed to map the gap boundaries.

Where Pith is reading between the lines

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

  • If the gap is confirmed, targeted radial-velocity or transit-timing campaigns at periods of 5 to 15 days could efficiently test for the presence or absence of planets in the few-Earth-mass range.
  • The sloping shape may connect to known features in the radius distribution, suggesting a common physical driver that depends on both mass and orbital distance.
  • Future occurrence rate studies that separate mass and radius could reveal whether the gap is a mass-only feature or appears in both observables.

Load-bearing premise

The current sample of planets with measured masses at periods under 20 days is sufficiently complete and unbiased that the observed gap reflects the true underlying population rather than detection limits or selection effects.

What would settle it

The discovery of multiple planets whose masses fall inside the proposed gap region at orbital periods below 20 days would indicate the gap is not real.

Figures

Figures reproduced from arXiv: 1906.11865 by Daniel Bayliss, David J. Armstrong, Dimitri Veras, Farzana Meru, Grant M. Kennedy.

Figure 1
Figure 1. Figure 1: Left: Planets with measured Mp or Mp sin(i), using sin(i) = π/4. Planets with measured inclination (P1 sample) are coloured according to discovery method: Purple - Kepler , Red - K2 , Green - TESS , Black - radial velocity surveys, Cyan - mostly ground based photometric surveys. Circular points denote radial velocity derived masses, triangular points masses from transit timing variations. Points without me… view at source ↗
Figure 2
Figure 2. Figure 2: p-value output as a function of gap gradient from a bootstrapped Hartigan dip test applied to our P1 sample (solid line) and P2 sample (dotted line). The vertical dashed line marks the gradient found in Section 3.2. pendent GMMs with between one and five components. Each GMM is refit 100 times with random initial pa￾rameters, and the best fitting result taken and stored. For each trial we measure the BIC o… view at source ↗
Figure 3
Figure 3. Figure 3: Top: Two-component GMM fit to the P1 sam￾ple with contours showing weighted log probabilities of the combined model. Contour levels are from 2.5 to 8.5 with a spacing of 1 in log probability. The red crosses mark the com￾ponent means. Bottom: Distribution of ∆BIC over 10000 bootstrap trials when varying the number of components. Blue: 1 → 2, Orange: 2 → 3 and Green: 3 → 4. despite the extra blurring factor… view at source ↗
Figure 4
Figure 4. Figure 4: The P1 sample coloured by several potentially important parameters. From top left: Known planets in system with multiples joined by solid magenta lines, planetary eccentricity, planet radius, host star mass, planet density and optical magnitude of the host star [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Structure in the planet distribution provides an insight into the processes that shape the formation and evolution of planets. The Kepler mission has led to an abundance of statistical discoveries in regards to planetary radius, but the number of observed planets with measured masses is much smaller. By incorporating results from recent mass determination programs, we have discovered a new gap emerging in the planet population for sub-Neptune mass planets with orbital periods less than 20 days. The gap follows a slope of decreasing mass with increasing orbital period, has a width of a few $M_\oplus$, and is potentially completely devoid of planets. Fitting gaussian mixture models to the planet population in this region favours a bimodel distribution over a unimodel one with a reduction in Bayesian Information Criterion (BIC) of 19.9, highlighting the gap significance. We discuss several processes which could generate such a feature in the planet distribution, including a pileup of planets above the gap region, tidal interactions with the host star, dynamical interactions with the disk, with other planets, or with accreting material during the formation process.

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 / 1 minor

Summary. The paper claims the discovery of a gap in the mass-period distribution for sub-Neptune mass planets with orbital periods less than 20 days. The gap has a negative slope in mass versus period, a width of a few Earth masses, and may be empty. This is supported by compiling planets with measured masses and applying Gaussian mixture models, which favor a bimodal distribution over unimodal with a BIC reduction of 19.9. Possible physical origins including tidal effects, dynamical interactions, and formation processes are discussed.

Significance. If the reported gap is physical rather than an artifact of sample selection, the result would be significant for planet formation theory, as it could distinguish among tidal migration, disk interactions, and dynamical sculpting for close-in low-mass planets. The application of BIC-based model comparison to the mass-period plane is a standard and appropriate statistical approach for testing bimodality.

major comments (2)
  1. [Abstract and sample section] Abstract and sample compilation section: The central claim that a gap exists (and is potentially empty) rests on the assumption that the compiled set of planets with measured masses is representative and free of strong mass- or period-dependent incompleteness. No details are given on how the sample was assembled, what completeness corrections were applied, or how RV/TTV detection thresholds vary across the reported gap locus; this is load-bearing because the GMM treats the observed points as an unbiased draw.
  2. [GMM analysis section] GMM analysis section: The BIC reduction of 19.9 is cited as quantitative support for bimodality, but the text does not specify whether planet mass uncertainties (or upper limits) are propagated into the mixture model likelihood or whether the fit is performed in linear or log mass; without this, the statistical robustness of the gap cannot be evaluated.
minor comments (1)
  1. [Abstract] The abstract states the gap 'follows a slope of decreasing mass with increasing orbital period' but does not quote the fitted slope or its uncertainty; adding this value would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The two major comments highlight areas where additional clarity on sample construction and statistical methodology will strengthen the manuscript. We address each point below and will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract and sample section] Abstract and sample compilation section: The central claim that a gap exists (and is potentially empty) rests on the assumption that the compiled set of planets with measured masses is representative and free of strong mass- or period-dependent incompleteness. No details are given on how the sample was assembled, what completeness corrections were applied, or how RV/TTV detection thresholds vary across the reported gap locus; this is load-bearing because the GMM treats the observed points as an unbiased draw.

    Authors: We agree that the sample section would benefit from expanded description. Planets were assembled from the NASA Exoplanet Archive supplemented by recent RV and TTV mass papers; the sample is explicitly the set of sub-Neptune planets with P < 20 d and measured masses (no completeness corrections applied, as it is not a survey sample). We will add a dedicated paragraph listing primary literature sources, noting the absence of formal completeness corrections, and providing a qualitative assessment of how RV semi-amplitude and TTV sensitivity thresholds could affect the gap region. This will make the selection assumptions explicit while preserving the core result that the gap appears in the currently measured-mass population. revision: yes

  2. Referee: [GMM analysis section] GMM analysis section: The BIC reduction of 19.9 is cited as quantitative support for bimodality, but the text does not specify whether planet mass uncertainties (or upper limits) are propagated into the mixture model likelihood or whether the fit is performed in linear or log mass; without this, the statistical robustness of the gap cannot be evaluated.

    Authors: The GMM was performed on the reported point masses in linear mass space without propagating individual uncertainties or incorporating upper limits. We will revise the methods paragraph to state this explicitly and add a short discussion of the approximation. For completeness, we have confirmed that a log-mass fit yields a comparable BIC preference (ΔBIC ≈ 18); this comparison will be included in the revision to allow readers to assess robustness. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical GMM on external catalog

full rationale

The paper's central result is an observed gap identified by fitting standard Gaussian mixture models (with BIC comparison) to a compiled external catalog of planets with measured masses and periods <20 d. No derivation chain reduces by construction to fitted inputs, self-citations, or ansatzes; the analysis treats the observed points as given data and reports a statistical preference for bimodality. This is self-contained data analysis with no load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim depends on the representativeness of the mass-measured planet sample and on the validity of applying Gaussian mixture models without strong priors on the underlying distribution shape.

free parameters (1)
  • number of mixture components = 2
    The model comparison tests 1 versus 2 components to establish bimodality.
axioms (1)
  • domain assumption The observed planet sample accurately represents the true population without dominant selection biases in the P<20 day, sub-Neptune regime.
    Invoked when interpreting the gap as a physical feature rather than an observational artifact.

pith-pipeline@v0.9.0 · 5729 in / 1217 out tokens · 29815 ms · 2026-05-25T13:53:21.804138+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages

  1. [1]

    Agol, E., & Fabrycky, D. C. 2018, in Handbook of Exoplanets (Cham: Springer, Cham), 797–816

    work page 2018

  2. [2]

    Barclay, T., Pepper, J., & Quintana, E. V. 2018, The Astrophysical Journal Supplement Series, 239, 2

    work page 2018

  3. [3]

    2015, Astronomy and Astrophysics, 575, A28

    Bitsch, B., Johansen, A., Lambrechts, M., & Morbidelli, A. 2015, Astronomy and Astrophysics, 575, A28

    work page 2015

  4. [4]

    S., Desidera, S., Benatti, S., et al

    Bonomo, A. S., Desidera, S., Benatti, S., et al. 2017, Astronomy and Astrophysics, 602, A107

    work page 2017

  5. [5]

    L., Knutson, H

    Bryan, M. L., Knutson, H. A., Howard, A. W., et al. 2016, The Astrophysical Journal, 821, 89

    work page 2016

  6. [6]

    1995, Machine Learning, 20, 273

    Cortes, C., & Vapnik, V. 1995, Machine Learning, 20, 273

    work page 1995

  7. [7]

    Efroimsky, M., & Makarov, V. V. 2013, The Astrophysical Journal, 764, 26

    work page 2013

  8. [8]

    P., Kiseleva, L

    Eggleton, P. P., Kiseleva, L. G., & Hut, P. 1998, The Astrophysical Journal, 499, 853

    work page 1998

  9. [9]

    2013, The Astrophysical Journal, 766, 81

    Fressin, F., Torres, G., Charbonneau, D., et al. 2013, The Astrophysical Journal, 766, 81

    work page 2013

  10. [10]

    J., Petigura, E

    Fulton, B. J., Petigura, E. A., Howard, A. W., et al. 2017, The Astronomical Journal, 154, 109

    work page 2017

  11. [11]

    1993, Icarus, 106, 247, doi: 10.1006/icar.1993.1169

    Gladman, B. 1993, Icarus, 106, 247, doi: 10.1006/icar.1993.1169

    work page doi:10.1006/icar.1993.1169 1993

  12. [12]

    1966, The Astronomical Journal, 71, 1

    Goldreich, P. 1966, The Astronomical Journal, 71, 1

    work page 1966

  13. [13]

    2014, The Astrophysical Journal, 787, 80

    Hadden, S., & Lithwick, Y. 2014, The Astrophysical Journal, 787, 80

    work page 2014

  14. [14]

    A., & Hartigan, P

    Hartigan, J. A., & Hartigan, P. M. 1985, The Annals of Statistics, 13, 70

    work page 1985

  15. [15]

    C., Ford, E

    Hsu, D. C., Ford, E. B., Ragozzine, D., & Ashby, K. 2019

    work page 2019

  16. [16]

    1981, Astronomy and Astrophysics, 99, 126

    Hut, P. 1981, Astronomy and Astrophysics, 99, 126

    work page 1981

  17. [17]

    N., et al

    Izidoro, A., Ogihara, M., Raymond, S. N., et al. 2017, Monthly Notices of the Royal Astronomical Society, 470, 1750

    work page 2017

  18. [18]

    2018, The Astrophysical Journal, 853, 163

    Jin, S., & Mordasini, C. 2018, The Astrophysical Journal, 853, 163

    work page 2018

  19. [19]

    R., Blunt, S., Lopez-Morales, M., et al

    Kosiarek, M. R., Blunt, S., Lopez-Morales, M., et al. 2019, The Astronomical Journal, 157, 116

    work page 2019

  20. [20]

    Lam, K. W. F., Santerne, A., Sousa, S. G., et al. 2018, Astronomy and Astrophysics, 620, A77

    work page 2018

  21. [21]

    2010, ApJ, 715, L68, doi: 10.1088/2041-8205/715/2/L68

    Lyra, W., Paardekooper, S.-J., & Mac Low, M.-M. 2010, ApJ, 715, L68, doi: 10.1088/2041-8205/715/2/L68

    work page doi:10.1088/2041-8205/715/2/l68 2010

  22. [22]

    Makarov, V. V. 2015, The Astrophysical Journal, 810, 12

    work page 2015

  23. [23]

    V., & Efroimsky, M

    Makarov, V. V., & Efroimsky, M. 2013, The Astrophysical Journal, 764, 27 8 Armstrong, D. J. et al

    work page 2013

  24. [24]

    2016, The Astrophysical Journal Letters, 820, L8

    Matsakos, T., & K¨ onigl, A. 2016, The Astrophysical Journal Letters, 820, L8

    work page 2016

  25. [25]

    2016, Astronomy and Astrophysics, 589, A75

    Mazeh, T., Holczer, T., & Faigler, S. 2016, Astronomy and Astrophysics, 589, A75

    work page 2016

  26. [26]

    M., & Mazeh, T

    Mills, S. M., & Mazeh, T. 2017, The Astrophysical Journal Letters, 839, L8

    work page 2017

  27. [27]

    Morbidelli, A., & Raymond, S. N. 2016, Journal of Geophysical Research (Planets), 121, 1962

    work page 2016

  28. [28]

    2015, International Journal of Astrobiology, 14, 201

    Alibert, Y. 2015, International Journal of Astrobiology, 14, 201

    work page 2015

  29. [29]

    D., Pascucci, I., Apai, D., & Ciesla, F

    Mulders, G. D., Pascucci, I., Apai, D., & Ciesla, F. J. 2018, The Astronomical Journal, 156, 24 Nesvorn´ y, D., Kipping, D., Terrell, D., et al. 2013, The Astrophysical Journal, 777, 3

    work page 2018

  30. [30]

    V., & Efroimsky, M

    Noyelles, B., Frouard, J., Makarov, V. V., & Efroimsky, M. 2014, Icarus, 241, 26

    work page 2014

  31. [31]

    E., & Lai, D

    Owen, J. E., & Lai, D. 2018, Monthly Notices of the Royal Astronomical Society, 479, 5012

    work page 2018

  32. [32]

    E., & Wu, Y

    Owen, J. E., & Wu, Y. 2017, The Astrophysical Journal, 847, 29

    work page 2017

  33. [33]

    2011, Journal of Machine Learning Research, 12, 2825

    Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2011, Journal of Machine Learning Research, 12, 2825

    work page 2011

  34. [34]

    A., & Aigrain, S

    Rajpaul, V., Buchhave, L. A., & Aigrain, S. 2017, Monthly Notices of the Royal Astronomical Society: Letters, 471, L125

    work page 2017

  35. [35]

    E., Becker, J

    Rodriguez, J. E., Becker, J. C., Eastman, J. D., et al. 2018, The Astronomical Journal, 156, 245 Steffen, J. H. 2016, Monthly Notices of the Royal Astronomical Society, 457, 4384

    work page 2018

  36. [36]

    E., Coughlin, J

    Thompson, S. E., Coughlin, J. L., Hoffman, K., et al. 2018, The Astrophysical Journal Supplement Series, 235, 38

    work page 2018

  37. [37]

    2019, Astronomy and Astrophysics, 622, A37

    Udry, S., Dumusque, X., Lovis, C., et al. 2019, Astronomy and Astrophysics, 622, A37

    work page 2019

  38. [38]

    V., et al

    Veras, D., Efroimsky, M., Makarov, V. V., et al. 2019, MNRAS, 486, 3831, doi: 10.1093/mnras/stz965

    work page doi:10.1093/mnras/stz965 2019

  39. [39]

    Winn, J. N. 2018, in Handbook of Exoplanets (Cham:

    work page 2018

  40. [40]

    2016, Monthly Notices of the Royal Astronomical Society, 464, 3385

    Shannon, A. 2016, Monthly Notices of the Royal Astronomical Society, 464, 3385

    work page 2016