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Revisiting the conundrum of the sub-Jovian and Neptune desert. A new approach that incorporates stellar properties

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The exoplanet desert is carved by starlight, not by orbital period, and its edges follow power laws in incident flux.

desk verdict Qualitative desert in flux space is real, but the fitted power-law boundaries rest on post-hoc choices and need a robustness pass before the slopes are quoted. read the letter →

arxiv 2411.16960 v1 pith:VXQSVP6X submitted 2024-11-25 astro-ph.EP astro-ph.SR

Christian Magliano , Giovanni Covone , Enrico Corsaro , Laura Inno , Luca Cacciapuoti , Stefano Fiscale , Isabella Pagano , Vito Saggese This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords sub-JoviandesertNeptuneincidentstellarfluxirradiationexoplanetdemographicspower-lawboundariesGaussianmixturemodelhotNeptunes
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 argues that the sub-Jovian and Neptune desert, the scarcity of Neptune- and Saturn-sized planets on very short orbits, is better traced by the stellar radiation a planet receives than by its orbital period. Working with 1,527 confirmed transiting planets with precisely measured radii and 512 with masses, the authors show that the desert appears as a triangular gap in the incident-flux versus radius and incident-flux versus mass planes. They fit the upper and lower edges of that gap and find both are power laws in flux, with slopes that differ between the radius and mass planes. If the claim holds, the period-based 'hot Neptune' population is largely a coordinate artifact: about 87% of hot Neptunes defined by period fall outside the flux-defined desert in the radius plane, and 63 of 110 do so in the mass plane.

What carries the argument

The load-bearing object is the incident stellar flux $F = L_*/(4\pi d^2)$, or in solar units $F/F_\oplus = (\rho_*/\rho_\odot)^{-2/3}(P/1\,\mathrm{yr})^{-4/3}(T_*/T_\odot)^4$, which folds orbital distance, stellar temperature, and stellar density into a single number. To place the desert edges, the paper runs a two-component Gaussian mixture model in $\log F$ versus $\log R_p$ (and $\log F$ versus $\log M_p$) to separate small planets from giants, then defines boundary points in flux slices as $\mu \pm z\sigma$ after removing contaminants, with $z=2$ in the radius plane and $z=1$ in the mass plane. A Bayesian nested-sampling fit then selects a pure power-law model over linear and quadratic alternatives by Bayes factors exceeding the strong-evidence threshold, producing the analytic boundary curves.

What would settle it

Recompute the boundary points in the same samples using $z=1$ and $z=3$ in the flux-radius plane and $z=2$ in the flux-mass plane, and recompute the flux thresholds from the 60th and 90th percentiles of the same radius and mass selections; if the fitted power-law slopes shift by more than the quoted 68.3% credible intervals, or the power-law model no longer wins the Bayes-factor comparison, the reported desert boundaries are an artifact of those choices.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that the boundaries of the sub-Jovian and Neptune desert are power-law relations in the incident stellar flux $F$, not in orbital period: $R_p/R_\oplus = \beta (F/F_\oplus)^\alpha$ with $\alpha = -0.27^{+0.02}_{-0.02}$ for the lower radius edge and $\alpha = 0.11^{+0.02}_{-0.03}$ for the upper radius edge, and $M_p/M_\oplus = \beta (F/F_\oplus)^\alpha$ with $\alpha = -0.70^{+0.16}_{-0.13}$ and $0.47^{+0.19}_{-0.22}$ in the flux-mass plane. The paper calls the depleted region the 'irradiation desert.' Combining the two planes yields mass-radius relations for the desert edges, with the upper edge consistent with very low-density gas giants around $0.1\,\mathrm{g/cm^3}$ and the lower edge spanning denser objects that could be silicate worlds or stripped cores. A direct consequence is that 194 of the 221 planets classified as hot Neptunes by the standard period-based boundaries lie outside the irradiation desert in the flux-radius plane, while only three planets previously outside the period desert move into it.

Load-bearing premise

The load-bearing premise is that the desert edges can be located by the paper's own statistical conventions, namely the 75th-percentile flux thresholds of $200\,F_\oplus$ and $550\,F_\oplus$, the $z=2$ and $z=1$ boundary definitions, and the 2-$\sigma$ clipping, so if a different reasonable choice of those conventions moves the edges, the power laws are not a stable physical feature.

Editorial extensions

If this is right

  • If the flux-based picture is right, about 87% of planets previously classified as hot Neptunes in the radius plane are ordinary planets once stellar luminosity and distance are folded in, so occurrence-rate studies based on period alone will misclassify the desert population.
  • Only 27 of the 221 period-defined hot Neptunes remain inside the flux-defined desert, and three new planets enter it, giving a different census of the desert's occupants.
  • The mass-radius relations for the two edges, $R_p \propto M_p^{0.23}$ on the upper edge and $R_p \propto M_p^{0.39}$ on the lower edge, associate the upper edge with tenuous gas giants and the lower edge with denser, partially stripped planets, connecting the desert to photoevaporation and migration scenarios.
  • The difference between the flux thresholds in the radius and mass planes (about $200\,F_\oplus$ versus $550\,F_\oplus$) survives Monte Carlo tests that equalize sample sizes, which the paper interprets as a physical rather than purely statistical difference.
  • Future surveys that measure masses for many more short-period Neptunes should shrink the uncertainties on the mass-plane power laws and test whether the two planes still agree.

Reading between the lines

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

  • A testable extension not in the paper: convert survey completeness maps from (period, radius) to (flux, radius) and check whether the irradiation-desert boundaries persist after selection-bias correction; if they weaken, part of the desert may be an artifact of transit detectability.
  • The z-score choices ($z=2$ in radius, $z=1$ in mass) and the 75th-percentile flux thresholds are the fragile link; re-running the boundary construction with $z=1$ and $z=3$ and with thresholds from the 60th and 90th percentiles would show whether the quoted exponents are stable.
  • If the flux-based desert is the physically meaningful one, theoretical models of photoevaporation and high-eccentricity migration should predict boundaries that move with stellar spectral type in flux space; comparing the power-law slopes with population-synthesis predictions would test the mechanism.
  • The paper's reclassification suggests that reported 'oases' or 'savannas' of hot Neptunes may depend on the coordinate choice, and a homogeneous re-analysis of new transit candidates in flux space would clarify whether the remaining desert occupants are a distinct sub-population or contaminants.
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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 / 6 minor

Summary. The paper proposes replacing the orbital period with the incident stellar flux F as the key variable for defining the sub-Jovian and Neptune desert. Using 1527 confirmed exoplanets with precise period, radius, and stellar parameters (sample S1) and a mass subsample of 512 planets (S3), the authors apply a two-component Gaussian mixture model to separate small/rocky planets from giants, then define lower and upper desert boundaries in the (F,Rp) and (F,Mp) planes from mean-plus/minus-z-sigma points in flux slices. Power-law models are fitted to these boundary points with the nested-sampling code Diamonds, yielding the slopes reported in Table 3. The paper also derives mass-radius relations for the two boundaries by eliminating F between the fits, and reports that about 87% of period-defined hot Neptunes fall outside the new irradiation desert.

Significance. If robust, the paper would provide a useful re-framing of the Neptune/sub-Jovian desert using a physically motivated stellar property, and the analytical boundary expressions would be directly testable with future transit samples. The qualitative message—that the dearth of highly irradiated Neptune-sized planets persists in flux space—is well supported by the figures and by the KS tests. The authors also make good use of Bayesian model comparison and include a Monte Carlo investigation of the F75th threshold. However, the central quantitative claim (the power-law slopes in Table 3) is currently conditional on a chain of a posteriori choices that are not stress-tested, and the mass-plane boundary rests on very few points. The paper is publishable only after the boundary-definition procedure is shown to be robust or its limitations are explicitly quantified.

major comments (4)
  1. [§2.2, Eqs. (3)-(4); §2.3, Eqs. (5)-(6)] The boundary points that drive the entire analysis are defined with arbitrarily chosen z-scores (z=2 for radius, z=1 for mass), a 2-sigma clipping procedure applied only to the lower-edge groups, and flux thresholds set to the 75th percentile of the same sample. The paper explicitly states that these choices were made after visual inspection (e.g., §2.2: 'The decision to define the boundary points ... is arbitrary, but was made in light of an a posteriori visual analysis'). No sensitivity test is provided for the z-score, the percentile defining F75th, the clipping level, or the mass cutoff of 600 M⊕. Because the fitted exponents in Table 3 describe points that are themselves defined by these choices, the abstract's claim that the boundaries are 'well described by a power-law model' is not yet established as a property of the desert rather than a property of the chosen boundary construction. I request a systematic robustness test (e.g., z=1 and z=3 for radius, 60th/90th percentiles for F75th, with/without clipping) and a report of how the exponents change.
  2. [§2.6, Table 2] The strong Bayesian preference for the power-law model over the linear and quadratic models is computed for the constructed boundary points, not for an independently defined boundary. The model comparison therefore shows only that a power law fits the constructed points, not that the boundary is intrinsically a power law. A more convincing test would be to define the boundary with one procedure (e.g., a density contour in the F-Rp plane) and check whether the power-law form predicts the location of a hold-out sample or a different flux range. Without such an independent check, the evidence ratios in Table 2 are circular with respect to the boundary definition.
  3. [§3.2, Table 3, Fig. 11] In the F-Mp plane the quoted power laws come from only 3 lower-edge points and 4 upper-edge points. The fitted parameters have very large uncertainties (e.g., lnβ = 1.78 ± 1.77 for the upper boundary), and the confidence bands of the two boundaries overlap in Fig. 11. The paper acknowledges the overlap but still presents the mass-plane constraints as if they support the power-law conclusion. With such a small number of points, the large Bayes factors in Table 2 are not compelling by themselves; the authors should either use more flux slices (with a lower minimum count or a bootstrap resampling) or explicitly demote the mass-plane power-law slopes to tentative values.
  4. [§3.3, Eqs. (14)-(15)] The mass-radius relations are obtained by eliminating F between two fitted power laws, so their exponents are ratios of the fitted slopes and their uncertainties are not independent. Moreover, the radius-plane fits use sample S1 over [200,4000] F⊕, while the mass-plane fits use the smaller sample S3 over [550,4000] F⊕, and the boundary points are defined with different z-scores in the two planes. Combining these two sets of fits into a single mass-radius relation without accounting for the different samples and thresholds is questionable. This should at least be stated as an inconsistency, or the relation should be derived from a common subsample with a consistent boundary definition.
minor comments (6)
  1. [Eq. (1) and throughout] The quantity F is called the 'insulation flux' throughout; the standard terms are 'incident flux' or 'instellation flux'. Please use one consistent term.
  2. [§2.3] The sentence 'the errors on the fitted parameters are relatively larger because the statistics in the flux-mass diagram are larger' appears to mean 'sparser' or 'poorer'; as written it contradicts the surrounding discussion and the description of sample S3.
  3. [§2.3] There is a typo in 'we only considered exoplanets that received at lest 550 F⊕' ('at least').
  4. [§2.2] Typo: 'the the Rp distributions of group AR' has a duplicated 'the'; also the unusual spacing in 'D iamonds' should be regularized to 'DIAMONDS' or 'Diamonds' throughout.
  5. [Fig. 11 caption vs §3.2] The figure caption calls the 110 period-defined hot Neptunes 'yellow dots', while the text refers to them as 'yellow triangles'; the caption and text should agree.
  6. [§3, first paragraph] The cross-reference 'as shown in Sects. 2.6 and 2.6' should cite the correct sections for the radius-plane and mass-plane fits.

Circularity Check

2 steps flagged · score 6.0 of 10

The 'power-law bounds' and the 87% hot-Neptune reclassification reduce to a posteriori quantile definitions; the headline empirical claims are conditional on the same data from which the boundaries were constructed.

  1. self definitional [Sect. 2.2, Eqs. (3)-(4); Sect. 4 reclassification claim]
    "We defined the lower boundary point in the ith slice of the flux grid related to group AR as Rlow,i = µAR,i + 2σAR,i ... The decision to define the boundary points as the points with a z−score equal to 2 in each distribution is arbitrary, but was made in light of an a posteriori visual analysis. ... Moreover, ≈ 87 % of planets in the desert defined by Mazeh et al. (2016) in the period-radius plane do not lie within the irradiation desert we defined in the flux-radius diagram."

    The lower edge is defined as the μ+2σ quantile of the same group AR distribution that contains the period-defined hot Neptunes. For a Gaussian population only about 2.5% of the objects lie above R_low, so the statement that most hot Neptunes fall outside the irradiation desert is a direct consequence of choosing z=2; the alternatives the paper itself considers, z=1 or z=3, would change the fraction. The reclassification is forced by the boundary definition rather than being an independent empirical discovery.

  2. fitted input called prediction [Sect. 2.6, Table 3; Sect. 2.3, Eqs. (5)-(6); abstract]
    "We find that the upper and lower bounds of the desert are well described by a power-law model in the (F,Rp) and (F,Mp) planes. ... The lower boundary point in the ith slice of the flux grid related to group AM was calculated as Mlow,i = µAM,i + σAM,i ... In this case as well, the choice of the proper z score was based on an a posteriori visual inspection."

    The power-law bounds in Table 3 are fits to boundary points that are themselves defined as arbitrary quantiles (z=2 for radius, z=1 for mass) of the same sample, after a posteriori selection of the F75th thresholds and sigma clipping. The Bayesian model comparison therefore only chooses among functional forms for the constructed points; it does not test whether the physical desert edge is intrinsically a power law. The claimed power-law description is an output of the definition pipeline, not a prediction checked against independently defined boundaries or an external sample.

full rationale

The central quantitative claims are descriptive fits to boundaries constructed from the same data. The boundary points are generated by μ±zσ rules with z chosen after visual inspection of the same diagrams; the flux thresholds F75th = 200 and 550 Fsun are set as percentiles of the same restricted samples; and 2σ clipping is applied to remove contaminants. Fitting a power law to these points (Table 3) and then reporting that 87% of Mazeh et al. hot Neptunes are reclassified outside the irradiation desert is therefore not a falsifiable prediction, because the latter percentage is essentially fixed by the z=2 quantile definition. The mass-radius relations in Eqs. (14)-(15) are obtained by eliminating F between the same two fitted power laws, so their exponents are ratios of fitted slopes rather than independent measurements. On the other hand, the paper is transparent about the arbitrariness of z, binning, and thresholds, and it does provide some robustness checks (10 vs 20 objects per bin, Monte Carlo on F75th). The qualitative existence of a flux-dependent paucity is supported by simple KS tests and by consistency with earlier period-based work, so the paper is not wholly circular. However, the headline 'power-law bounds' and the '87%' reclassification reduce by construction to the chosen quantile and threshold definitions, warranting a partial-circularity score of 6.

Assumptions & free parameters 14 free parameters · 6 assumptions · 0 invented entities

The central results depend on multiple fitted power-law parameters, arbitrary z-scores, sample-specific flux thresholds, and a mass cutoff. No new physical entities are introduced. The main axioms are the physical relevance of flux, the reality of the desert as a physical feature, the GMM two-population split, and the assumed power-law functional form. These choices are mostly acknowledged in the text but are not independently justified or stress-tested.

free parameters (14)
  • Lower boundary power-law slope alpha (F-Rp) = -0.27 +/- 0.02
    Fitted with Diamonds to the lower boundary points in the flux-radius plane (Table 3).
  • Lower boundary power-law intercept ln beta (F-Rp) = 2.64 +/- 0.11
    Fitted with Diamonds to the lower boundary points in the flux-radius plane (Table 3).
  • Upper boundary power-law slope alpha (F-Rp) = 0.11 +/- 0.02
    Fitted with Diamonds to the upper boundary points in the flux-radius plane (Table 3).
  • Upper boundary power-law intercept ln beta (F-Rp) = 1.56 +/- 0.17
    Fitted with Diamonds to the upper boundary points in the flux-radius plane (Table 3).
  • Lower boundary power-law slope alpha (F-Mp) = -0.70 +/- 0.16
    Fitted with Diamonds to the lower boundary points in the flux-mass plane (Table 3).
  • Lower boundary power-law intercept ln beta (F-Mp) = 7.82 +/- 1.03
    Fitted with Diamonds to the lower boundary points in the flux-mass plane (Table 3).
  • Upper boundary power-law slope alpha (F-Mp) = 0.47 +/- 0.19
    Fitted with Diamonds to the upper boundary points in the flux-mass plane (Table 3).
  • Upper boundary power-law intercept ln beta (F-Mp) = 1.78 +/- 1.77
    Fitted with Diamonds to the upper boundary points in the flux-mass plane (Table 3).
  • z-score for radius boundary points = 2
    Chosen a posteriori by visual inspection; sets the boundary positions in the flux-radius plane (Sect. 2.2).
  • z-score for mass boundary points = 1
    Chosen a posteriori by visual inspection; sets the boundary positions in the flux-mass plane (Sect. 2.3).
  • Flux threshold F75th (F-Rp) = 200 F_sun
    75th percentile of the flux distribution of planets with radius 3-11 R_earth; defines the desert onset in the flux-radius plane (Sect. 2.4).
  • Flux threshold F75th (F-Mp) = 550 F_sun
    75th percentile of the flux distribution of planets with mass 10-200 M_earth; defines the desert onset in the flux-mass plane (Sect. 2.4).
  • Mass cutoff for S3 sample = 600 M_earth
    Arbitrary cutoff to remove extremely massive planets that would distort the upper boundary computation (Sect. 2.3).
  • Minimum objects per flux slice = 20
    Arbitrary trade-off between statistical robustness and the number of boundary points available for fitting (Sect. 2.2).
assumptions (6)
  • domain assumption Incident stellar flux F is the physically relevant coordinate for the desert, rather than orbital period P.
    The paper's premise is that F captures both proximity and stellar radiation; this is asserted, not derived.
  • domain assumption The desert is a real physical feature, not primarily an observational selection effect.
    Relies on prior work (Sanchis-Ojeda et al. 2014) to rule out bias; the new analysis adopts this without re-testing it.
  • ad hoc to paper A two-component Gaussian mixture model adequately separates the small-planet and giant-planet populations.
    K=2 is assumed; boundary definitions depend on this split.
  • ad hoc to paper The desert boundary can be described by a power-law in F.
    The power-law family is selected among linear and quadratic models via Bayesian evidence; it is not derived from physics.
  • ad hoc to paper The 2-sigma clipping removes contamination without biasing the lower boundary.
    Used to exclude hot sub-Jovians in the savanna; the clipping level is chosen by hand.
  • domain assumption The sample S1 after the 10% uncertainty filter is representative of the underlying planet population.
    Removing 54% of planets could introduce bias; the paper acknowledges but does not correct for it.

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Pith. "Pith review of Revisiting the conundrum of the sub-Jovian and Neptune desert. A new approach that incorporates stellar properties." pith.science (2026). https://pith.science/paper/VXQSVP6X

@misc{pith2026241116960,
  author       = {Pith},
  title        = {Pith review of: Revisiting the conundrum of the sub-Jovian and Neptune desert. A new approach that incorporates stellar properties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VXQSVP6X}},
  note         = {Machine review of arXiv:2411.16960}
}
abstract

The search for exoplanets has led to the identification of intriguing patterns in their distributions, one of which is the so-called sub-Jovian and Neptune desert. The occurrence rate of Neptunian exoplanets with an orbital period $P\lesssim 4$ days sharply decreases in this region in period-radius and period-mass space. We present a novel approach to delineating the sub-Jovian and Neptune desert by considering the incident stellar flux $F$ on the planetary surface as a key parameter instead of the traditional orbital period of the planets. Through this change of perspective, we demonstrate that the incident flux still exhibits a paucity of highly irradiated Neptunes, but also captures the proximity to the host star and the intensity of stellar radiation. Leveraging a dataset of confirmed exoplanets, we performed a systematic analysis to map the boundaries of the sub-Jovian and Neptune desert in the $(F,R_p)$ and $(F,M_p)$ diagrams, with $R_p$ and $M_p$ corresponding to the planetary radius and mass, respectively. By using statistical techniques and fitting procedures, we derived analytical expressions for these boundaries that offer valuable insights into the underlying physical mechanisms governing the dearth of Neptunian planets in close proximity to their host stars. We find that the upper and lower bounds of the desert are well described by a power-law model in the $(F,R_p)$ and $(F,M_p)$ planes. We also obtain the planetary mass-radius relations for each boundary by combining the retrieved analytic expressions in the two planes. This work contributes to advancing our knowledge of exoplanet demographics and to refining theoretical models of planetary formation and evolution within the context of the sub-Jovian and Neptune desert.

Figures

Figures reproduced from arXiv: 2411.16960 by the authors.

Figure 1
Figure 1. Distribution of the confirmed exoplanets of the S 1 sample in the log P – log Rp diagram for different ranges of the insulation flux. The upper left panel shows the 586 planets that receive ≤ 50 F⊕, the upper right panel shows the 364 planets that receive between 50 F⊕ and 200 F⊕, the lower left panel depicts the 238 planets that receive between 200 F⊕ and 550 F⊕, and the lower right panel illustrates the 339 planet… view at source ↗
Figure 2
Figure 2. Analysis of the planetary distribution in the F – Rp plane and the flux cumulative distribution function. Left panel: Distribution of the 1527 planets of the S 1 set in the F – Rp plane. The yellow triangles represent planets that would be referred to as hot Neptunes according to the limits obtained by Mazeh et al. 2016. The grey triangle is a qualitative representation of the desert. Right panel: Cumulative distrib… view at source ↗
Figure 3
Figure 3. Application of a two-component bivariate GMM over S 1 sample in the log F – log Rp space. We found two separate populations: Group AR (purple dots) with a mean value of (1.70, 0.34), and Group BR (yel￾low dots) with a mean value of (2.72, 1.12). particular, the main purpose of the grid-based analysis was to calculate the points that were used below to derive the borders (see Sect. 3.1). Group AR is slightly larger t… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Calculated boundaries in (F, Rp) space: (Flow,i , Rlow,i) pairs (pur￾ple points) sample the lower boundary, and (Fup,i , Rup, j) pairs (red points) mark the upper boundary. 2.3. The sub-Jovian/Neptunian desert in the flux-mass plane Within our initial sample, 609 plane…
Figure 5
Figure 5. Figure 5: Analysis of the planetary distribution in the F – Mp plane and the flux cumulative distribution function. Left panel: Distribution of the 609 planets of the S 2 set in the F – Mp plane. The yellow triangles represent planets that would be referred to as hot Neptunes ac…
Figure 6
Figure 6. Figure 6: Application of a two-component bivariate GMM on the sample S 2 in the log F – log Mp space. We identified two separate populations: Group AM (purple dots) with a mean value of (1.8, 1.4), and group BM (yellow dots) with a mean value of (2.9, 2.5). in group AM on averag…
Figure 7
Figure 7. Figure 7: Calculated boundaries in the (F, Mp) space: (Flow,i , Mlow,i) pairs (purple points) sample the lower boundary, and (Fup,i , Mup, j) pairs (red points) mark the upper boundary of the desert. In particular, the lower boundary point in the ith slice of the flux grid relat…
Figure 9
Figure 9. Figure 9: Distribution of 512 objects of sample S 3 within the log Rp – log Mp plane, coloured according to their classification with respect to the radius and mass. 271 blue dots (ARAM) represent the planets classi￾fied as not giants for the radius and mass, 211 red dots (BRBM)…
Figure 10
Figure 10. Figure 10: Comparison of the S 1 sample distribution in the P – Rp and F – Rp planes to highlight the irradiation desert. Left: Distribution of the S 1 sample in the P – Rp diagram along the edges obtained by Mazeh et al. 2016. The yellow triangles represent the 221 hot Neptunes…
Figure 11
Figure 11. Figure 11: Comparison of the S 3 sample distribution in the P – Mp and F – Mp planes to highlight the irradiation desert. Left: Distribution of the S 3 sample in the P – Mp diagram along the edges obtained by Mazeh et al. 2016. The yellow dots represent the 110 hot Neptunes with…
Figure 12
Figure 12. Figure 12: Mass-radius relations for the upper (orange line) and lower boundary (blue line) given by Eqs. (14) and (15), respectively. We present different curves at fixed density (left). While the upper boundary is consistent with a very low mean planetary density (≈ 0.1 g/cm3 …

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