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REVIEW 3 major objections 6 minor 118 references

Ultra-wide exoplanets already set competitive limits on large primordial density peaks that would seed ultra-compact dark minihalos.

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2026-07-12 14:04 UTC pith:63GJYX4N

load-bearing objection Solid new dynamical probe that converts non-disruption of a dozen ultra-wide exoplanets into competitive PPS peak limits via a careful UCMH population model; the statistics are the softest link but not fatal. the 3 major comments →

arxiv 2606.14827 v2 pith:63GJYX4N submitted 2026-06-12 astro-ph.CO astro-ph.EPastro-ph.GAhep-ph

Probing the fate of large primordial perturbations with exoplanets

Th\'eo Par\'e , Julien Lavalle This is my paper
classification astro-ph.CO astro-ph.EPastro-ph.GAhep-ph PACS 12.60.-i95.35.+d98.35.Gi
keywords ultra-wide exoplanetsultra-compact minihalosprimordial power spectrumimpulsive heatingdark matter substructuredynamical constraints
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that planets on extremely wide orbits around their stars act as sensitive gravitational thermometers for compact dark objects that may populate the Galaxy. If the primordial density spectrum rose sharply on small scales, those peaks would collapse into dense ultra-compact minihalos. Repeated fly-bys of such minihalos would inject enough energy to unbind the loosest planetary systems. Because a dozen known wide-orbit planets are still bound after several billion years, the amplitude of any such primordial peak is already limited at levels competitive with cosmic-microwave-background and pulsar-timing bounds. Future direct-imaging surveys that find more of these fragile systems will tighten the limits further, and the same heating can leave a distinctive orbital-misalignment signature that would positively identify a dark-object population.

Core claim

A carefully selected sample of twelve ultra-wide-orbit exoplanets already excludes primordial power-spectrum peaks of amplitude A• ≳ 10^{-4}–10^{-2} on comoving scales k• ∼ 10^2–10^4 Mpc^{-1} that would produce ultra-compact minihalos heavier than ∼10^5 solar masses, at 1–5σ depending on whether pre-accreted minihalos are counted.

What carries the argument

Impulsive heating rate of a planet–star binary by a Galactic population of ultra-compact minihalos, converted into a Poisson survival probability and combined across systems into a global P_surv that is compared with nσ thresholds.

Load-bearing premise

Each planet’s survival probability is treated as statistically independent and is computed from a Poisson number of encounters whose mean is fixed by a semi-analytic model of the local ultra-compact-minihalo density; any residual correlation or density error simply rescales the global exclusion.

What would settle it

Discovery of even one additional, older, more loosely bound planet whose calculated heating-to-binding ratio exceeds unity under the same minihalo population would push the global survival probability below the claimed nσ contour and falsify or tighten the exclusion.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes ultra-wide-orbit exoplanets as a dynamical probe of Galactic compact dark-matter objects, specializing to ultra-compact minihalos (UCMHs) formed from a peaked enhancement of the primordial power spectrum. Impulsive heating of a planet–star system is derived in the weak-encounter limit (Eqs. 2–11), disruption is diagnosed via a heating-to-binding ratio R_heat (Eq. 13), and a Poisson encounter model is used to define individual disruption probabilities that are multiplied into a global survival probability P_surv (Eq. 22). A semi-analytic excursion-set/merger-tree UCMH population (App. A), including tidal stripping, is mapped onto the two peak parameters (A•, k•). From a catalogue cut yielding twelve systems (Table I, Fig. 2), the authors report 1–5σ exclusions on large-amplitude peaks that produce UCMHs ≳10^5 M⊙ (Fig. 4), and they derive adiabatic-invariant evolution equations for semi-major axis, eccentricity, and inclination as potential positive signatures (Sect. V, App. B).

Significance. If the statistical combination and local UCMH density are under control, the work opens a genuinely new dynamical channel for small-scale primordial power, complementary to CMB, Lyman-α, spectral distortions, and PTA limits, and it is well timed for Roman and ELT direct-imaging yields. Strengths that should be credited include: (i) a self-contained EST-based UCMH mass function and host-halo merger tree (App. A) that cleanly links A• and k• to a Galactic population; (ii) closed-form orbital-evolution equations from actions (Eqs. 27–28, App. B) that make a falsifiable multi-planet inclination signature; and (iii) an explicit mock-population check against selection bias (App. C). The result is therefore of clear interest to both cosmology and exoplanetary dynamics, provided the load-bearing statistical steps are tightened.

major comments (3)
  1. Eq. (22) and surrounding text in Sect. IV define the nσ contours of Fig. 4 from the product of individual survival probabilities, treating the twelve systems as statistically independent. Fig. 2 shows that all selected systems lie within a few hundred parsecs to ~kpc of the Sun and therefore sample essentially the same local UCMH density and velocity field. Any residual spatial correlation or shared systematic in the App. A merger-tree/tidal-stripping prediction multiplies rather than averages in P_surv. The manuscript should either (a) quantify the impact of a coherent shift in local n• (or of a modest correlation coefficient) on the 3–5σ contours, or (b) report single-system and leave-one-out limits alongside the product so that the headline exclusion is not driven solely by the independence assumption.
  2. In the light-UCMH regime that sets the tightest bounds (b_min ≪ R_p; cf. the asymptotic scalings after Eq. 13 and the estimate in Eq. 19), the mean encounter number N_bar (Eq. 15) is typically ≪1. Disruption then sits in the Poisson tail of Eq. (17)–(18), which is sensitive to the precise local density, to 〈v_rel〉, and to the somewhat conventional b_max cut in Eq. (12). A 30–50% coherent uncertainty in the predicted local UCMH density (or a change in the b_max prescription) would rescale A• at fixed CL by a comparable factor. The paper should propagate these systematics into the exclusion bands of Fig. 4 (or show a dedicated sensitivity plot) rather than presenting only the two discrete ‘conservative/optimistic f’ curves.
  3. The disruption criterion R_heat ≥ 1 (Eq. 13) is converted to a Poisson probability of ‘enough’ encounters, each depositing the average heat 〈δε〉. For rare, high-impact encounters this mean-field step can mis-estimate the true disruption probability relative to a Monte-Carlo sampling of the full (m•, b) distribution. At minimum, the authors should validate the Poisson-plus-mean-heat approximation against a direct Monte-Carlo of encounter histories for a representative subset of the twelve systems (especially those with the largest R_p T / m⋆ in Table I), and state the fractional change in P_disr.
minor comments (6)
  1. Numerous typographical and spacing errors remain (e.g. abstract ‘noval’; p. 2 ‘deonstrate’, ‘indentical’; ‘Obvioulsy’; section headers with broken spaces such as ‘HEA TING’, ‘POPULA TION’; ‘seee.g.’). A full proof-read is needed.
  2. Fig. 4 left panel: the 1–5σ curves for conservative vs optimistic f are hard to distinguish at small k; a clearer linestyle/legend or separate panels would help.
  3. Eq. (12): the numerical prefactor in b_max = 〈v_rel〉 P / (3√3) is not derived in the text; a one-line justification (or a reference to the exact impulse-duration criterion) would improve reproducibility.
  4. Table I lists twelve systems but the text says ‘a selected sample of 128 objects’ and ‘the 10 most constraining… with 8 common’. A short table or appendix listing the full cut criteria and the discarded objects would make the sample transparent.
  5. App. A, Eq. (A17)–(A19): the (G0, γ1, γ2) = (0.57, 0.38, −0.01) correction is taken from the literature; state explicitly whether results change under pure Press–Schechter (no G factor), at least for the UCMH fraction F_host•.
  6. Sect. V / Fig. 5: the analytic low-e solutions underestimate a(t) and overestimate e(t); the text already notes this, but quoting the fractional error on t_ej (~20%) in the caption would help readers who use only the analytic formulae.

Circularity Check

0 steps flagged

No significant circularity: exoplanet catalogue is external data fed into a forward UCMH population model whose free parameters are the PPS peak parameters being constrained.

full rationale

The derivation chain is self-contained and non-circular. The heating rate (Eqs. 8–11), disruption criterion (Eq. 13), Poisson encounter statistics (Eqs. 14–18), and global survival probability (Eq. 22) are standard dynamical constructions applied to an external exoplanet catalogue (exoplanet.eu). The only free parameters of the model are the two PPS peak parameters (A•, k•) that are being constrained; no quantity is fitted to the exoplanet sample and then re-used as a prediction. The Galactic UCMH mass function and tidal-stripping model of App. A are built from excursion-set theory plus the authors’ earlier semi-analytic machinery (Refs. [71, 73, 74, 86]), but those citations supply an independent forward model of structure formation, not a result that already encodes the exoplanet survival data. The orbital-evolution signatures of Sect. V follow from adiabatic invariants and are likewise independent of the exclusion contours. The softest links (independence of the twelve systems, Poisson assumption for N̄ ≪ 1) are modelling assumptions that affect the numerical strength of the limits, not circular reductions of the claimed derivation. Score 1 reflects only the minor, non-load-bearing self-citation of the authors’ prior tidal-stripping papers.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim rests on standard stellar-dynamics and structure-formation machinery plus a handful of modelling choices that convert an observed catalogue into PPS limits. No new particles or forces are postulated; the free parameters are the two that are being constrained.

free parameters (4)
  • A• (peak amplitude)
    Free parameter of the injected PPS peak; the quantity being constrained, not fitted a priori.
  • k• (peak injection scale)
    Second free parameter of the PPS peak; likewise constrained rather than fitted.
  • local DM density ρ_dm(⊙)
    Taken from McMillan 2017 NFW fit (∼0.01 M⊙ pc^{-3}); enters the encounter rate linearly.
  • relative velocity 〈v_rel〉
    Set to ∼300 km s^{-1}; appears in both the heating rate and the impact-parameter cut-offs.
axioms (5)
  • domain assumption Impulsive, weak-encounter approximation (deflection angle ≪ π/2, positions fixed during fly-by)
    Used from Eq. (2) onward; standard for wide binaries but becomes marginal for the closest encounters.
  • domain assumption Number of encounters follows a Poisson distribution with mean fixed by the local UCMH density and b_max
    Eq. (17); converts mean heating into a disruption probability.
  • domain assumption UCMH population fully predicted by excursion-set theory with a δ-function peak in the PPS plus the semi-analytic merger tree of App. A
    Core of Sect. IV and App. A; inherits all standard EST assumptions (sharp-k filter, spherical collapse barrier, etc.).
  • ad hoc to paper Individual planet survival probabilities are statistically independent
    Explicitly stated before Eq. (22); allows the product form of the global survival probability.
  • domain assumption Ages of the selected exoplanets equal the ages of their host stars and are accurately known
    Used to compute total injected energy; justified by stellar-evolution arguments but carries observational uncertainty.

pith-pipeline@v1.1.0-grok45 · 33338 in / 2761 out tokens · 27464 ms · 2026-07-12T14:04:13.701134+00:00 · methodology

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read the original abstract

We propose ultra-wide-orbit exoplanets as a novel probe of small-scale dark matter objects. These systems are highly sensitive to gravitational perturbations that could be induced by a Galactic population of compact baryon-free dark matter objects -- whether point-like or extended. Focusing on ultra-compact minihalos, which may arise from large primordial perturbations deviating from the canonical scale-invariant power spectrum, we derive new constraints on their injection scale and amplitude. These constraints complement existing dynamical limits and are expected to improve with upcoming exoplanet surveys. Furthermore, the detection of additional loosely bound exoplanets with these surveys could significantly tighten these constraints. Beyond constraints, we also identify characteristic observational signatures in these systems that could help trace a population of dark matter objects. All this strengthens the potential of exoplanetary science to probe the dark universe back to its very primordial properties.

Figures

Figures reproduced from arXiv: 2606.14827 by Julien Lavalle, Th\'eo Par\'e.

Figure 1
Figure 1. Figure 1: FIG. 1. Hyperbolic encounter between a DMO and a simple [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Distribution of exoplanets by distance to the Sun and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Prediction of the DM subhalo mass function for a [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Subhalo mass function predicted for a host halo simi [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗

discussion (0)

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