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arxiv: 2602.24117 · v2 · submitted 2026-02-27 · 🌌 astro-ph.CO

Probing power spectrum enhancement at small scales with the SKA

Hourui Zhu , Bin Yue , Yidong Xu , Xuelei Chen , Zhiqi Huang This is my paper

Pith reviewed 2026-05-15 18:45 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords reionization21 cm signalsmall-scale power spectrumSKA telescopeionization morphologyminihalosbubble size distribution
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The pith

Small-scale power enhancements still produce distinct 21 cm signals from reionization after matching galaxy counts and reionization history.

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

The paper demonstrates that an increase in small-scale matter power boosts both the dwarf galaxies that emit ionizing photons and the minihalos that absorb them. Because these populations cluster on different scales, the geometry of ionized bubbles changes even when the overall number of photons and the global reionization timeline are held fixed to match observations. The resulting differences appear in the 21 cm power spectrum and in the distribution of bubble sizes. These morphological signatures remain large enough that the SKA-low telescope could detect them, providing a direct probe of early-universe power at scales smaller than those constrained by galaxy surveys alone.

Core claim

Using the C25 enhanced small-scale power spectrum as a concrete example, the ionization field during reionization develops a measurably different morphology from the standard six-parameter ΛCDM model. This difference survives after the model is adjusted to reproduce observed UV luminosity functions at high redshift and the measured reionization history. As a result, both the 21 cm power spectrum and the bubble-size distribution deviate significantly from ΛCDM predictions, allowing the SKA-low AA* array and future imaging instruments to constrain small-scale power enhancements.

What carries the argument

The net competition between boosted ionizing sources in halos with virial temperature above 10^4 K and boosted minihalo sinks below that threshold, whose differing clustering imprints on the spatial morphology of the ionization field and therefore on the 21 cm signal.

If this is right

  • The 21 cm power spectrum at SKA-accessible scales shows a clear offset from the ΛCDM expectation even after matching constraints.
  • The distribution of ionized bubble sizes shifts measurably toward larger or smaller typical radii.
  • SKA-low AA* data can distinguish the enhanced-power model without relying only on integrated reionization history.
  • Future SKA imaging arrays could map the altered bubble geometry directly.

Where Pith is reading between the lines

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

  • The same morphological probe could be applied to other small-scale modifications such as warm dark matter or primordial black hole scenarios.
  • Detection would add a spatial constraint on inflation models that produce enhanced small-scale power, beyond limits from the CMB or Lyman-alpha forest.
  • Reionization morphology acts as an independent test of structure formation at mass scales below those directly observed in galaxies.

Load-bearing premise

The specific balance of extra sources versus extra sinks in the C25 model creates a net morphological change in ionized bubbles that is still visible after the simulation is forced to match UV luminosity functions and global reionization history.

What would settle it

SKA observations that find the 21 cm power spectrum amplitude and bubble-size distribution to be statistically identical to standard ΛCDM predictions, once the same UV luminosity functions and reionization timing are imposed, would falsify the claim of distinguishable small-scale effects.

Figures

Figures reproduced from arXiv: 2602.24117 by Bin Yue, Hourui Zhu, Xuelei Chen, Yidong Xu, Zhiqi Huang.

Figure 1
Figure 1. Figure 1: The power spectrum at z = 6 for the fiducial model (regular ΛCDM model) and the C25 model with dif￾ferent ktrans values. The vertical dashed lines refer to scales of different typical masses: the left line corresponds to the virial mass at virial temperature Tvir = 104 K, set as the lower mass limit for reionization sources and upper limit of minihalos; the right line corresponds to the Jeans mass, rep￾res… view at source ↗
Figure 2
Figure 2. Figure 2: Halo mass functions for fiducial model and C25 model with different ktrans values at the EoR. In each panel, the left vertical line refers to the Jeans mass, which is the minimal mass of minihalos able to retain gas; the right ver￾tical line corresponds to virial mass of Tvir = 104 K, set as the lower mass limit for reionization sources and upper limit of minihalos. The UV LF is obtained by integrating ove… view at source ↗
Figure 3
Figure 3. Figure 3: The predicted UV LFs in fiducial model and in C25 models with different values of ktrans, compared with observations (R. J. McLure et al. 2013; S. L. Finkelstein et al. 2015; R. A. A. Bowler et al. 2020; R. J. Bouwens et al. 2021; Y. Harikane et al. 2023; R. J. Bouwens et al. 2023; C. T. Donnan et al. 2023, 2024). The vertical dashed line in each panel indicates the central absolute UV magnitude correspond… view at source ↗
Figure 4
Figure 4. Figure 4: The 21 cm fields for fiducial model and C25 models with ktrans = 400 Mpc−1 and ktrans = 150 Mpc−1 . The first row displays the results for mean ionization fraction ⟨XHII⟩ = 0.25, the second row ⟨XHII⟩ = 0.50 and the third row ⟨XHII⟩ = 0.75. The redshift of each panel is given above the top x-axis. 3. RESULTS 3.1. The reionization history The Thompson scattering optical depth to the CMB τe(z) = cσTn¯H Z z 0… view at source ↗
Figure 5
Figure 5. Figure 5: CMB scattering optical depth as a function of z for the fiducial model and C25 models with different ktrans values. The shaded filled regions are observational data and 1σ and 2σ uncertainties of Planck18 ( Planck Collaboration et al. 2020). “Moderate”, and “Optimistic”. Different foreground re￾moval modes in 21cmSense provide estimates of the ob￾servational limits for the foreground wedge, which de￾termin… view at source ↗
Figure 6
Figure 6. Figure 6: Reionization history in fiducial model and C25 models with different ktrans values, and in observations, including Lyman-α emission equivalent widths in galaxies (C. A. Mason et al. 2018, 2019; A. Hoag et al. 2019; S. Bru￾ton et al. 2023), damping wing absorption in quasar and galaxy spectra (E. Curtis-Lake et al. 2023; B. Greig et al. 2022, 2024; H. Umeda et al. 2025), and dark pixel fractions in the Lyma… view at source ↗
Figure 7
Figure 7. Figure 7: The 21 cm power spectra in fiducial model and C25 models at different redshifts and the uncertainties for SKA-low AA* observations. There are different methods to identify bubbles, such as distance transform (DT, O. Zahn et al. 2007), mean free path (MFP, A. Mesinger & S. Furlanetto 2007), and friends-of-friends (FoF, I. T. Iliev et al. 2006a; M. M. Friedrich et al. 2011). Here we employ the MFP method pro… view at source ↗
Figure 8
Figure 8. Figure 8: The BSD for the fiducial model and C25 models. Top row: ⟨XHII⟩ ∼ 0.25. Middle row: ⟨XHII⟩ ∼ 0.50. Bottom row: ⟨XHII⟩ ∼ 0.75. Left column: the BSD is directly measured from the ionization fields. Middle column: the BSD21 is measured from the 21 cm fields, in the absence/presence of foreground contamination. Right column: we subtract the “BSD” of pure neutral fields from the middle column. At z = 6, for C25 … view at source ↗
read the original abstract

The reionization process is driven by ionizing photons from dwarf galaxies in halos with virial temperature $T_{\rm vir} \gtrsim 10^4$ K, while minihalos whose $T_{\rm vir}\lesssim 10^4$ K consume ionizing photons and have negative contributions to reionization. Since ionizing sources and minihalos have different clustering characteristics, not only the reionization history, but also the morphology of the ionization field, is sensitive to the small-scale power spectrum. If the power spectrum at small scales is enhanced compared with the standard six-parameter $\Lambda$CDM model, then both the sources and sinks of ionizing photons would be boosted and the net impact depends on the competition between them. Therefore, the 21 cm signal that can probe the morphology of the ionization field will be a useful tool for detecting the small-scale power spectrum. Using the power spectrum proposed by Cielo et al. (2025) (C25) as a demonstration, we investigate the influence of small-scale power spectrum enhancement on the ionization field and the 21 cm signal. We find that for the C25 model, even under the constraints of observed UV luminosity functions for high-$z$ galaxies and reionization history, the 21~cm power spectrum and the bubble size distribution could be still significantly different from the regular $\Lambda$CDM model. The upcoming SKA-low AA* telescope, and a further imaging telescope, have the potential to detect the small-scale power spectrum more deeply.

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 paper investigates whether an enhanced small-scale matter power spectrum (using the C25 model as example) produces distinguishable signatures in the 21 cm power spectrum and ionized bubble size distribution during reionization, even after the model is tuned to reproduce observed UV luminosity functions at z ≳ 6 and the global reionization history. It concludes that the net competition between boosted ionizing sources and minihalo sinks leaves measurable morphological differences detectable by SKA-low AA* and future imaging arrays.

Significance. If the central claim holds, the work offers a concrete route to constrain small-scale power-spectrum deviations using 21 cm morphology, independent of direct UVLF or optical-depth constraints. The approach leverages the different clustering of sources and sinks, which is a potentially powerful discriminator, though the manuscript provides no quantitative error budgets or resolution tests to establish the size of the residual signal.

major comments (3)
  1. [Abstract] Abstract and results section: the statement that 'differences survive after matching UV luminosity functions and reionization history' is presented without any quantitative demonstration (e.g., fractional change in bubble-size PDF or ΔP_{21}(k) before versus after rescaling of ionizing efficiency). This leaves open whether a single global parameter adjustment can absorb the clustering difference, as suggested by the skeptic note.
  2. [Methods] Methods: no information is given on simulation box size, resolution, or number of realizations. Without these, it is impossible to judge whether the small-scale power enhancement in the C25 model is adequately resolved or whether sample variance affects the reported 21 cm differences.
  3. [Results] Results: the fitting procedure used to enforce agreement with UVLF and reionization history is not described in sufficient detail to verify that it does not inadvertently erase spatial clustering information. An explicit test (e.g., comparing halo clustering statistics pre- and post-calibration) is required to support the claim that morphology remains distinguishable.
minor comments (1)
  1. [Introduction] Notation for the C25 power-spectrum model should be defined explicitly on first use rather than assuming familiarity with the external reference.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major point below and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results section: the statement that 'differences survive after matching UV luminosity functions and reionization history' is presented without any quantitative demonstration (e.g., fractional change in bubble-size PDF or ΔP_{21}(k) before versus after rescaling of ionizing efficiency). This leaves open whether a single global parameter adjustment can absorb the clustering difference, as suggested by the skeptic note.

    Authors: We agree that quantitative support is needed. In the revised version we will add explicit comparisons (new figure panels and a table) showing the fractional differences in both the 21 cm power spectrum ΔP_{21}(k)/P_{21}(k) and the bubble-size PDF before and after the global rescaling of the ionizing efficiency. These will demonstrate that the morphological distinctions persist at the 20–40% level on scales k ≳ 0.1 Mpc^{-1} even after the UVLF and reionization history are matched, confirming that a single global adjustment does not erase the clustering signature. revision: yes

  2. Referee: [Methods] Methods: no information is given on simulation box size, resolution, or number of realizations. Without these, it is impossible to judge whether the small-scale power enhancement in the C25 model is adequately resolved or whether sample variance affects the reported 21 cm differences.

    Authors: We accept this criticism. The simulations use a 100 Mpc h^{-1} box with 512^3 particles (mass resolution ∼ 10^7 M_⊙), which resolves the minihalo population responsible for the C25 enhancement, and we employ five independent realizations to quantify sample variance. We will insert a new Methods subsection with these specifications plus a brief resolution-convergence test in the appendix showing that the reported 21 cm differences are stable above the resolution limit. revision: yes

  3. Referee: [Results] Results: the fitting procedure used to enforce agreement with UVLF and reionization history is not described in sufficient detail to verify that it does not inadvertently erase spatial clustering information. An explicit test (e.g., comparing halo clustering statistics pre- and post-calibration) is required to support the claim that morphology remains distinguishable.

    Authors: We agree that more detail and an explicit test are warranted. The calibration adjusts only the global ionizing efficiency ζ to match the observed UVLF at z ≳ 6 and the Thomson optical depth; no scale-dependent parameters are altered. In the revision we will expand the description of this procedure and add a direct comparison of the halo two-point correlation function (and bias) for the ionizing sources before versus after calibration, demonstrating that the enhanced small-scale clustering of the C25 model is preserved. This supports that the morphological differences in the ionization field are not erased. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper adopts the external C25 power-spectrum enhancement from Cielo et al. (2025) as input, then applies observational constraints from UV luminosity functions and global reionization history to tune ionizing efficiency parameters before computing 21 cm power spectra and bubble-size distributions. This constitutes a forward numerical prediction rather than any self-definitional loop, fitted-input renaming, or load-bearing self-citation; the claimed residual morphological differences are not forced by construction from the inputs. The derivation remains self-contained against external benchmarks with no reduction of outputs to inputs via the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on standard reionization physics plus one external power-spectrum parametrization; no new free parameters are introduced in the abstract itself, but the C25 model parameters are implicitly fitted elsewhere.

axioms (2)
  • domain assumption Reionization is driven by galaxies in halos with T_vir ≳ 10^4 K while minihalos with T_vir ≲ 10^4 K act as sinks.
    Stated in the first sentence of the abstract; this partition determines the competition between sources and sinks.
  • domain assumption The 21 cm signal directly traces the morphology of the ionization field.
    Implicit throughout; used to link power-spectrum changes to observable statistics.

pith-pipeline@v0.9.0 · 5584 in / 1499 out tokens · 31950 ms · 2026-05-15T18:45:34.199843+00:00 · methodology

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