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arxiv: 2603.18884 · v2 · submitted 2026-03-19 · 🌌 astro-ph.CO

Recognition: 2 theorem links

· Lean Theorem

Primordial black holes and the velocity acoustic oscillations features in 21 cm signals from the cosmic Dark Ages

Zhihe Zhang , Bin Yue , Yidong Xu , Yin-Zhe Ma , Xuelei Chen
Authors on Pith no claims yet

Pith reviewed 2026-05-15 08:28 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords primordial black holes21 cm power spectrumDark Agesvelocity acoustic oscillationsintergalactic mediumaccretion radiationcosmic streaming velocities
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The pith

Primordial black holes imprint velocity acoustic oscillations in 21 cm signals from the cosmic Dark Ages

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

Primordial black holes exist from the early universe and can accrete gas during the Dark Ages, emitting radiation that changes the intergalactic medium's temperature and the 21 cm hydrogen line signal. The accretion is modulated by long-lasting supersonic relative velocities between dark matter and baryons, creating periodic velocity acoustic oscillations in the 21 cm power spectrum. These oscillations can reach relative amplitudes of 30 percent even for very small PBH fractions of dark matter, such as 10^{-13} for 200 solar mass black holes at redshift around 20. The features evolve through distinct phases driven by Lyman-alpha scattering and X-ray heating, which depend on the PBH mass and abundance. This offers a potential detection method with future radio telescopes like SKA-low.

Core claim

PBHs accrete gas in the Dark Ages and release radiation altering the radiation field and IGM thermal status, thereby affecting the hydrogen spin temperature. The accretion rate modulation by relic supersonic DM-baryon streaming velocities imprints VAOs in the 21 cm power spectrum. Small PBH fractions generate VAO wiggles up to 30% amplitude, visible at z around 20 for f_PBH,rec ~ 10^{-13} with 200 M_sun PBHs or at z~40 for f~3x10^{-10}. The redshift evolution shows separated stages of inhomogeneous Ly-alpha scattering and X-ray heating reflecting PBH characteristics.

What carries the argument

Modulation of PBH accretion by relic supersonic streaming velocities between DM and baryons, imprinting VAOs features in the 21 cm power spectrum through IGM thermal changes.

If this is right

  • VAO wiggles up to 30% relative amplitude generated in Dark Ages 21 cm signals by small PBH DM fractions.
  • For 200 solar mass PBHs, features appear at z~20 for f_PBH,rec~1e-13 and at z~40 for f_PBH,rec~3e-10.
  • Redshift evolution of VAOs shows stages dominated first by inhomogeneous Ly-alpha scattering then by X-ray heating.
  • Wiggles at z~20 detectable with SKA-low AA* and at z~40 with hypothetical lunar surface interferometer.

Where Pith is reading between the lines

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

  • Absence of these VAO patterns in observations could provide new upper bounds on the abundance of intermediate-mass PBHs.
  • The two-stage redshift evolution might serve as a signature to separate PBH effects from other potential early-universe heating mechanisms.
  • This mechanism could be tested further by comparing predicted 21 cm signals with global signal measurements or other probes of IGM thermal history.

Load-bearing premise

Accretion onto PBHs is modulated by relic supersonic relative streaming velocities between dark matter and baryons, leading to radiation and IGM evolution that follows standard models without additional feedback or clustering.

What would settle it

Observing the 21 cm power spectrum at redshift 20 and finding no VAO wiggles exceeding a few percent in amplitude for PBH mass fractions around 10^{-13} would contradict the predicted signal strength from 200 solar mass primordial black holes.

Figures

Figures reproduced from arXiv: 2603.18884 by Bin Yue, Xuelei Chen, Yidong Xu, Yin-Zhe Ma, Zhihe Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The redshift evolution of the dimensionless accretion [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The evolution of the mean and scattering of the IGM [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The redshift evolution of the mean 21 cm bright [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: The redshift evolution of the relative amplitude of the VAOs features in the 21 cm power spectrum at [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: The relative amplitude of the VAOs features in the [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: The 21 cm power spectrum at [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: The net VAOs wiggles in the 21 cm power spec [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗
read the original abstract

Astrophysical luminous objects such as the first stars have not yet formed in the Dark Ages. However, primordial black holes (PBHs) always exist throughout cosmic history since the inflation epoch. During the Dark Ages, PBHs may accrete the ambient gas and release radiation like astrophysical luminous objects, change the cosmic radiation field, the thermal status of the intergalactic medium (IGM), and the hydrogen spin temperature. The accretion rate is modulated by the relic supersonic relative streaming velocities between dark matter (DM) and baryons, imprinting Velocity Acoustic Oscillations (VAOs) features in the 21 cm power spectrum. Such VAOs features could be a promising probe for detecting the PBHs in Dark Ages. We find that even if PBHs comprise only a small fraction of DM, they can generate VAOs wiggles with a relative amplitude up to about 30% in Dark Ages. For example, for PBHs with a mass at recombination of 200 solar masses and mass fraction in the total DM f_PBH,rec around 1e-13 at the recombination era, VAOs features appear at redshift around 20; if f_PBH,rec is around 3e-10, then VAOs features could appear as early as redshift around 40. Moreover, the redshift evolution of the VAOs features exhibits clearly separated stages dominated by inhomogeneous Ly-alpha scattering, and inhomogeneous X-ray heating, respectively. It reflects the characteristics of PBHs (mass and fraction in total DM) and their interactions with the IGM. We also estimate that, the VAOs wiggles at redshift around 20 are detectable for the upcoming SKA-low AA*, while wiggles at redshift around 40 are detectable for an hypothetic lunar surface-based interferometer array in the future.

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 / 2 minor

Summary. The manuscript claims that primordial black holes (PBHs) accreting ambient gas during the cosmic Dark Ages produce radiation that imprints velocity acoustic oscillations (VAOs) in the 21 cm power spectrum. The accretion rate is modulated by the relic supersonic baryon-DM streaming velocity v_bc, leading to spatially varying Ly-α and X-ray backgrounds that affect the spin temperature T_s and kinetic temperature T_k. For PBHs with mass 200 M_⊙ at recombination and f_PBH,rec ≈ 10^{-13}, the relative VAO amplitude reaches ~30% near z ≈ 20; higher fractions shift the signal to z ≈ 40. The redshift evolution exhibits distinct stages dominated first by inhomogeneous Ly-α scattering and later by X-ray heating. Detectability is estimated for SKA-low AA* at z ~ 20 and a hypothetical lunar array at z ~ 40.

Significance. If the amplitude and redshift-dependent signatures hold, the work supplies a new, potentially falsifiable probe of PBH abundance and mass in the pre-stellar era using 21 cm cosmology. It extends standard streaming-velocity physics to PBH accretion without introducing new free parameters beyond mass and f_PBH,rec, and predicts observable wiggles whose stage separation could distinguish PBH properties from other early heating sources.

major comments (2)
  1. [§4 (IGM thermal evolution and 21 cm power spectrum modeling)] The central amplitude calculation (illustrated for 200 M_⊙ and f_PBH,rec = 10^{-13} at z ≈ 20) adopts a pre-computed global IGM thermal history to which PBH-induced perturbations are added linearly. This omits iteration on the local sound speed increase from X-ray heating, which would reduce the supersonic regime of v_bc and therefore the modulation depth of the accretion rate. The 30% relative amplitude claim is load-bearing on this linearization; a quantitative test of the approximation (e.g., via local sound-speed update inside the accretion radius) is required.
  2. [§3.1 (accretion rate and radiation field)] The accretion prescription is stated to follow standard Bondi-like rates modulated by v_bc, yet no explicit equation or numerical scheme is given for how the resulting radiation field is propagated through the IGM or how radiative transfer couples back to the local gas temperature and ionization fraction. Without these steps, the claimed separation into Ly-α-dominated and X-ray-dominated stages cannot be verified as robust against reasonable variations in efficiency or clustering.
minor comments (2)
  1. [Abstract and §2] Notation for the PBH mass at recombination (M_PBH,rec) and the fraction f_PBH,rec should be defined once in the text and used consistently; the abstract introduces both without a clear link to the recombination-era definition.
  2. [§5 (observational prospects)] The detectability estimates for SKA-low AA* and the lunar array lack quantitative signal-to-noise calculations or foreground assumptions; these should be moved to a dedicated subsection with explicit integration times or array specifications.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight important aspects of our modeling assumptions and presentation. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [§4 (IGM thermal evolution and 21 cm power spectrum modeling)] The central amplitude calculation (illustrated for 200 M_⊙ and f_PBH,rec = 10^{-13} at z ≈ 20) adopts a pre-computed global IGM thermal history to which PBH-induced perturbations are added linearly. This omits iteration on the local sound speed increase from X-ray heating, which would reduce the supersonic regime of v_bc and therefore the modulation depth of the accretion rate. The 30% relative amplitude claim is load-bearing on this linearization; a quantitative test of the approximation (e.g., via local sound-speed update inside the accretion radius) is required.

    Authors: We agree that a fully iterative treatment of the local sound speed would be more complete. However, for the tiny PBH fractions we consider (f_PBH,rec ≈ 10^{-13}), the X-ray heating is strongly perturbative. A simple order-of-magnitude estimate shows that the induced change in sound speed reduces the accretion-rate modulation depth by only a few percent, leaving the reported ~30% VAO amplitude essentially unchanged. In the revised manuscript we will add this quantitative estimate together with a brief discussion of the linearization's validity. revision: partial

  2. Referee: [§3.1 (accretion rate and radiation field)] The accretion prescription is stated to follow standard Bondi-like rates modulated by v_bc, yet no explicit equation or numerical scheme is given for how the resulting radiation field is propagated through the IGM or how radiative transfer couples back to the local gas temperature and ionization fraction. Without these steps, the claimed separation into Ly-α-dominated and X-ray-dominated stages cannot be verified as robust against reasonable variations in efficiency or clustering.

    Authors: The accretion rate is computed from the standard Bondi-Hoyle-Lyttleton formula with the supersonic streaming velocity v_bc (as in the references we cite). The radiation field is obtained by volume-integrating the PBH emissivity (power-law X-ray spectrum plus Ly-α line emission) and the IGM thermal and ionization response follows the usual inhomogeneous equations for T_k and x_e. We will insert the explicit equations and a concise description of the numerical scheme into the revised §3.1 so that the stage separation and its robustness can be directly verified. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives VAO amplitudes in the 21 cm power spectrum by applying standard Bondi accretion modulated by relic v_bc streaming velocities to chosen PBH mass and f_PBH,rec values, then propagating the resulting inhomogeneous Ly-alpha and X-ray fields through pre-existing IGM thermal and spin-temperature models. No quantity is defined in terms of the output signal, no parameters are fitted to the target VAO wiggles, and no load-bearing step reduces to a self-citation or ansatz imported from the authors' prior work. The quoted examples (e.g., 30% amplitude at z~20 for f_PBH,rec~1e-13) are forward calculations from fixed inputs rather than tautological re-expressions of those inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard cosmological assumptions about PBH accretion, IGM radiative transfer, and relic streaming velocities; no new entities are introduced.

free parameters (2)
  • PBH mass at recombination = 200 solar masses
    Fixed at 200 solar masses for the example calculations that set the redshift of VAO appearance.
  • f_PBH,rec = 1e-13 or 3e-10
    Mass fraction in total DM chosen at 1e-13 or 3e-10 to produce detectable VAO features at z~20 or z~40.
axioms (2)
  • domain assumption PBHs accrete ambient gas and release radiation that alters IGM thermal status and hydrogen spin temperature.
    Invoked to link accretion rate to changes in the 21 cm signal.
  • standard math Relic supersonic relative streaming velocities between DM and baryons modulate the accretion rate.
    Standard early-universe velocity field used to generate the oscillatory imprint.

pith-pipeline@v0.9.0 · 5647 in / 1508 out tokens · 45421 ms · 2026-05-15T08:28:47.044465+00:00 · methodology

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Reference graph

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