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arxiv: 2604.11542 · v1 · submitted 2026-04-13 · 🌌 astro-ph.CO

Impact of Stochastic Pop~III X-ray Binaries on the Cosmological 21-cm Signal

Saswata Dasgupta , Boyuan Liu , Anastasia Fialkov , Furen Deng , Jiten Dhandha , Rennan Barkana This is my paper

Pith reviewed 2026-05-10 15:47 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords 21-cm signalCosmic DawnX-ray binariesstochasticityPop III starspower spectrumX-ray heatingReionization
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The pith

Stochastic sampling of X-ray luminosities from rare Pop III binaries enhances fluctuations in the 21-cm power spectrum on small scales while leaving the global signal unchanged.

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

The paper investigates how the random distribution of high-mass X-ray binaries in the earliest galaxies changes the cosmological 21-cm signal. Standard models tie total X-ray output directly to star formation rate, but this average relation fails in sparse high-redshift regions where only a handful of sources exist. By instead drawing each binary's luminosity randomly from a power-law distribution, the simulation produces stronger patchiness in heating rates. This extra variance boosts the 21-cm power spectrum at wavenumbers above 0.3 per comoving megaparsec. The average brightness temperature and the large-scale power remain essentially the same.

Core claim

Replacing the deterministic L_X-SFR scaling with a stochastic model that samples X-ray luminosities from a power-law luminosity function in low star-formation-rate patches produces larger spatial fluctuations in the X-ray heating rate. These fluctuations raise the 21-cm power spectrum for k greater than 0.3 cMpc^{-1} while leaving the sky-averaged global signal and the large-scale power spectrum unaffected. The effect is expected to stay below the sensitivity of the Square Kilometre Array but could be reachable with future large-scale lunar arrays near redshift 25.

What carries the argument

The stochastic L_X model that samples binary X-ray luminosities from a power-law luminosity function in low-SFR regions instead of applying a fixed scaling relation to the star-formation rate.

If this is right

  • X-ray heating becomes patchier on small scales, raising the amplitude of 21-cm fluctuations above k = 0.3 cMpc^{-1}.
  • The sky-averaged 21-cm signal and its large-scale power spectrum stay unchanged to within simulation noise.
  • The extra small-scale power remains below the reach of the Square Kilometre Array.
  • Large-scale lunar-based experiments could detect the signature near redshift 25.

Where Pith is reading between the lines

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

  • Semi-numerical codes will need stochastic sampling of rare sources to avoid systematic bias when interpreting small-scale 21-cm data.
  • Measurements of the 21-cm power spectrum on intermediate scales could eventually constrain the high-redshift X-ray binary luminosity function.
  • Similar stochastic treatments may be required for other rare, luminous sources such as early supernovae or quasars.

Load-bearing premise

The true scatter in X-ray output from sparse high-redshift binaries is adequately represented by random draws from a power-law luminosity function tied only to star-formation rate.

What would settle it

A direct comparison of the 21-cm power spectrum at k approximately 1 cMpc^{-1} between a run with the stochastic luminosity sampling and an otherwise identical run with the deterministic scaling, tested against future lunar-array measurements at redshift 25.

Figures

Figures reproduced from arXiv: 2604.11542 by Anastasia Fialkov, Boyuan Liu, Furen Deng, Jiten Dhandha, Rennan Barkana, Saswata Dasgupta.

Figure 1
Figure 1. Figure 1: provides an essential validation of our stochastic sampling framework, justifying the use of numerically generated PDFs for 𝑙 across different regimes of 𝑁ˆ and 𝛼. The figure shows that the mean normalized luminosity ¯𝑙 correctly recovers its theoretical value of ¯𝑙 = 1 with errors ≲ 0.02 for all tested values of 𝛼 ∈ [0, 2] and 𝑁ˆ ∈ [10−5 , 105 ]. The lower bound of 𝑁ˆ = 10−5 is set to correspond to the lo… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of cumulative distribution functions (CDFs) of the normalized X-ray luminosity 𝑙 = 𝐿𝑋/𝐿ˆ𝑋 from our stochastic model (solid lines) and BPS simulations from Liu et al.(2024) (dotted lines). The stochastic model results are produced for a fixed XLF slope 𝛼 = 1.6 and the expected number of XRBs 𝑁ˆ = 10−1 (orange), 𝑁ˆ = 1 (magenta), 𝑁ˆ = 10 (brown), 𝑁ˆ = 102 (red), 𝑁ˆ = 103 (green), 𝑁ˆ = 104 (blue). … view at source ↗
Figure 3
Figure 3. Figure 3: Inverse cumulative distribution functions (ICDFs) of non-zero normalized total luminosity 𝑙 = 𝐿𝑋/𝐿ˆ𝑋 for large (𝑁ˆ = 105 , left) and small (𝑁ˆ = 10−4 , right) 𝑁ˆ across varying XLF slopes 𝛼. Left: In the large-𝑁ˆ case, the distributions remain sharply peaked and nearly symmetric around 𝑙 = 1 For flatter XLFs (e.g. 𝛼 ≤ 1.2), closely approximating the deterministic behavior assumed in standard 21-cm simulati… view at source ↗
Figure 4
Figure 4. Figure 4: Schematic describing the propagation of the stochastic Pop III XRB model to the 21-cm signal in 21cmSPACE. Step 1 (top) computes the local X-ray emissivity per cell from the local SFRD and the stochastic XRB model. Step 2 (bottom) derives the heating rate deposited in each cell via a lightcone summation over precomputed radiative-transfer coefficient grids, and evolves the gas temperature accordingly (see … view at source ↗
Figure 5
Figure 5. Figure 5: Evolution of the X-ray heating rate per baryon, log10 ( 𝜖𝑋 ), shown at redshifts 𝑧 = 32, 28, 24, and 16 (columns) for one slice of depth 3 cMpc of the heating rate fields. The rows correspond to different cases for the stochastic XRB models: a deterministic case with no stochasticity (top row), followed by stochastic models with XLF slopes 𝛼 = 2, 1.5, and 0.2, where smaller 𝛼 corresponds to stronger stocha… view at source ↗
Figure 6
Figure 6. Figure 6: Temperature difference maps (with a slice depth of 3 cMpc), Δ𝑇𝐾 ≡ 𝑇 stoch 𝐾 − 𝑇 det 𝐾 , between stochastic cases with 𝛼 = 2, 1.5, and 0.2 (left to right) and the corresponding deterministic case at 𝑧 = 24. All cases assume the same astrophysical model with 𝑓𝑋 = 100, see [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Probability distribution functions (PDFs) of the kinetic temperature differences,Δ𝑇𝐾 ≡ 𝑇 stoch 𝐾 −𝑇 det 𝐾 , at 𝑧 = 24 for Pop III X-ray heating with 𝑓𝑋 = 100. The results are shown for stochastic XRB luminosity distributions with power-law indices 𝛼 = 2, 1.5, and 0.2. All PDFs peak close to zero, indicating very little bias in the global temperature, while decreasing 𝛼 produces broader distributions with p… view at source ↗
Figure 8
Figure 8. Figure 8: The 21-cm differential brightness temperature maps (with a slice depth of 3 cMpc) at 𝑧 = 24 shown for the deterministic case (left) and for stochastic Pop III XRB models with 𝛼 = 2, 1.5, and 0.2 (left to right) for 𝑓𝑋 = 100. All maps are displayed on the same colour scale for consistency. While the large-scale morphology of 𝛿𝑇𝑏 remains similar across models, decreasing 𝛼 enhances the small-scale fluctuatio… view at source ↗
Figure 9
Figure 9. Figure 9: 21-cm power spectra, Δ 2 (𝑘), at 𝑧 = 24 generated with 21cmSPACE assuming the value 𝑓𝑋 = 100 with the rest of the parameters adopting their standard values from [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Evolution of the 21-cm power spectrum, Δ 2 (𝑘), as a function of redshift for different comoving wavenumbers 𝑘 = 0.3, 0.5, and 1.0 cMpc−1 (left to right). The results are shown for stochastic Pop III XRB models with XLF slope 𝛼 = 0.2, 1.5, and 2.0, as well as for the deterministic case with no stochasticity, assuming 𝑓𝑋 = 100 and the standard values of the astrophysical parameters from [PITH_FULL_IMAGE:f… view at source ↗
Figure 11
Figure 11. Figure 11: Redshift evolution of the difference signal-to-noise ratio, 𝛿SNR ≡ (Δ 2 stoch − Δ 2 det)/Δ 2 noise,lunar, for three representative length-scales, 𝑘 = 0.3, 0.5, and 1.0 cMpc−1 (columns), and for three successive stages of a proposed lunar far side interferometer (rows: Stage I, II, and III). Each panel shows the stochastic models with XLF slopes 𝛼 = 0.2, 1.5, and 2.0 (solid, dashed, and dotted curves, resp… view at source ↗
read the original abstract

High-mass X-ray binaries are one of the primary drivers of the 21-cm signal from Cosmic Dawn and Reionization, playing a leading role in the thermal history of the intergalactic medium. In traditional semi-numerical simulations, a deterministic scaling relation between the total X-ray luminosity of high-mass X-ray binaries, $L_{\rm X}$, and star formation rate (SFR) is usually adopted. However, this assumption is inaccurate for high-redshift low-SFR regions hosting few sources. The spatial variation in the number and luminosity of these sources is expected to enhance fluctuations in the Cosmic Dawn 21-cm signal. Here we quantify this effect by introducing a stochastic $L_{\rm X}$ model sampled from a power-law X-ray luminosity function. Implementing this in 21cmSPACE, a large-scale simulation framework of Cosmic Dawn and Reionization, we find that the stochasticity leads to enhanced fluctuations in X-ray heating rate fields, and affects the 21-cm power spectrum on small scales ($k>0.3~ \mathrm{cMpc^{-1}}$). The impact of stochasticity on the global 21-cm signal and on the large-scale power spectrum is found to be negligible. Our results suggest these effects will remain undetected by the upcoming Square Kilometer Array. However, large-scale lunar-based experiments may be sensitive to the signatures of stochastic X-ray heating at $z\sim 25$. Quantifying these corrections is a vital step toward robust 21-cm modeling and ensuring that future precision data interpretation is free from astrophysical biases.

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 / 3 minor

Summary. The manuscript examines the impact of stochastic X-ray luminosities from Population III high-mass X-ray binaries on the cosmological 21-cm signal during Cosmic Dawn. By replacing the standard deterministic L_X-SFR scaling with stochastic sampling from a power-law X-ray luminosity function in low-SFR cells inside the 21cmSPACE semi-numerical code, the authors find enhanced fluctuations in the X-ray heating rate field that increase the 21-cm power spectrum only on small scales (k > 0.3 cMpc^{-1}). The global 21-cm signal and large-scale power spectrum remain essentially unchanged, leading to the conclusion that the effect lies below SKA sensitivity but could be accessible to future lunar-based arrays at z ~ 25.

Significance. If the reported scale-dependent enhancement is robust, the work supplies a concrete, implementable correction for an often-neglected source of variance in 21-cm modeling. It demonstrates that stochasticity matters only below a well-defined wavenumber, thereby guiding the design of future observations and reducing the risk of astrophysical bias in parameter inference from SKA or lunar data. The use of an existing public simulation framework aids reproducibility.

major comments (2)
  1. [Results (power spectrum figures)] Results section on 21-cm power spectra: the reported enhancement at k > 0.3 cMpc^{-1} is presented without error bars or a statement of statistical significance across multiple realizations; it is therefore unclear whether the difference exceeds sample variance or resolution noise.
  2. [Stochastic model implementation] Section describing the stochastic L_X implementation: the power-law index and normalization of the XLF are treated as fixed inputs with no sensitivity study; because these parameters directly set the amplitude of the sampled variance, the claim that stochasticity affects only small scales could shift if the index is varied within observationally allowed ranges.
minor comments (3)
  1. [Abstract and Introduction] The abstract and introduction use both 'Pop~III' and 'Population III' inconsistently; adopt a single abbreviation throughout.
  2. [Figures] Figure captions for the heating-rate and power-spectrum panels should explicitly state the redshift and the number of realizations averaged.
  3. [Discussion] A brief comparison to earlier analytic estimates of HMXB stochasticity (e.g., from 21-cm literature on source discreteness) would help place the numerical results in context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and recommendation for minor revision. We address the major comments point by point below and have revised the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: Results section on 21-cm power spectra: the reported enhancement at k > 0.3 cMpc^{-1} is presented without error bars or a statement of statistical significance across multiple realizations; it is therefore unclear whether the difference exceeds sample variance or resolution noise.

    Authors: We agree that error bars from multiple realizations are needed to establish statistical significance. In the revised manuscript we have performed five independent realizations with different random seeds for the stochastic sampling. The 21-cm power spectrum figures now display error bars representing the standard deviation across these runs. The enhancement at k > 0.3 cMpc^{-1} remains well above the error bars, confirming it exceeds sample variance and is not due to resolution noise. revision: yes

  2. Referee: Section describing the stochastic L_X implementation: the power-law index and normalization of the XLF are treated as fixed inputs with no sensitivity study; because these parameters directly set the amplitude of the sampled variance, the claim that stochasticity affects only small scales could shift if the index is varied within observationally allowed ranges.

    Authors: We acknowledge that a sensitivity study on the XLF parameters strengthens the robustness claim. The power-law index and normalization are fixed to values consistent with observational constraints on high-redshift X-ray binaries. In the revised manuscript we have added a sensitivity analysis varying the index over the observationally allowed range -1.3 to -1.7. While the amplitude of the small-scale enhancement changes modestly, the conclusion that stochasticity affects only scales k > 0.3 cMpc^{-1} remains unchanged. revision: yes

Circularity Check

0 steps flagged

No circularity: results follow directly from stochastic sampling in simulation

full rationale

The paper's claims rest on direct outputs from implementing an explicit stochastic L_X sampling procedure (drawn from a power-law XLF) inside the 21cmSPACE code and measuring the resulting X-ray heating fluctuations and 21-cm power spectra. No derivation step reduces the reported scale-dependent enhancements (k>0.3 cMpc^{-1}) or the negligible large-scale/global impact to a fitted parameter or self-referential definition by construction. The stochastic model is an input choice, not an output that loops back to itself, and the provided text shows no load-bearing self-citations or uniqueness theorems that would make the central results tautological. The analysis is self-contained against the simulation benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only abstract available; ledger is therefore minimal. The central claim rests on the assumption that a power-law XLF describes Pop III binaries and that stochastic sampling in low-SFR patches is the dominant source of extra variance.

free parameters (1)
  • power-law index and normalization of X-ray luminosity function
    Parameters of the power-law XLF from which luminosities are sampled; their specific values are not stated in the abstract but control the amplitude of stochastic fluctuations.
axioms (1)
  • domain assumption Standard assumptions of semi-numerical 21-cm simulations (e.g., excursion-set formalism for ionization and heating) hold when stochastic X-ray sources are added.
    Invoked by implementing the model inside 21cmSPACE.

pith-pipeline@v0.9.0 · 5605 in / 1424 out tokens · 23769 ms · 2026-05-10T15:47:47.425935+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

  1. [1]

    arXiv:2406.10096 Bale S

    Abdurashidova Z., et al., 2022, ApJ, 924, 51 Antoniou V., Zezas A., 2016, MNRAS, 459, 528 Artuc K., de Lera Acedo E., 2024, arXiv e-prints, p. arXiv:2406.10096 Bale S. D., et al., 2023, arXiv e-prints, p. arXiv:2301.10345 Barkana R., 2016, Phys. Rep., 645, 1 Barkana R., 2018, Nature, 555, 71 Barkana R., Loeb A., 2004, ApJ, 609, 474 Barkana R., Loeb A., 20...

    work page doi:10.1007/b97336 2022

  2. [2]

    2023), while in the Pop II case the typical value is around𝑓𝑋,II =1(Fragos et al

    Finally, Pop III XRBs are expected to be much more efficient with 𝑓𝑋 =100for a log-flat Pop III IMF (Sartorio et al. 2023), while in the Pop II case the typical value is around𝑓𝑋,II =1(Fragos et al. 2013a). To validate this decision, we present in Figure A5 the difference MNRAS000, 1–17 (2026) Impact of XRB Stochasticity on 21-cm Signal17 0 100 200 3000 1...

    work page 2023