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arxiv: 2605.15287 · v1 · pith:QC7KCAVSnew · submitted 2026-05-14 · 🌌 astro-ph.CO · hep-th

Peculiar-velocity distribution functions and 21-cm fluctuations

Ryan Yuran Zhang , Marc Kamionkowski This is my paper

Pith reviewed 2026-05-19 16:18 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-th
keywords 21-cm fluctuationspeculiar velocitiesbaryon-dark matter relative velocitystar formation rate densityjoint probability distributioncosmological correlationslinear perturbation theory
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The pith

Accounting for the difference between parallel and perpendicular peculiar-velocity correlations improves 21-cm fluctuation predictions.

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

The paper derives the complete joint probability distribution for the squares of peculiar velocities at two separated points, without assuming that the parallel and perpendicular components have identical correlations. This distribution enters the calculation of spatial correlations in star-formation-rate density, which depends nonlinearly on the baryon-dark-matter relative velocity. Earlier work used a simpler approximation that ignored the directional distinction. The resulting error in the predicted 21-cm power spectrum is usually a few percent or less, but grows when different contributions to the signal nearly cancel.

Core claim

The full joint PDF of the squares of the peculiar velocity at two different points is obtained from the two-point velocity statistics that distinguish the parallel and perpendicular components. When this PDF is used instead of the prior simplifying assumption, the predicted fluctuations in the cosmological 21-cm background change by an amount that is generally less than a few percent but can be larger at certain wavenumbers k and redshifts z where cancellations between contributions occur.

What carries the argument

The full joint PDF of the squares of the peculiar velocity at two points, constructed from separate parallel and perpendicular velocity correlations.

If this is right

  • The correct PDF expression can be coded directly into existing 21-cm prediction routines.
  • The added computation raises total run time by only a few percent.
  • Errors from the earlier approximation remain below a few percent for most k and z but become appreciable when opposing signal contributions cancel.
  • The refined calculation supplies a ready-to-use correction for any study that needs percent-level accuracy in 21-cm forecasts.

Where Pith is reading between the lines

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

  • Future high-precision 21-cm surveys may need this correction to avoid systematic offsets in extracted cosmological parameters.
  • Analogous directional refinements could matter for other observables that depend nonlinearly on relative velocities.
  • Direct tests against N-body simulations of the velocity field at the relevant redshifts would confirm the size of the correction.

Load-bearing premise

The peculiar velocity field obeys the two-point statistics given by linear perturbation theory in the standard cosmological model.

What would settle it

Measurements of the 21-cm power spectrum at the specific k and z values where cancellations are predicted would show a difference larger than a few percent between the approximate and the full-PDF calculations.

Figures

Figures reproduced from arXiv: 2605.15287 by Marc Kamionkowski, Ryan Yuran Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. The velocity correlation coefficients as functions of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Here we show [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The top panel shows the 21-cm intensity-fluctuation [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Predictions for observables involving the cosmological 21-cm background require calculations of spatial correlations of star formation rate densities (SFRDs) which have a nonlinear dependence on the baryon-dark matter relative velocity. Prior work derived these SFRD correlations with a simplifying assumption that neglected the difference between the correlations of the components of the velocity parallel and perpendicular to the separation between the two points being correlated. Here we calculate the full joint PDF of the squares of the peculiar velocity at two different points. The error that arises in predictions for 21-cm fluctuations if this subtlety is overlooked is generally less than a few percent, but it can be larger for some values of wavenumber $k$ and redshift $z$ if there are cancellations between different contributions to the total signal. The correct expression is easily implemented and increases the run time of the code by only a few percent.

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

1 major / 2 minor

Summary. The manuscript calculates the full joint PDF of the squares of peculiar velocities at two spatially separated points, properly distinguishing the parallel and perpendicular components of the velocity correlations. It shows that the simplifying assumption used in prior work on SFRD correlations for 21-cm fluctuations produces an error that is generally less than a few percent, although larger deviations can appear for specific values of wavenumber k and redshift z when cancellations occur among contributions to the total signal. The correct expression is stated to be straightforward to implement and to increase code runtime by only a few percent.

Significance. If the result holds, the work supplies a modest but practical refinement to the modeling of 21-cm fluctuations driven by baryon-dark matter relative velocities. By remaining entirely within linear perturbation theory for the velocity two-point functions, the calculation strengthens the accuracy of existing predictions without introducing new free parameters or substantial computational cost. This is a useful technical improvement for codes that forecast 21-cm observables.

major comments (1)
  1. The central claim that the overlooked subtlety produces an error 'generally less than a few percent' (with larger values only in cancellation regimes) is load-bearing for the paper's conclusion. The abstract states this bound, but the manuscript must supply explicit numerical comparisons or plots (e.g., fractional difference versus k at several z) with error bars to substantiate the quoted magnitude; without them the quantitative statement remains unverified.
minor comments (2)
  1. Clarify in the text how the joint PDF is constructed from the parallel and perpendicular velocity correlations (standard linear-theory expressions) so that readers can reproduce the final expression without ambiguity.
  2. Add a short table or figure caption that lists the maximum fractional error found across the explored (k, z) range to make the 'generally less than a few percent' statement immediately quantifiable.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive overall assessment. We respond to the single major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The central claim that the overlooked subtlety produces an error 'generally less than a few percent' (with larger values only in cancellation regimes) is load-bearing for the paper's conclusion. The abstract states this bound, but the manuscript must supply explicit numerical comparisons or plots (e.g., fractional difference versus k at several z) with error bars to substantiate the quoted magnitude; without them the quantitative statement remains unverified.

    Authors: We agree that the quantitative bound requires explicit numerical support to be fully convincing. In the revised manuscript we will add a new figure (or panel set) that directly plots the fractional difference between the approximate and exact 21-cm power spectra versus wavenumber k at several representative redshifts. The plots will include the range of variation arising from the different velocity-component contributions, thereby illustrating both the typical magnitude of the error (generally below a few percent) and the larger deviations that appear only when cancellations occur. This addition will substantiate the claim made in the abstract and strengthen the paper's central conclusion. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper computes the joint PDF of peculiar-velocity squares directly from the two-point velocity correlations of linear perturbation theory, comparing the full result against a prior simplifying assumption that neglected parallel/perpendicular distinctions. This comparison yields an error estimate for 21-cm fluctuations without any parameter fitting inside the paper, without self-definitional loops, and without load-bearing self-citations that substitute for independent derivation. The central claim remains a straightforward extension of standard cosmological velocity statistics and is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard assumptions in cosmological perturbation theory for velocity fields. No new free parameters or invented entities are mentioned.

axioms (1)
  • domain assumption Peculiar velocities follow linear perturbation theory from density fluctuations in the standard Lambda-CDM cosmology.
    This underpins the two-point velocity statistics and the parallel/perpendicular decomposition used for the joint PDF.

pith-pipeline@v0.9.0 · 5669 in / 1308 out tokens · 95256 ms · 2026-05-19T16:18:45.694130+00:00 · methodology

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Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages · 2 internal anchors

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