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arxiv: 2606.24846 · v1 · pith:PKNUMTWQnew · submitted 2026-06-23 · 🌌 astro-ph.CO

Using SKAO to Understand the Clustering of Gravitational Wave Sources

Michele Bosi , Sarah Libanore , Nicola Bellomo , Caterina Scarpel , Federico Semenzato , Alvise Raccanelli , Michele Liguori This is my paper

Pith reviewed 2026-06-25 23:03 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords gravitational wavesbinary black holeslarge scale structurecross correlationSKAOtime delay distributionclustering bias
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The pith

Cross-correlating gravitational wave sources with SKA-Mid can constrain the time-delay distribution of binary black hole mergers.

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

The paper models gravitational wave sources from binary black holes and forecasts their cross-correlation with SKA-Mid intensity maps and radio surveys. It develops a semi-analytic model that ties these sources to galaxies via the uncertain time delay between binary formation and merger. The authors calculate the expected signal-to-noise for these cross-correlations using next-generation detectors like the Einstein Telescope and Cosmic Explorer. If the forecasts hold, this method will help determine the clustering properties of GW events and improve knowledge of when and where these mergers occur.

Core claim

SKA-Mid×ET2CE cross-correlations, using a semi-analytic model of GW events as a function of time-delay distribution, will allow extraction of the GW clustering bias and foster understanding of the time-delay distribution.

What carries the argument

The semi-analytic model for GW events hosted by SKAO galaxies as a function of the time-delay distribution between binary formation and merger, used to forecast cross-correlation signal-to-noise ratios.

If this is right

  • Measurements of GW clustering bias will indicate whether progenitors formed through stellar evolution or as primordial black holes.
  • Cross-correlations will probe the epochs and environments where stellar BBHs form most efficiently.
  • The approach mitigates uncertainties in individual GW detections by leveraging large-scale structure data.

Where Pith is reading between the lines

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

  • Similar cross-correlation techniques could be applied to other upcoming LSS surveys to study additional GW properties.
  • Success here might motivate more detailed simulations of binary formation in different galactic environments to refine the model.

Load-bearing premise

The semi-analytic model for GW events hosted by SKAO galaxies as a function of the time-delay distribution, together with the adopted number density and bias prescriptions for the three tracers, accurately represents the underlying astrophysics.

What would settle it

A measured cross-correlation signal-to-noise ratio that does not match the predicted values for any reasonable time-delay distribution would falsify the model's applicability.

Figures

Figures reproduced from arXiv: 2606.24846 by Alvise Raccanelli, Caterina Scarpel, Federico Semenzato, Michele Bosi, Michele Liguori, Nicola Bellomo, Sarah Libanore.

Figure 1
Figure 1. Figure 1: On the left: normalized redshift-dependent number density distribution of SKAO RC sources (dark red) and ET2CE GW events (blue), and normalized brightness temperature of the HI-IM survey (orange) expected for the Wide Band 1 Survey of SKA-Mid. On the right: redshift-dependent linear bias of the three tracers. Details on the modeling are provided in Sec. 2.2 for SKAO tracers, Sec. 3 for GWs (for which we sh… view at source ↗
Figure 2
Figure 2. Figure 2: Forecast constraints on the GW bias using ET2CE alone (left panel), in cross-correlation with RC galaxies (middle panel), and with the HI-IM (right panel) survey observed by SKA-Mid. The errorbars show the forecasts per each 𝑧-bin, while the shaded area extrapolates to the full redshift range. Each panel shows results for two choices of ℓmax for the GW survey. Our result is shown in figure 2, where we marg… view at source ↗
Figure 3
Figure 3. Figure 3: Redshift distribution (left) and bias (right) of GW events expected for ET2CE. In the 𝑓PBH = 0 scenario (blue), only ABHs are present; when 𝑓PBH = 1 (brown) the survey only contains PBHs. The color￾coded curves show intermediate scenarios, with relative ABHs, EPBHs, LPBHs abundances set by 𝑓PBH. Finally, we forecast the ability of SKA-Mid×ET2CE cross correlation to detect the contribution of LPBHs and EPBH… view at source ↗
Figure 4
Figure 4. Figure 4: Total SNR of the difference between only-ABH and ABH+EPBH+LPBH scenarios, vary￾ing A𝑚, 𝑓PBH. On the left, we cross-correlate GW with RC, on the right with HI-IM. 6 Constraining the time-delay distribution Phenomenological models such as those presented in Sec. 3 are widely used to connect the observed merger rate to the underlying physical properties of GW sources and hosts, especially with the SFR, althou… view at source ↗
Figure 5
Figure 5. Figure 5: GW bias obtained for different choices of the time-delay power-law distribution, and fixing either the BBH formation rate (left panel) or their merger rate (right panel). Insets: GW redshift-dependent number density distribution in arbitrary units (au) for the same two scenarios, following the same conventions of the main panels. In both cases, we model the SFR-𝑀ℎ relation using the T-RECS parameterization… view at source ↗
Figure 6
Figure 6. Figure 6: 𝜒 2 detectability of different time-delay distributions 𝑝(𝑡𝑑) ∝ 𝑡 𝛼𝑑 𝑑 , with respect to the fiducial case 𝛼𝑑 = −1. Results are obtained from the RC×GW cross-angular power spectra, by modeling the GW bias as function of 𝑝(𝑡𝑑) and of the SFR of the host galaxies, with the T-RECS (square markers) and UM (circle markers) parametrization. More conservative results (ℓmax = 100) are shown in blue, more optimisti… view at source ↗
Figure 7
Figure 7. Figure 7: we compare its results with what we previously obtained in [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
read the original abstract

Coalescing Binary Black Holes (BBHs) trace the Large-Scale Structure (LSS) of the Universe, and their clustering properties can be extracted from Gravitational Wave (GW) data. Next-generation detectors, such as the Einstein Telescope and Cosmic Explorer, will enable statistical studies of GW sources thanks to the massive number of detected events. However, such events will still suffer from significant instrumental and theoretical uncertainties. Cross-correlating GW maps with other LSS surveys provides a promising strategy to mitigate these limitations. The SKA-Mid intensity mapping and radio continuum surveys offer ideal datasets for cross-correlation studies with GWs (SKAO$\times$ET2CE). Their wide sky coverage and deep redshift sensitivity will allow precise probing of the epochs and environments where stellar BBHs form most efficiently. In this chapter, we forecast the potential of cross-correlation angular power spectra to extract information on the distribution and clustering properties of GW events. First, we model the number density and bias of three independent tracers: GW sources, neutral hydrogen intensity maps, and radio galaxies. We estimate the constraining power of SKA-Mid$\times$ET2CE on the GW clustering bias, which carries information on the origin of GW progenitors, e.g., whether they formed through stellar evolution or are primordial black holes. Finally, we develop a semi-analytic model for GW events hosted by SKAO galaxies as a function of the time-delay distribution between the binary formation and merger, which is still largely uncertain to date. We forecast the signal-to-noise ratio of their cross-correlation with SKA-Mid, and demonstrate that SKA-Mid$\times$ET2CE will foster our understanding of the time-delay distribution.

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 paper models the number density and bias of three tracers (GW sources, HI intensity maps, radio galaxies), develops a semi-analytic model linking GW events hosted by SKAO galaxies to the time-delay distribution, and forecasts the SNR of SKA-Mid × ET2CE angular cross-power spectra to constrain the GW clustering bias and time-delay distribution parameters.

Significance. If the forecasts hold under the stated assumptions, the work shows that SKAO×ET2CE cross-correlations can help constrain the uncertain time-delay distribution and distinguish GW progenitor channels via bias measurements. The explicit functional forms, redshift kernels, and bias parametrizations supplied in the full manuscript allow the SNR calculation to be reproduced under those inputs.

major comments (2)
  1. [§3] §3 (semi-analytic model): the SNR forecast for the time-delay distribution depends on the specific parametrization of the delay-time kernel and the assumed host-galaxy occupation; the manuscript should report how the SNR changes when the delay-time parameters are varied over their prior range, as this directly tests the central claim that the cross-correlation constrains the distribution.
  2. [§4] §4 (bias and number-density prescriptions): the adopted bias factors and number densities for the GW, HI, and radio-galaxy tracers are fixed inputs to the SNR calculation; if these are not marginalized or varied, the reported constraining power on the time-delay distribution may be overstated, and an explicit error budget or sensitivity test is needed.
minor comments (3)
  1. [Abstract] Abstract: the phrase 'in this chapter' appears to be a thesis remnant and should be replaced with 'in this work' for journal submission.
  2. [Throughout] Notation: ensure consistent abbreviation of SKA-Mid versus SKAO throughout the text and figures.
  3. [Figures] Figure captions: add explicit mention of the redshift range and k-range used for the SNR integration to improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. We address the two major comments below. Both can be addressed with targeted additions to the manuscript that test the robustness of the reported forecasts without altering the core methodology.

read point-by-point responses

  1. Referee: [§3] §3 (semi-analytic model): the SNR forecast for the time-delay distribution depends on the specific parametrization of the delay-time kernel and the assumed host-galaxy occupation; the manuscript should report how the SNR changes when the delay-time parameters are varied over their prior range, as this directly tests the central claim that the cross-correlation constrains the distribution.

    Authors: We agree that demonstrating robustness to the choice of delay-time kernel is important for supporting the central claim. In the revised manuscript we will add a short subsection (or appendix) that recomputes the SNR for the cross-power spectrum while sampling the delay-time parameters across their prior ranges (log-uniform in t_min and power-law index). The resulting range of SNR values will be reported explicitly, confirming that the forecast remains informative over the plausible parameter space. revision: yes

  2. Referee: [§4] §4 (bias and number-density prescriptions): the adopted bias factors and number densities for the GW, HI, and radio-galaxy tracers are fixed inputs to the SNR calculation; if these are not marginalized or varied, the reported constraining power on the time-delay distribution may be overstated, and an explicit error budget or sensitivity test is needed.

    Authors: The bias and number-density models are taken from the literature values cited in the manuscript and are treated as fixed for the baseline forecast, as is standard in such forecasting studies. To address the concern we will add a sensitivity test in §4 that varies each tracer’s bias and number density within the 1σ uncertainties quoted in the source references and recomputes the SNR on the time-delay parameters. The resulting variation will be presented as an explicit error budget on the forecasted constraints. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's core outputs are forecasts of SNR for SKA-Mid × ET2CE cross-power spectra, constructed from explicitly stated inputs: modeled number densities, bias prescriptions for GW sources, HI intensity maps and radio galaxies, plus a semi-analytic mapping from time-delay distribution to host-galaxy occupation. These functional forms, redshift kernels and bias parametrizations are supplied as assumptions rather than derived quantities; the SNR calculation is a forward propagation under those assumptions and does not reduce algebraically to the inputs by construction. No self-citation load-bearing steps, fitted-parameter renamings, or uniqueness theorems appear in the provided derivation outline. The forecast therefore remains internally consistent and non-circular under the stated modeling choices.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The forecasts rest on standard cosmological clustering assumptions plus domain-specific models for source densities, biases, and time-delay distributions that are not independently constrained within the abstract.

free parameters (2)
  • time-delay distribution parameters
    The semi-analytic model for GW events hosted by SKAO galaxies is built as a function of the still-uncertain time-delay distribution.
  • bias and number-density parameters for GW, HI, and radio-galaxy tracers
    These are modeled to compute the angular power spectra and their constraining power.
axioms (2)
  • standard math Standard flat LCDM cosmology governs the large-scale structure traced by all three populations.
    Invoked when computing angular power spectra and clustering bias.
  • domain assumption The adopted prescriptions for BBH formation rates and host-galaxy associations are sufficiently accurate for forecasting purposes.
    Required for the number-density and bias modeling described in the abstract.

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Reference graph

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