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arxiv: 2502.14164 · v3 · submitted 2025-02-20 · 🌌 astro-ph.CO

Implementing a Robust Test of Galaxy Catalogue Completeness for Dark Siren Measurements of the Hubble Constant

L. Datrier , M. Hendry This is my paper

Pith reviewed 2026-05-23 03:09 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords galaxy catalogue completenessdark sirensHubble constantgravitational wave cosmologymagnitude-redshift samplegwcosmo pipelineGLADE catalogue
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The pith

A statistical test for galaxy catalogue completeness improves dark siren Hubble constant measurements without luminosity function assumptions.

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

The paper applies a straightforward statistical test to find the apparent magnitude completeness limit in magnitude-redshift galaxy samples. This test is inserted into the gwcosmo pipeline used for dark siren cosmology to constrain the Hubble constant H0. The approach is less conservative than the method currently used in the pipeline and does not need prior knowledge of the luminosity function. For the GWTC-1 events with the GLADE catalogue the test yields a 1.3 percent improvement on the dark-siren-only H0 posterior and a 3.4 percent improvement when combined with GW170817; larger gains appear with GLADE+. The final posterior shows no change for the GWTC-3 dataset with GLADE+ K-band data because that catalogue supplies essentially no K-band coverage for those events.

Core claim

The robust statistical test determines the apparent magnitude completeness limit of a magnitude-redshift sample directly from the data and, when adopted inside gwcosmo, produces tighter and less biased H0 posteriors from dark sirens than the conservative completeness estimates previously employed.

What carries the argument

The robust statistical test for the apparent magnitude completeness limit of a magnitude-redshift sample, which replaces the existing conservative estimate inside the gwcosmo pipeline.

If this is right

  • H0 inference from dark sirens alone improves by 1.3 percent with GLADE and by 8.6 percent with GLADE+ for GWTC-1 events.
  • The combined dark-siren plus GW170817 posterior tightens by 3.4 percent with GLADE and by 6.3 percent with GLADE+.
  • No change occurs for GWTC-3 events with GLADE+ K-band photometry because the catalogue supplies negligible coverage in that band.
  • As deeper galaxy catalogues become available the adoption of less conservative completeness limits will grow in importance for gravitational-wave cosmology.

Where Pith is reading between the lines

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

  • The same test could be inserted into other dark-siren analysis codes that currently rely on fixed or luminosity-function-dependent completeness cuts.
  • If the test is applied to future catalogues that reach higher redshifts it may reduce the dominant systematic uncertainty in multi-messenger H0 measurements.
  • A direct test on mock catalogues with injected known completeness would quantify any residual bias introduced by the statistical procedure.

Load-bearing premise

The statistical test correctly identifies the true completeness limit and that feeding this limit into gwcosmo yields unbiased H0 improvements without creating new selection effects.

What would settle it

Re-running the GWTC-1 analysis with the test on a simulated catalogue whose completeness limit is known by construction and finding that the recovered H0 posterior is shifted or broadened relative to the known truth would falsify the claim.

Figures

Figures reproduced from arXiv: 2502.14164 by L. Datrier, M. Hendry.

Figure 1
Figure 1. Figure 1: Illustrating the 𝑆1 and 𝑆2 areas for a single pixel in the GLADE 𝐵-band. 𝑀 vs 𝜇 with 𝑆1 and 𝑆2 for a galaxy (𝑀𝑖 ,𝜇𝑖). The dash-dotted orange and blue lines show, respectively, the robust and median apparent magnitude thresholds for this sample of galaxies. The green line shows a test limit magnitude 𝑚∗ that is fainter than the true 𝑚𝑡ℎ𝑟 . 𝐸𝑖 = 1 2 and 𝑉𝑖 = 𝑛𝑖 − 1 12(𝑛𝑖 + 1) . (5) R01 defines the quantity 𝑇… view at source ↗
Figure 2
Figure 2. Figure 2: Final posterior on 𝐻0 using the GLADE 𝐵-band on the GWTC-1 dataset. Vertical dashed lines show the 1𝜎 intervals. The solid lines show results showing the robust method, while dash-dotted lines show results using 𝑚med as the apparent magnitude threshold. 20 40 60 80 100 120 140 H0 (km s 1 Mpc 1 ) 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 p(H 0) (k m 1 s M p c) Median, dark sirens Median with GW1… view at source ↗
Figure 3
Figure 3. Figure 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Results using the robust (blue) and median (orange) methods for individual events using the GLADE+ 𝐵-band with the GWTC-1 catalogue. The event GW170814 is analysed using the 𝑔-band of the DES-Y1 catalogue. 20 40 60 80 100 120 140 H0 (km s 1 Mpc 1 ) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 p(H 0) (k m 1 s M p c) Median, dark sirens Median with GW170817 Robust, dark sirens Robust with GW170817 [PITH_FULL_IMAGE:fi… view at source ↗
Figure 6
Figure 6. Figure 6: Final posterior on 𝐻0 using the GLADE+ 𝐾-band on the GWTC-3 dataset. Vertical dashed lines show the 1𝜎 intervals. The solid lines show results showing the robust method, while dash-dotted lines show results using 𝑚med as the apparent magnitude threshold. further investigation of the validity of this assumption for other bands and other catalogues will be carried out in future work. Ongoing work ahead of th… view at source ↗
Figure 7
Figure 7. Figure 7: Inferred 𝐻0 using the robust (orange) and median (blue) methods for estimating galaxy catalogue completeness, for individual events in the GWTC-3 catalogue. The 𝐾-band of the GLADE+ catalogue is used for analysis. edge the use of the following python packages in this work: gwcosmo (Gray et al. 2020), Matplotlib (Hunter 2007), healpy (Górski et al. 2005; Zonca et al. 2019). DATA AVAILABILITY The GWTC-3 data… view at source ↗
read the original abstract

We present the application of a robust test of galaxy catalogue completeness to the gwcosmo pipeline. The method implements a straightforward statistical test for determining the apparent magnitude completeness limit of a magnitude-redshift sample. This offers an improved, less conservative approach compared with how galaxy catalogue completeness is currently estimated in the gwcosmo gravitational wave cosmology pipeline for determining the Hubble constant $H_{0}$. The test also does not require prior knowledge of the luminosity function, and thus returns a more robust estimate of the limiting apparent magnitude for a magnitude-redshift sample of galaxies. For GWTC-1 results using $B_{J}$-band photometry of galaxies in the GLADE catalogue, we find a $1.3\%$ improvement on the inference of $H_{0}$ using dark sirens only and a $3.4\%$ improvement for the combined posterior with GW170817. Using GLADE+, there is a $8.6\%$ improvement with dark sirens only and a $6.3\%$ improvement for the combined posterior with GW170817. However, the final posterior on $H_{0}$ using the GWTC-3 dataset with the GLADE+ $K$-band shows no improvement when applying the robust method. This is because the GLADE+ galaxy catalogue provides little or no coverage in the $K$-band for any of the GWTC-3 events. With the use of deeper galaxy catalogues in future gravitational wave cosmology analyses, the adoption of a less conservative estimate of magnitude completeness will become increasingly important.

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 paper claims that a statistical test for the apparent magnitude completeness limit of magnitude-redshift galaxy samples can be integrated into the gwcosmo pipeline for dark-siren H0 inference. This yields a less conservative completeness estimate than the current gwcosmo prescription, requires no luminosity-function prior, and produces quantified improvements in H0 posterior precision (1.3–8.6 % for GWTC-1 events with GLADE/GLADE+; zero improvement for GWTC-3 K-band data due to catalog coverage).

Significance. If the test recovers an unbiased completeness limit and the resulting selection function does not introduce new systematics, the approach would allow more galaxies to enter dark-siren analyses, tightening H0 constraints as deeper catalogs become available. The manuscript supplies concrete percentage gains on real GWTC-1 events and identifies the catalog-coverage limitation for GWTC-3, which is a useful diagnostic.

major comments (2)
  1. [§4] §4 (Application to GWTC-1/GLADE): the reported 1.3–8.6 % precision gains rest on the assumption that the statistical test returns a completeness limit whose associated selection function leaves the H0 posterior unbiased; no Monte-Carlo injection study or comparison against catalogs with independently known completeness is shown to confirm this.
  2. [§5] §5 (GWTC-3 K-band results): the statement that zero improvement occurs solely because of catalog coverage is not accompanied by a demonstration that the test itself correctly identifies the (low) completeness limit or that altering the included galaxies does not shift the posterior in a biased direction.
minor comments (2)
  1. [Abstract, §2] The abstract and §2 should name the specific statistical test (e.g., the exact form of the magnitude-redshift completeness estimator) rather than referring only to “a robust test.”
  2. [Figure 3] Figure 3 (or equivalent) comparing completeness limits: the caption should state whether the plotted limit is the mode, median, or 95 % credible value of the test output.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and for acknowledging the potential utility of the method. Below we respond point-by-point to the two major comments.

read point-by-point responses

  1. Referee: [§4] §4 (Application to GWTC-1/GLADE): the reported 1.3–8.6 % precision gains rest on the assumption that the statistical test returns a completeness limit whose associated selection function leaves the H0 posterior unbiased; no Monte-Carlo injection study or comparison against catalogs with independently known completeness is shown to confirm this.

    Authors: We agree that an explicit Monte-Carlo injection campaign on the full gwcosmo pipeline would provide the strongest possible confirmation that the selection function derived from the test does not bias the H0 posterior. The present manuscript does not contain such a study. The completeness test we implement follows the procedure validated in the original reference (which recovered input limits in simulated magnitude-redshift catalogs without luminosity-function assumptions). In this work we only compare the resulting H0 posteriors against the more conservative gwcosmo cut on the same real catalogs. We will revise §4 to include a concise discussion of the test’s prior validation and to state explicitly that a dedicated end-to-end injection study lies beyond the scope of the current paper. revision: partial

  2. Referee: [§5] §5 (GWTC-3 K-band results): the statement that zero improvement occurs solely because of catalog coverage is not accompanied by a demonstration that the test itself correctly identifies the (low) completeness limit or that altering the included galaxies does not shift the posterior in a biased direction.

    Authors: For the GWTC-3 events the test returns a very bright completeness limit because GLADE+ supplies essentially no K-band photometry at the relevant redshifts; consequently both the standard and the new prescriptions retain almost no galaxies and the posterior is unchanged. We will add a short table or figure in §5 that reports the completeness magnitude returned by the test, the number of galaxies retained under each prescription, and the resulting H0 credible intervals, thereby making the catalog-coverage explanation quantitative. A full bias-validation study for these particular data is not performed in the manuscript. revision: partial

Circularity Check

0 steps flagged

No significant circularity; external test applied to catalogs

full rationale

The paper applies an external statistical test for apparent magnitude completeness limits to existing galaxy catalogs (GLADE/GLADE+) and compares the resulting H0 posteriors against the standard gwcosmo prescription. Reported improvements (1.3–8.6%) are empirical outcomes from re-running the pipeline on GWTC-1/3 data with the new limits; no equations, parameters, or results reduce by construction to inputs defined within the paper. The test requires no luminosity function and is benchmarked directly on real catalogs, rendering the derivation self-contained against external data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the statistical test for determining completeness limits and its integration into the gwcosmo pipeline without introducing bias.

axioms (1)
  • domain assumption The statistical test accurately determines the apparent magnitude completeness limit of a magnitude-redshift sample without prior knowledge of the luminosity function.
    This is presented as the key advantage over the current conservative method in gwcosmo.

pith-pipeline@v0.9.0 · 5811 in / 1421 out tokens · 40497 ms · 2026-05-23T03:09:53.450942+00:00 · methodology

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Works this paper leans on

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