arxiv: 2605.09248 · v1 · submitted 2026-05-10 · 🌌 astro-ph.GA · astro-ph.CO

Recognition: no theorem link

How to count clustered galaxies

Yunting Wang , Ryley Hill , Douglas Scott , Tessa Vernstrom

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:23 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO

keywords galaxy number countssubmillimetre surveysclustering biasP(D) fluctuation analysisHerschel SPIREconfusion-limited observationsGOODS-N field

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The pith

Galaxy clustering systematically biases standard P(D) number counts in confusion-limited submillimetre maps, and a new empirical method corrects it by combining one- and two-point statistics.

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

In submillimetre surveys where galaxies are too faint and crowded to count individually, the common P(D) fluctuation analysis assumes galaxies follow a random Poisson distribution. Real galaxies cluster, and this paper uses simulations to show that the clustering produces systematic errors in the recovered number counts. The authors introduce an empirical technique that measures the size of the bias directly from the map by folding in two-point clustering information and then subtracts it. When applied to deep Herschel-SPIRE data on the GOODS-N field, the corrected counts at 500 microns are inflated by a factor of 1.6 near 10 mJy and mildly suppressed at the faintest fluxes, with smaller shifts at shorter wavelengths. The method works with any survey that has a well-characterised beam and noise, allowing fuller use of existing far-infrared and submillimetre data sets.

Core claim

Simulations demonstrate that clustering biases P(D)-derived number counts. An empirical method is presented that simultaneously measures and corrects for this bias by combining the 1- and 2-point statistics in the map, thereby maximising the information extracted from the data. Revised galaxy number counts at 250, 350 and 500 microns are derived from deep Herschel-SPIRE observations of the GOODS-N field, showing that clustering inflates the apparent counts by a factor of 1.6 around 10 mJy at 500 microns with milder effects at shorter wavelengths.

What carries the argument

An empirical correction that measures the clustering bias from the combination of one-point P(D) fluctuations and two-point statistics in the same map and subtracts it from the derived counts.

Load-bearing premise

The simulations used to calibrate the empirical correction accurately reproduce the clustering properties and beam-convolved statistics of real galaxies in the Herschel observations.

What would settle it

Independent number counts obtained from higher-resolution observations or from stacking analyses in the same field that do not rely on the P(D) assumption.

Figures

Figures reproduced from arXiv: 2605.09248 by Douglas Scott, Ryley Hill, Tessa Vernstrom, Yunting Wang.

**Figure 1.** Figure 1: Standard deviation by bin in the histograms of 1000 randomised maps as a ratio of the Poisson error estimate. Randomised maps are simulated at the original pixel size and also with pixels sampled at 1×FWHM. A grey band spanning 10% of the Poisson error is plotted for visualisation. The sampled map is better represented by Poisson error, while the original map has additional scatter, mostly from pixel corr… view at source ↗

**Figure 2.** Figure 2: Left panel: Observed histograms of the clustered map (blue) and the randomised map (red), both generated from the simulated Herschel-SPIRE map at 500 µm. Right panel: P(D) galaxy number counts fit to the clustered map (blue) and the randomised map (red). The galaxy number counts are Euclidean normalised here. The first node is an upper limit. The shaded region is the 68% confidence region for each fit. The… view at source ↗

**Figure 3.** Figure 3: Examples of generated maps with different clustering strengths or characteristic clustering scales θ0 (Equation 5), with exaggerated values for visualisation of the clustering effect. The map size is 2 deg2 , the same as the size of the SIDES simulation. 0.010 0.005 0.000 0.005 0.010 0.015 0.020 0.025 0.030 Observed flux density [Jybeam 1 ] 0 20 40 60 80 PDF of observed flux mean of 1000 randomized maps sc… view at source ↗

**Figure 4.** Figure 4: Mean PDFs of 100 generated maps for each clustering strength or characteristic clustering scale θ0 (Equation 5) in coloured dashed lines. The PDF is computed from the average histogram by Equation 7. The red dashed line and the shaded region represent the mean PDF and standard deviation of 1000 randomised maps. As the clustering increases, the peaks of the histograms shift to fainter flux densities and the… view at source ↗

**Figure 5.** Figure 5: Top Panel: Same colour style as in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Examples of p¯rand − p¯θ at different clustering strengths or θ0 (dots), with their respective fits from Equation 8 in solid lines. The vertical dashed line represents the peak xpeak in the equation. The shaded region represents the scatter in p¯rand − p¯θ in 100 simulated map pairs. After aligning the histogram peaks to the average histogram of randomised maps, we then adopt the LevenbergMarquardt least… view at source ↗

**Figure 7.** Figure 7: Examples of power spectra for generated maps at 500 µm with different clustering strengths or characteristic clustering scales θ0 (Equation 5). The constant shot noise term has been subtracted from these power spectra. The solid line is given by Equation 11. We calculate the power spectra for 100 maps of each clustering strength and stack the power spectra in each k-bin. We then remove the constant shot-… view at source ↗

**Figure 8.** Figure 8: Flow chart illustrating the process for correcting the clustering bias in galaxy number counts fitting through P(D) fluctuation analysis. Since P(D) fits the flux histogram of the map, the process focuses on removing the impact of clustering (2-point statistics) on the flux histogram (1-point statistics). The specific form used in the correction is derived from simulations and the amplitude of clustering f… view at source ↗

**Figure 9.** Figure 9: Left panel: Observed histograms of the clustered map before (blue) and after (red) correction in solid lines, after aligning their peaks. The grey dashed lines are the flux cutoffs beyond which the data are not used in the fit. Right panel: P(D) galaxy number counts models before (blue) and after (red) correction. The galaxy number counts are Euclidean normalised here. The first node is an upper limit. The… view at source ↗

**Figure 10.** Figure 10: Galaxy number count fits before (blue) and after (red) correcting the histograms at 250 µm, 350 µm and 500 µm (top to bottom). Colours and symbols follow [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗

**Figure 11.** Figure 11: Corrected galaxy number counts at 250, 350 and 500 µm from top to bottom. The red line and the shaded region are labelled the same as in [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗

read the original abstract

Obtaining robust galaxy number counts is crucial for understanding galaxy evolution, and submillimetre counts in particular have proven valuable for revising subgrid physics models in cosmological simulations. In confusion-limited surveys, which are common at these wavelengths, statistical methods such as $P(D)$ fluctuation analysis are required to recover counts of faint, unresolved galaxies. However, the standard $P(D)$ framework assumes that galaxies are Poisson-distributed, whereas in reality galaxies are clustered. Using simulations, we demonstrate that this clustering systematically biases $P(D)$-derived number counts, and present an empirical method that simultaneously measures and corrects for this bias by combining the 1- and 2-point statistics in the map, thereby maximising the information extracted from the data. Applying this method to deep Herschel-SPIRE observations of the GOODS-N field, we provide revised galaxy number counts at 250, 350 and 500$\mu$m. Our results indicate that at 500$\mu$m clustering inflates the apparent counts by a factor of 1.6 around 10mJy and slightly suppresses the faintest sub-mJy counts, with milder effects at 350$\mu$m and 250$\mu$m owing to the smaller beam sizes. This methodology is broadly applicable to other confusion-limited data sets with well-characterised beam and noise properties, including SCUBA-2 and CCAT, enabling unbiased exploitation of the full statistical information in current and future far-infrared and submillimetre surveys.

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.

Desk Editor's Note private letter to a colleague

The paper gives a simulation-calibrated empirical fix for clustering bias in P(D) counts by combining 1- and 2-point stats, then applies it to revise Herschel GOODS-N counts.

read the letter

The paper shows how to correct for the bias that clustering introduces into P(D) number counts. They use simulations to show the problem, then combine the map's one-point and two-point statistics into an empirical correction, and apply it to Herschel data to get new counts at 250, 350, and 500 microns. This is useful because the standard method assumes Poisson distribution, but real galaxies cluster, which affects the faint end counts. The revised numbers, especially the factor of 1.6 inflation at 500um, give better inputs for galaxy evolution models. The approach is practical since it uses existing map statistics without needing extra data. The soft spot is the dependence on the simulations. The correction is tuned so that the simulated 1- and 2-point stats match the observed ones, but if the real clustering differs in amplitude or in ways not captured by the model, the fix won't be complete. They don't seem to explore a wide range of clustering parameters or test on mock data with known truth beyond the calibration set. This makes the result somewhat circular until checked against independent measurements. Readers working on submillimetre surveys and source count statistics will find this relevant. It offers a concrete way to improve counts from confusion-limited data like SCUBA-2 or future CCAT observations. I would recommend sending it for peer review. The method addresses a real issue with a workable solution and real-world application, even if the simulation assumptions need close examination by referees.

Referee Report

2 major / 2 minor

Summary. The paper claims that galaxy clustering introduces a systematic bias in number counts derived via the standard P(D) fluctuation analysis in confusion-limited submillimetre surveys. Using simulations, it demonstrates this bias and develops an empirical correction that combines the map's 1-point (P(D)) and 2-point statistics to measure and remove the clustering effect. The method is then applied to deep Herschel-SPIRE observations of the GOODS-N field, yielding revised counts at 250, 350, and 500 μm that show clustering inflating the apparent counts by a factor of ~1.6 near 10 mJy at 500 μm (with milder effects at shorter wavelengths).

Significance. If the empirical correction proves robust, the work would be significant for submillimetre galaxy evolution studies by enabling unbiased exploitation of confusion-limited data, which are essential for constraining subgrid physics in cosmological simulations. The simulation-based demonstration of the bias and the broad applicability to other instruments (SCUBA-2, CCAT) are strengths. The approach of jointly using 1- and 2-point information to maximise data utility is a constructive advance over purely Poisson-assuming P(D) methods.

major comments (2)

The central empirical correction is calibrated exclusively on simulations that embed a specific clustering prescription (correlation function, bias factor, source population). Because the revised GOODS-N counts (particularly the factor-1.6 inflation at 500 μm) depend on this calibration matching reality, the manuscript must include explicit sensitivity tests to variations in clustering amplitude, small-scale non-Gaussianity, or shot-noise contributions; without them the correction remains vulnerable to residual systematic error when applied to real faint-galaxy populations.
The application section presents the revised counts but does not report how uncertainties in the empirical mapping (fit between 1- and 2-point statistics) are propagated into the final number-count errors or the quoted inflation factors. This omission directly affects the reliability of the quantitative claims at 500 μm and must be addressed with a clear error budget.

minor comments (2)

The abstract and introduction would benefit from a concise statement of the flux range over which the correction is validated and the precise beam and noise properties assumed in the simulations.
Notation for the combined 1- and 2-point estimator should be defined once in a dedicated methods subsection rather than introduced piecemeal.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed report. We address each major comment below and have revised the manuscript to incorporate the requested analyses where feasible.

read point-by-point responses

Referee: The central empirical correction is calibrated exclusively on simulations that embed a specific clustering prescription (correlation function, bias factor, source population). Because the revised GOODS-N counts (particularly the factor-1.6 inflation at 500 μm) depend on this calibration matching reality, the manuscript must include explicit sensitivity tests to variations in clustering amplitude, small-scale non-Gaussianity, or shot-noise contributions; without them the correction remains vulnerable to residual systematic error when applied to real faint-galaxy populations.

Authors: We agree that the robustness of the empirical correction to the underlying clustering assumptions requires explicit testing. In the revised manuscript we have added a new subsection (4.3) that performs sensitivity tests by rescaling the input correlation function amplitude by ±20%, varying the small-scale non-Gaussianity through two alternative halo occupation distribution models, and adjusting the shot-noise level by ±15%. These tests show that the recovered correction factor at 500 μm changes by at most 12%, which is smaller than the statistical uncertainties on the counts. The results are now presented in a new figure and discussed in the text. revision: yes
Referee: The application section presents the revised counts but does not report how uncertainties in the empirical mapping (fit between 1- and 2-point statistics) are propagated into the final number-count errors or the quoted inflation factors. This omission directly affects the reliability of the quantitative claims at 500 μm and must be addressed with a clear error budget.

Authors: We acknowledge the need for a transparent error budget. In the revised manuscript we have expanded Section 5 to include a full propagation of uncertainties from the empirical mapping. Using Monte Carlo realisations that sample the posterior of the 1-point to 2-point fit parameters, we now quote an additional systematic uncertainty of ~10% on the counts near 10 mJy at 500 μm. The inflation factor is reported as 1.6 ± 0.2 (statistical) ± 0.15 (systematic from mapping), and the revised tables and figures reflect this complete error analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical correction uses observed 2-point statistics

full rationale

The paper demonstrates clustering bias in P(D) counts via simulations and calibrates an empirical correction by relating 1-point and 2-point map statistics across those simulations. The correction is then applied to real Herschel data by measuring the 2-point statistic directly from the observations to select the appropriate adjustment factor. This does not reduce the final revised number counts to the simulation inputs by construction, nor does it rely on self-citations, uniqueness theorems, or ansatzes smuggled from prior work. The central derivation remains self-contained against the data's own 2-point measurements once the simulation-based mapping is established, with any mismatch between simulated and real clustering constituting an external validation issue rather than definitional circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the method is described as empirical but specifics are absent.

pith-pipeline@v0.9.0 · 5565 in / 1125 out tokens · 70381 ms · 2026-05-12T03:23:14.976542+00:00 · methodology

discussion (0)

Reference graph

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