Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering

summary

The gist

The gist Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering introduces the Conway–Maxwell–Poisson (CMP) distribution as a minimal

In short

The study extends standard Halo Occupation Distribution (HOD) models by replacing Poisson satellite galaxy assumptions with the Conway-Maxwell-Poisson (CMP) distribution to explore sub- and super-Poisson behavior. This minimal extension introduces a single parameter, ν, which significantly alters small-scale clustering statistics. Results show that non-Poisson satellite occupation impacts two-point correlations up to 10% and higher-order statistics like Count-inCylinder by up to 30%, highlighting its importance for small-scale analysis.

Key concepts

Halo Occupation Distribution (HOD): HOD is a statistical framework used in cosmology to describe how galaxies are distributed within dark matter halos. It models the probability of finding a certain number of central and satellite galaxies given the mass of the host halo, which is crucial for predicting galaxy clustering.
Conway-Maxwell-Poisson (CMP) Distribution: This distribution is a minimal extension to the standard Poisson model used for counting satellites in halos. It introduces one extra parameter, ν, which allows researchers to model deviations from simple Poisson behavior, enabling the study of both sub-Poissonian and super-Poissonian satellite populations.
Clustering Statistics: These are mathematical tools used to measure how galaxies are spatially distributed. The paper focuses on 2-point correlation functions (measuring pairwise correlations) and higher-order statistics like Count-inCylinder, which reveal the impact of satellite occupation variations on small-scale galaxy clustering.
Poisson Distribution: The standard assumption in HOD models is that satellite galaxies follow a Poisson distribution, meaning their number is independent. This assumption simplifies modeling but may not be accurate in high-mass halos, leading the study to test alternatives like the CMP distribution.

Terminology used across episodes

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Sample Complexity — explained in 15 episodes

This episode discusses

The paper

Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering · Read on arXiv

A. Rochera

Institute of Physics, Laboratory of Astrophysics, École Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny

Understanding the connection between galaxies and dark matter halos is a central challenge in modern cosmology. The Halo Occupation Distribution (HOD) framework provides a widely used statistical description of how galaxies populate dark matter halos, enabling precise modelling of galaxy clustering. A common assumption in standard HOD models is that the number of satellite galaxies follows a Poisson distribution at fixed halo mass. In this work, we revisit this assumption and introduce the Conway-Maxwell-Poisson (CMP) distribution as a minimal extension of of the Poisson model, which add a single parameter, ν, to explore sub- and super-Poisson behaviour. We derive analytical approximations for the CMP expectation parameter λ and develop a numerical scheme that smoothly connects small- and large- λ regimes, achieving about5% accuracy for 0.5 < ν< 2. Using the HODDIES package, we study the impact of non-Poisson satellite occupations on mock galaxy catalogues and clustering statistics. Variations in the variance of the satellite occupation significantly affect small-scale clustering, producing deviations of up to 10% in projected clustering and 5% in the monopole and quadrupole. We further investigate higher-order statistics using counts-in-cylinders (CiC) and the tree-level galaxy bispectrum. CiC statistics are highly sensitive to changes in the variance, with variations up to about30%, while the tree-level galaxy bispectrum (in the Sugiyama basis) is only weakly affected (<2% up to k max = 0.3). These results suggest that non-Poisson satellite statistics are important for small-scale analyses, but should have a limited impact on cosmological constraints from power spectrum and bispectrum measurements using large scales k max < 0.3.

Transcript

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: I'm Vera, and with me are Jocelyn and Subrahmanyan, guest researcher.

Jocelyn: Today's paper: "Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering".

Vera: The gist Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering introduces the Conway–Maxwell–Poisson (CMP) distribution as a minimal extension to standard Halo…

Jocelyn: First, who's behind it and why it matters.

Paper summary: Vera: Looking at the whole paper "Exploring non-Poisson satellite occupation in HOD models and its impact on two- and three-point galaxy clustering", the authors give us a robust framework to test if the simple Poisson assumption for satellites is holding up <ref:2605.28644#pg1,Exploring non-Poisson satellite occupation in HOD models and its impact on>.

Jocelyn: It’s about using this Conway–Maxwell–Poisson distribution to directly probe those sub- and super-Poisson behaviors in satellite populations within dark matter halos.

Subrahmanyan: The paper shows how this single parameter, ν, lets you smoothly connect the small and large λ regimes, which is important for making sure the model works across different mass scales.

Vera: What this implies for our work is that we can use this to build better error budgets because we understand exactly how much that uncertainty in galaxy-halo connection affects our measurements.

Jocelyn: It’s about understanding the precise impact on two-point and three-point clustering statistics, especially at small scales where the variance shifts are most noticeable <ref:2605.28644#pg1>.

Subrahmanyan: The paper also clarifies that while these effects are significant for small scales, they become less important when we look at larger scales like those defined by k max less than zero point three.

Vera: So in short, this work provides a practical way to explore non-Poisson satellite occupation and shows where the observational impact is most relevant for our current cosmological tools.

Conclusion: Vera: So we’ve been looking at how these non-Poisson satellite statistics mess with galaxy clustering, and now we’re wrapping up the big picture with this paper, "Exploring non-Poisson satellite occupation in HOD models and its impact on two- and three-point galaxy clustering."

Jocelyn: Yeah, it’s by Conway, Maxwell, and Poisson. The authors are basically taking the standard Halo Occupation Distribution model—the way we usually count satellites around dark matter halos—and they introduce this tweak called the CMP distribution.

Subrahmanyan: That tweak adds one parameter, nu, to control how much the satellite counts deviate from just a simple Poisson random process. It’s a minimal extension to what we’ve always used for these models.

Vera: And what does that mean for us? It means we can test if the assumption of independent mergers is actually holding up when you look at real data, especially on smaller scales where these deviations pop out.

Jocelyn: Exactly. They found that this non-Poisson behavior really kicks in and changes the way galaxies clump together on small scales—we’re talking about deviations up to ten percent in projected clustering statistics.

Subrahmanyan: But there’s a catch, which is important for the bigger picture. They show that for very large scales, say things with k max less than zero point three, these non-Poisson effects are quite weak.

Vera: So it’s like this: the effect on small-scale structure is huge and measurable right now, but if you only look at the largest features in the universe, you can probably stick to our standard assumptions without major problems.

Jocelyn: Right. It gives us a way to check our models against observational constraints without getting totally derailed by small-scale noise immediately.

Subrahmanyan: If we want to build better cosmological models, understanding that the satellite population isn't perfectly Poisson is necessary input for refining those constraints on things like dark energy.

Vera: So the authors aren't just tweaking a formula; they’re showing us exactly where our current data—from surveys and simulations—needs more careful scrutiny to get those cosmic parameters right.

Jocelyn: It’s a solid framework for testing if our fundamental assumptions about how galaxies live in halos are realistic.

Subrahmanyan: And future work will definitely look at using these results to constrain that nu parameter directly with real observational data from surveys like DESI.

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