Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering
Abstract
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 ∼5% accuracy for 0.5 < ν< 2. Using the \texttt{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 ∼30%, while the tree-level galaxy bispectrum (in the Sugiyama basis) is only weakly affected (<2% up to kmax = 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 kmax < 0.3.
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BibTeX
@misc{rocher2026exploring,
title = {{Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering}},
author = {Antoine Rocher},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.28644},
eprint = {2605.28644},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28644},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering
AU - Antoine Rocher
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2605.28644
UR - https://arxiv.org/abs/2605.28644
AB - 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 ∼5% accuracy for 0.5 < ν< 2. Using the \texttt{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 ∼30%, 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.
ER -