Improving and extending non-Poissonian distributions for satellite galaxies sampling in HOD: applications to eBOSS ELGs

TL;DR

This paper introduces a new binomial-based distribution for satellite galaxy assignment in HOD models, allowing for sub-Poisson variances, and demonstrates its impact on galaxy clustering and statistical measures in mock catalogues.

Contribution

It proposes a novel binomial distribution for satellite galaxy PDFs in HOD models, enabling continuous sub-Poisson variances and improving galaxy clustering analysis.

Findings

Variance of satellite galaxy PDFs influences the one-halo term in clustering.

Sub-Poissonian PDFs better fit eBOSS ELG clustering data.

Count-In-Cells statistics effectively constrain satellite galaxy PDF variance.

Abstract

Halo Occupation Distribution (HOD) models help us to connect observations and theory, by assigning galaxies to dark matter haloes. In this work we study one of the components of HOD models: the probability distribution function (PDF), which is used to assign a discrete number of galaxies to a halo, given a mean number of galaxies. For satellite galaxies, the most commonly used PDF is a Poisson Distribution. PDFs with super-Poisson variances have also been studied, allowing for continuous values of variances. This has not been the case for sub-Poisson variances, for which only the Nearest Integer distribution, with a single variance, has been used in the past. In this work we propose a distribution based on the binomial one, which provides continuous sub-Poisson variances. We have generated mock galaxy catalogues from two dark-matter only simulations, UNIT and OUTERIM, with HOD models assuming different PDFs. We show that the variance of the PDF for satellite galaxies affects the one-halo term of the projected correlation function, and the Count-In-Cells (CIC) one point statistics. We fit the clustering of eBOSS Emission Line Galaxies, finding a preference for a sub-poissonian PDF, when we only vary the parameter controlling the PDF variance and the fraction of satellites. Using a mock catalogue as a reference, we have also included both the clustering and CIC to constrain the parameters of the HOD model. CIC can provide strong constraints to the PDF variance of satellite galaxies.