# Global analysis of luminosity- and colour-dependent galaxy clustering in the Sloan Digital Sky Survey

## TL;DR

This paper introduces a novel Halo Occupation Distribution analysis of galaxy clustering in SDSS, using a combined likelihood approach and direct halo correlation functions to accurately model luminosity and colour dependencies.

## Contribution

It presents a new global likelihood method for HOD analysis that incorporates direct halo correlation functions and models colour-dependent clustering without group-finding algorithms.

## Key findings

- Luminosity dependence of HOD parameters is well described by simple functions.
- The satellite red fraction varies with luminosity, showing a shallower trend than in group catalogues.
- The methods enable realistic mock galaxy catalogues for low-redshift universe simulations.

## Abstract

We present a Halo Occupation Distribution (HOD) analysis of the luminosity- and colour-dependent galaxy clustering in the Sloan Digital Sky Survey. A novelty of our technique is that it uses a combination of clustering measurements in luminosity bins to perform a global likelihood analysis, simultaneously constraining the HOD parameters for a range of luminosity thresholds. We present simple, smooth fitting functions which accurately describe the resulting luminosity dependence of the best-fit HOD parameters. To minimise systematic halo modelling effects, we use theoretical halo 2-point correlation functions directly measured and tabulated from a suite of $N$-body simulations spanning a large enough dynamic range in halo mass and spatial separation. Thus, our modelling correctly accounts for non-linear and scale-dependent halo bias as well as any departure of halo profiles from universality, and we additionally account for halo exclusion using the hard sphere approximation. Using colour-dependent clustering information, we constrain the satellite galaxy red fraction in a model-independent manner which does not rely on any group-finding algorithm. We find that the resulting luminosity dependence of the satellite red fraction is significantly shallower than corresponding measurements from galaxy group catalogues, and we provide a simple fitting function to describe this dependence. Our fitting functions are readily usable in generating low-redshift mock galaxy catalogues, and we discuss some potentially interesting applications as well as possible extensions of our technique.