Halo Occupation Distribution estimation performance for LSST data

Upcoming imaging surveys, such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), will enable high signal-to-noise measurements of galaxy clustering. The halo occupation distribution (HOD) is a widely used framework to describe the connection between galaxies and dark matter haloes, playing a key role in evaluating models of galaxy formation and constraining cosmological parameters. Consequently, developing robust methods for estimating this statistic is crucial to fully exploit data from current and future galaxy surveys. The main goal of this project is to extend a background subtraction method to estimate the HOD with more photometry-based information in preparation for the clustering analysis of the upcoming LSST data and to enable the study of the HOD with significantly improved statistical power. We evaluate the performance of the method using a mock galaxy redshift survey constructed from the cosmoDC2 catalogue. We implement an extension of the background subtraction technique to utilize information from photometric galaxy surveys. To identify the centres of galaxy groups, we implement an iterative centroiding approach (Central Galaxy Finder). We evaluate the impact of each step in our pipeline, including group size estimation from luminosity and purity, and completeness on group identification, along with the influence of observational systematics such as the use of photometric redshifts and halo mass uncertainties. We demonstrate the validity of the proposed method using a mock galaxy catalogue, recovering the HOD from cosmoDC2 over the absolute magnitude range $M_r = -20.0$ to $-17.0$ and halo masses up to $10^{15}\, \mathrm{M_\odot}$. We present key performance metrics to quantify the precision and reliability of the group finder and the resulting HOD measurements.