The Clustering of DESI-like Luminous Red Galaxies Using Photometric Redshifts

We present measurements of the redshift-dependent clustering of a DESI-like luminous red galaxy (LRG) sample selected from the Legacy Survey imaging dataset, and use the halo occupation distribution (HOD) framework to fit the clustering signal. The LRG sample contains 2.7 million objects over the redshift range of $0.4 < z < 0.9$ over 5655 sq. degrees. We have developed new photometric redshift (photo-$z$) estimates using the Legacy Survey DECam and WISE photometry, with $\sigma_{\mathrm{NMAD}} = 0.02$ precision for LRGs. We compute the projected correlation function using new methods that maximize signal-to-noise while incorporating redshift uncertainties. We present a novel algorithm for dividing irregular survey geometries into equal-area patches for jackknife resampling. For a 5-parameter HOD model fit using the MultiDark halo catalog, we find that there is little evolution in HOD parameters except at the highest-redshifts. The inferred large-scale structure bias is largely consistent with constant clustering amplitude over time. In an appendix, we explore limitations of MCMC fitting using stochastic likelihood estimates resulting from applying HOD methods to N-body catalogs, and present a new technique for finding best-fit parameters in this situation. Accompanying this paper we have released the PRLS (Photometric Redshifts for the Legacy Surveys) catalog of photo-$z$'s obtained by applying the methods used in this work to the full Legacy Survey Data Release 8 dataset. This catalog provides accurate photometric redshifts for objects with $z < 21$ over more than 16,000 square degrees of sky.