HOD-Dependent Systematics for Luminous Red Galaxies in the DESI 2024 BAO Analysis

In this paper, we present the estimation of systematics related to the halooccupation distribution (HOD) modeling in the baryon acoustic oscillations(BAO) distance measurement of the Dark Energy Spectroscopic Instrument (DESI)2024 analysis. This paper focuses on the study of HOD systematics for luminousred galaxies (LRG). We consider three different HOD models for LRGs, includingthe base 5-parameter vanilla model and two extensions to it, that we refer toas baseline and extended models. The baseline model is described by the 5vanilla HOD parameters, an incompleteness factor and a velocity bias parameter,whereas the extended one also includes a galaxy assembly bias and a satelliteprofile parameter. We utilize the 25 dark matter simulations available in theAbacusSummit simulation suite at $z=$ 0.8 and generate mock catalogs for ourdifferent HOD models. To test the impact of the HOD modeling in the position ofthe BAO peak, we run BAO fits for all these sets of simulations and compare thebest-fit BAO-scaling parameters $\alpha_{\rm iso}$ and $\alpha_{\rm AP}$between every pair of HOD models. We do this for both Fourier and configurationspaces independently, using post-reconstruction measurements. We find a3.3$\sigma$ detection of HOD systematic for $\alpha_{\rm AP}$ in configurationspace with an amplitude of 0.19%. For the other cases, we did not find a3$\sigma$ detection, and we decided to compute a conservative estimation of thesystematic using the ensemble of shifts between all pairs of HOD models. Bydoing this, we quote a systematic with an amplitude of 0.07% in $\alpha_{\rmiso}$ for both Fourier and configuration spaces; and of 0.09% in $\alpha_{\rmAP}$ for Fourier space.