DESI Early Data Release: Galaxy-Dark-Matter-Halo Connection*

The connection between dark matter haloes and galaxies describes the galaxy formation process in the dark matter field. It is crucial for modelling galaxy clustering on small scales and constructing high-fidelity large-scale simulations for galaxies. The Early Data Release (EDR) of DESI is a powerful dataset for understanding this galaxy-halo relation down to megaparsec scales, with the help of modern large-volume and high-resolution dark matter simulations. The DESI EDR sample consists of luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasi-stellar objects (QSOs) in a redshift range of [0.4, 3.5], taken by the Mayall 4-m telescope in a few months, with a similar number density as the SDSS eBOSS data accumulated in 4 years. We analyze the galaxy-halo connection of DESI EDR with UNIT N-body simulations and a general subhalo abundance matching (SHAM) algorithm. This algorithm works for all three tracers and takes into account observational systematics like redshift uncertainty and stellar mass completeness. We detect the quenching of ELG star formation and QSO black-hole activity in a dense environment, and massive LRGs are found to be complete. The redshift uncertainty plays a role for LRGs and QSOs at 10-20Mpc/h but ELGs are immune to it on megaparsec scales. Similar studies using different SHAM and halo occupation distribution (HOD) methods and with alternative simulations report more properties of the DESI tracer. For instance, the average number of satellites of LRGs and QSOs increases as their host halo mass, while ELG satellites illustrate the opposite trend. In addition, there is no evidence of assembly bias for LRGs and QSOs. Besides, DESI ELGs do not include the most luminous OII emitters for z<0.8.