PAC in DESI. I. Galaxy stellar mass function into the 10⁶ M⊙ frontier

The Photometric objects Around Cosmic webs (PAC) method integrates cosmological photometric and spectroscopic surveys, offering valuable insights into galaxy formation. PAC measures the excess surface density of photometric objects, n 2wp, with specific physical properties around spectroscopic tracers. In this study, we improve the PAC method to make it more rigorous and eliminate the need for redshift bins. We apply the enhanced PAC method to the DESI Y1 BGS Bright spectroscopic sample and the deep Dark Energy Camera Legacy Survey (DECaLS) photometric sample, obtaining n 2wp measurements across the complete stellar mass range, from 105.3 to 1011.5 M circle dot for blue galaxies, and from 106.3 to 1011.9 M circle dot for red galaxies. We combine n 2wp with wp measurements from the BGS sample, which is not necessarily complete in stellar mass. Assuming that galaxy bias is primarily determined by stellar mass and colour, we derive the galaxy stellar mass functions (GSMFs) down to 105.3 M circle dot for blue galaxies and 106.3 M circle dot for red galaxies, while also setting lower limits for smaller masses. The blue and red GSMFs are well described by single and double Schechter functions, respectively, with low-mass end slopes of alpha blue = -1.54+0.02 -0.02 and alpha red = -2.50+0.08 -0.08, resulting in the dominance of red galaxies below 107.6 M circle dot. Stage-IV cosmological photometric surveys, capable of reaching 2-3 mag deeper than DECaLS, present an opportunity to explore the entire galaxy population in the local universe with PAC. This advancement allows us to address critical questions regarding the nature of dark matter, the physics of reionization, and the formation of dwarf galaxies.