Measuring the conditional luminosity and stellar mass functions of galaxies by combining the DESI LS DR9, SV3 and Y1 data

In this investigation, we leverage the combination of Dark Energy Spectroscopic Instrument Legacy imaging Surveys Data Release 9 (DESI LS DR9), Survey Validation 3 (SV3), and Year 1 (Y1) data sets to estimate the conditional luminosity and stellar mass functions (CLFs & CSMFs) of galaxies across various halo mass bins and redshift ranges. To support our analysis, we utilize a realistic DESI Mock Galaxy Redshift Survey (MGRS) generated from a high-resolution Jiutian simulation. An extended halo-based group finder is applied to both MGRS catalogs and DESI observation. By comparing the r and z-band luminosity functions (LFs) and stellar mass functions (SMFs) derived using both photometric and spectroscopic data, we quantified the impact of photometric redshift (photo-z) errors on the galaxy LFs and SMFs, especially in the low redshift bin at low luminosity/mass end. By conducting prior evaluations of the group finder using MGRS, we successfully obtain a set of CLF and CSMF measurements from observational data. We find that at low redshift the faint end slopes of CLFs and CSMFs below $10^{9}h^{-2}L_{sun}$ (or $h^{-2}M_{sun}$) evince a compelling concordance with the subhalo mass functions. After correcting the cosmic variance effect of our local Universe following arXiv:1809.00523, the faint end slopes of the LFs/SMFs turn out to be also in good agreement with the slope of the halo mass function.