DESI DR2 Galaxy Luminosity Functions

Abstract: We present luminosity functions (LFs) in the g, r, z, and W_1 bands from the DESI Year 3 Bright Galaxy Survey (BGS), spanning redshifts 0.002<z\<0.6. We detail our methodology, including updated k-corrections, evolutionary corrections, and completeness weights. New polynomial k-correction fits based on BGS Y1 supersede those from GAMA DR4. Our LFs reach very faint magnitudes, down to M - 5 log h ~ -10 in r. Independent North and South estimates agree well near the LF knee, with very small statistical errors. These errors reveal that simple analytic forms poorly fit the LFs: the bright end deviates from an exponential, and the faint end shows complex, non-power-law behaviour. We detect an upturn at M - 5 log h > -15, stronger in red galaxies. Below -13, local overdensities and fragmentation of large galaxies amplify this upturn. A systematic offset between North and South appears at the brightest magnitudes, driven by red galaxies. Blue LFs match well across regions, suggesting the discrepancy arises from red galaxy profiles blending into noise in shallower North photometry. This remains inconclusive, so the bright-end offset is treated as a systematic uncertainty. We also present LFs using model Petrosian magnitudes, which are less sensitive to this issue. Splitting by redshift reveals small but significant residuals, indicating our global evolution model, while accurate near the LF knee, misses more complex trends. Using Loveday (2011) redshift limits, we find excellent agreement with GAMA, but with smaller errors. Our methods and results provide a foundation for studying LF dependence on environment, such as local density and cosmic web classification, offering strong constraints on galaxy formation models.