DESI DR2 Galaxy Luminosity Functions

TL;DR

This study delivers DESI Y3 BGS g, r, z, and W1 luminosity functions across 0.002 < z < 0.6 using updated k- and e-corrections and a detailed completeness framework. The authors demonstrate that the LFs cannot be well described by simple Schechter fits due to a bright-end North–South offset and a pronounced faint-end upturn, the latter largely influenced by local density fluctuations and imaging artefacts. They introduce a color-dependent, rest-frame–based k-correction scheme and a single-parameter evolution model with Q ≈ 0.78, while validating results against GAMA and exploring Petrosian magnitudes to mitigate systematic differences. The work provides a robust platform for studying LF dependence on environment and for constraining galaxy formation models, though it notes residual evolutionary complexities and data-imaging limitations at the faint and bright extremes.

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.

Figures (19)

• Figure 1: The Y3 DESI Footprint - showing the North (blue) and South (red). The different shades of blue and red highlight the jackknife regions (see Section \ref{['Luminosity Functions']} for details). The solid red curve shows the galactic plane while the dotted red curve shows the ecliptic plane.
• Figure 2: The empirical redshift completeness as a function of the fibre magnitude, $r_\textrm{fibre}$, and the TSNR2$\_$BGS. TSNR2$\_$BGS is the expected spectral target signal-to-noise ratio for a fiducial BGS source. This plot is for the South region. All the galaxies in this region are plotted as red points with low opacity. The majority fall where the redshift completeness is very high. To define a weight, $w_{\rm z}$, to correct for this incompleteness we interpolate the binned incompletness using the Cloud-In-Cell technique and take its inverse. Note that for empty pixels, we default to a value of 1.
• Figure 3: The median rest-frame $^{0.1}(g-r)$ colour of galaxies from the FSF South catalogue in bins of redshift and observer-frame colour. This provides a look-up table to infer the rest-frame colour from the observed properties. A separate lookup table is used for the North.
• Figure 4: The k-correction polynomials to the SDSS $g$, $r$, $z$ and WISE $w_1$ bands with $z_{\rm ref} = 0.1$ from the respective observer frame DECaLS band (South, solid line), BASS/MzLS band (North, dashed line) and WISE bands. The $r$, $z$ and $w_1$-band k-corrections are direct fits to the FSF data. For the $g$ band, the $r$-band polynomials are transformed to the $g$ band using Eqn. \ref{['eq:k-corr_eq']} and the figure shows polynomial fits to the resulting $g$-band k-correction.
• Figure 5: Rest-frame colour vs. absolute magnitude distributions in North and South. Contours are plotted representing number density, with each successive contour a factor of 2 larger in number density (starting at 160 objects per bin). The top histogram shows the $^{0.1}(g-r)$ colour distribution for North and South. The right histogram shows the $r$-band absolute magnitude distribution. Both histograms have been normalised by sky-area to adjust for the fact that South is approximately double the size of North.