PAC in DESI. I. Galaxy Stellar Mass Function into the $10^{6}{\rm M}_{\odot}$ Frontier

TL;DR

This work advances the PAC method by removing the need for redshift binning and implementing a weighted estimator, enabling robust measurements of the galaxy stellar mass function (GSMF) to stellar masses as low as $M_* o 10^{5.3} m{M_igodot}$ for blue galaxies and $M_* o 10^{6.3} m{M_igodot}$ for red galaxies using DESI Y1 BGS and DECaLS data. By interpolating photometric properties across the full redshift range, applying colour cuts, and fitting a colour- and mass-dependent bias, the authors derive separate blue/red GSMFs and a combined GSMF, finding low-mass slopes of $oldsymbol{oldsymbol{oldsymbol{eta_{ m blue}}}=-1.54}$ and $oldsymbol{oldsymbol{eta_{ m red}}=-2.50}$, with red dwarfs dominating below $oldsymbol{M_* u rightarrow 10^{7.6} m{M_igodot} }$. The results reveal a steep red dwarf rise and suggest potential tensions with simple quenching models, emphasizing dark matter and reionization physics. The methodology and findings demonstrate the PAC method’s viability in the Stage-IV era and promise substantial gains for dwarf-galaxy science as deeper surveys (e.g., LSST, Euclid, Roman) come online, enabling comprehensive population studies in the local universe.

Abstract

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, $\bar{n}_2w_{\rm{p}}$, 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 DECaLS photometric sample, obtaining $\bar{n}_2w_{\rm{p}}$ measurements across the complete stellar mass range, from $10^{5.3}{\rm M}_{\odot}$ to $10^{11.5}{\rm M}_{\odot}$ for blue galaxies, and from $10^{6.3}{\rm M}_{\odot}$ to $10^{11.9}{\rm M}_{\odot}$ for red galaxies. We combine $\bar{n}_2w_{\rm{p}}$ with $w_{\rm{p}}$ 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 $10^{5.3}{\rm M}_{\odot}$ for blue galaxies and $10^{6.3}{\rm M}_{\odot}$ 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 $α_{\rm{blue}}=-1.54^{+0.02}_{-0.02}$ and $α_{\rm{red}}=-2.50^{+0.08}_{-0.08}$, resulting in the dominance of red galaxies below $10^{7.6}{\rm M}_{\odot}$. Stage-IV cosmological photometric surveys, capable of reaching 2-3 magnitudes 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.

Figures (27)

• Figure 1: Distributions of redshift and stellar mass for the DESI Y1 BGS Bright sample that overlaps with the DECaLS footprint.
• Figure 2: $V_{\rm{max}}$-weighted rest-frame $g-r$ colour vs. stellar mass distribution for BGS with $z<0.2$. The distribution is further normalized within each stellar mass bin for clearer visualization. The line $g-r=0.04\log_{10}(M_*/{\rm M}_{\sun})+0.2$ is used to separate the blue and red populations.
• Figure 3: Mean errors and 1 $\sigma$ scatter in interpolated stellar mass $\Delta\log_{10}M_{*}$ at 241 redshifts interpolated from the values at 44 reference redshifts within the range of $0.001<z<1$. For these reference redshifts, 31 of them are chosen with an equal interval of $\Delta\log_{10}(1+z)=0.01$, while the other 13 indicated by dotted lines are included to account for the rapid changes in stellar mass with a given redshift due to specific structures in the galaxy spectrum.
• Figure 4: The observed $g-r$ vs. $r-z$ colour diagrams for DESI BGS for two redshift bins. The red solid lines represent the colour cuts used to exclude background galaxies in DECaLS for PAC measurements at each redshift bin.
• Figure 5: Comparing the angular surface density of galaxies as a function of stellar mass, calculated at an assumed redshift of $z=0.025$, between the entire DECaLS sample and for deep regions with an $r$-band $10\sigma$ PSF depth greater than 23.8. The stellar mass limit is defined as the stellar mass at which the angular surface density of DECaLS decreases to 95 per cent of the deeper sample, which in this case occurs at $10^{7.2}{\rm M}_{\odot}$ for $z=0.025$.