DESI Legacy Imaging Surveys DR8

• DESI Legacy Imaging Surveys DR8 is a wide-area, multi-band photometric survey covering 18,253 deg² to support DESI and cosmological research.
• It employs THE TRACTOR pipeline and machine learning for photometric redshift estimation, achieving a precision of σ_photo ≈ 0.01 + 0.015z.
• The survey underpins detailed galaxy clustering, group catalog construction, and bias analyses with over 129 million galaxies and robust two-point correlation measurements.

The DESI Legacy Imaging Surveys Data Release 8 (DR8) is a wide-area, multi-band optical and mid-infrared photometric survey designed to support the Dark Energy Spectroscopic Instrument (DESI) experiment. DR8 forms the backbone of several major extragalactic investigations, including galaxy clustering analyses, group and cluster identification, and studies of cosmic structure growth to $z\sim1$. The survey achieves unprecedented sky coverage, depth, photometric uniformity, and multi-wavelength integration, with over 129 million galaxies cataloged to $z\leq21$ mag and photometric redshift precision established for $0<z\leq1.0$ (Yang et al., 2020).

1. Survey Characteristics and Data Products

DR8 provides contiguous imaging over both the North and South Galactic Caps, offering 18,253 deg² of effective area after star and quality masks. Imaging is in $g$, $r$, $z$ (optical), supplemented by WISE $W1$, $W2$ (mid-IR), and processed uniformly with THE TRACTOR pipeline for source characterisation and photometry. The $5\sigma$ point-source depth reaches $g=24.0$, $r=23.4$, $z=22.5$ AB mag for an exponential profile with half-light radius $0.45''$. Morphological, photometric, and quality cuts (FRACMASKED, FRACIN, FRACFLUX, masking by bright stars with MASKBITS) yield a final sample of 129.35 million galaxies (Yang et al., 2020).

Photometric redshifts are computed via machine learning (random-forest, PRLS), achieving a typical scatter $\sigma_{\rm photo} = 0.01 + 0.015\,z$, with a redshift coverage of $0<z_{\rm phot}\leq 1.0$. $2.1$ million galaxies benefit from matched spectroscopic redshifts from external surveys.

2. Galaxy Sample Definition and Clustering Analyses

For clustering and bias studies, galaxies are binned in eight redshift intervals with width $\Delta z=0.2$ (centered at $z=0.2,0.3,\dots,0.9$; $0.1\leq z\leq 1.0$), and in $z$-band absolute magnitude bins ($M_z^{0.5}-5\log h\leq -20$, with further sub-binning to $M_z^{0.5}-5\log h = -23$). Color-based division uses the rest-frame (K-corrected to $z=0.5$) criterion

$$C \equiv M_r^{0.5} - M_z^{0.5} = -0.8 - 0.08 (M_z^{0.5}-5\log h) - 0.22(z-0.5),$$

defining "red" and "blue" subsamples. These yield 60 volume-limited (sub-)samples: 20 each of "all," "red," and "blue" (Wang et al., 2021).

Projected two-point correlation functions (2PCFs) $w_p(r_p)$ are measured with Landy–Szalay estimators, integrated to $r_{\pi,\rm max}=50$ and $100\,h^{-1}$ Mpc. Photometric redshift errors are modeled as Gaussian random scatters around the true redshift, leading to a probabilistic convolution with the matter 2PCF in redshift-space. Both galaxy linear bias $b$ and redshift scatter $\sigma_z$ are jointly fit for each sample via MCMC, using jackknife covariances and uniform priors, with fitting over projected separations $1\leq r_p\leq 10\,h^{-1}$ Mpc.

3. Group and Cluster Catalog Construction

An extended halo-based group finder, adapted from the Yang et al. (2005, 2007) methodology, utilizes both photometric and (where available) spectroscopic redshifts to robustly identify galaxy systems in DR8. All galaxies are initially assigned as singleton tentative groups, and the iterative scheme involves (1) accumulative group luminosity computation, (2) abundance matching to obtain mass-to-light ratios, (3) assignment of halo properties (mass, $r_{180}$, velocity dispersion), (4) membership reassignment via phase-space likelihood, and (5) iteration to convergence (Yang et al., 2020).

Key steps incorporate:

• Absolute magnitude and K-correction:

$M_z - 5\log h = m_z - DM(z) - K_z^{0.5}(z)$

• Mass assignment via abundance matching with the Sheth, Mo & Tormen (2001) halo function
• Halo properties:

$$r_{180} = 0.781\,h^{-1}\,{\rm Mpc}\,\left(\frac{M_L}{\Omega_m\times 10^{14}h^{-1}M_\odot}\right)^{1/3}$$

$$\sigma_{180} = 632\left(\frac{M_L\,\Omega_m}{10^{14}h^{-1}M_\odot}\right)^{0.3224}$$

• Redshift-separation distribution includes both intrinsic velocities and photometric error, with $$\sigma = \max\{\sigma_{180},c\,\sigma_{\rm photo}\}$$.

Performance on simulated data demonstrates $>90\%$ group purity for $M_L\gtrsim 10^{12}h^{-1}M_\odot$, a log-scatter on mass assignment from $0.15$ dex (high mass) to $0.4$ dex (low mass), and typical group redshift accuracy of $\sim0.008$ for systems with $N_g\geq10$.

Application to DR8 yields 5.2 million groups with $N_g\geq3$ and 387,000 rich groups ($N_g\geq10$). Catalog records include ID, richness, coordinate centroid, redshift, halo mass, and total luminosity, with public data available for cosmological reinterpretation (Yang et al., 2020).

4. Statistical Trends and Systematics in Galaxy and Group Properties

The joint 2PCF fitting recovers both intrinsic clustering amplitudes and redshift errors. Key results (Wang et al., 2021):

• Photometric redshift scatter $\sigma_z$ increases with both redshift and fainter luminosity, e.g., for $M_z^{0.5}<-22$, $\sigma_z\sim0.007$ at $z=0.2$ rising to $0.017$–$0.026$ at $z=0.8-1.0$; in fainter samples, $\sigma_z$ reaches $\sim0.03$ at $z\gtrsim0.6$.
• Red subsamples exhibit $\sim10$–$20\%$ lower $\sigma_z$ than all galaxies.
• Linear bias $b$ increases with both luminosity and redshift; at $z\approx0.2$, faint galaxies ($-21<M_z^{0.5}<-20$) show $b\approx1.06$ ("all") and $1.24$ ("red"); the brightest bins rise to $b\approx1.7$, and up to $b\approx2.34$ at $z\approx0.8$ ("red").
• At fixed redshift and luminosity, red galaxies are $10$–$15\%$ more biased than the global sample, demonstrating robust color dependence.
• Approximately a quarter of blue subsamples display anomalously high $w_p$ on large scales, inconsistent with Gaussian photo-$z$ errors and indicative of systematics or photo-$z$ outliers; they are excluded from quantitative bias and error studies.

The high-precision $w_p(r_p)$ measurements for 40 ("all" and "red") subsamples are corrected for $r_{\pi,\max}\rightarrow\infty$ and constrain the color-, redshift-, and luminosity-dependent clustering to percent-level uncertainties.

5. Scientific Applications and Cosmological Implications

The derived group and clustering catalogs facilitate a broad range of cosmological and astrophysical inferences:

• Mapping galaxy populations to dark matter halos enables halo occupation distribution (HOD) and conditional luminosity function (CLF) modeling, yielding constraints on halo mass, satellite fraction, and assembly bias (Wang et al., 2021).
• Systematic color-luminosity-redshift dependence of bias substantiates hierarchical structure formation and galaxy quenching paradigms, with red, massive, high-$z$ galaxies occupying the most massive, highest-bias halos.
• The consistency of measured $w_p(r_p)$ with $\Lambda$CDM predictions and the low photo-$z$ scatter confirm the viability of wide-field photometric surveys for clustering measurements at high fidelity.
• The cataloged group sample (with cosmological re-scalability) directly supports studies of the galaxy–halo connection, environmental effects, large-scale structure analyses, Sunyaev–Zel’dovich stacking, weak lensing, and constraints on galaxy evolution mechanisms (Yang et al., 2020).

A plausible implication is that DR8’s combination of photometric depth, area, and redshift calibration yields data products adequate for statistical cosmology and physical galaxy formation studies prior to the completion of spectroscopic DESI redshifts. The survey’s methodological rigor and public group catalogs expedite joint interpretations of large-scale structure, galaxy environments, and cosmological evolution.