DESI DR1 Luminous Red Galaxy Sample

Updated 14 August 2025

The DESI DR1 LRG sample is a high-quality dataset of hundreds of thousands of massive, passively evolving galaxies selected via precise photometric and spectroscopic criteria.
It employs rigorous target selection with defined color–magnitude cuts and fiber magnitude limits, achieving >98.9% spectroscopic efficiency with minimal contamination.
Advanced clustering measurements, halo occupation modeling, and mock catalog techniques enable robust inference of dark energy, large-scale structure, and galaxy–halo connections.

The DESI DR1 Luminous Red Galaxy (LRG) sample is a cornerstone dataset for contemporary large-scale structure and cosmological analyses, as established by the Dark Energy Spectroscopic Instrument (DESI) survey. This sample comprises hundreds of thousands of massive, passively evolving galaxies—selected via well-calibrated color and magnitude cuts—that span the redshift range 0.4 ≲ z ≲ 1.1. The design, selection, and validation of the DR1 LRG sample have prioritized achieving high redshift success, minimal contamination, robust control of observational systematics, and statistical power suited to probe dark energy, large-scale structure growth, and fundamental physics.

1. Target Selection, Sample Definition, and Spectroscopic Quality

The core DESI LRG selection uses photometry from the DESI Legacy Imaging Surveys Data Release 9 in the $g$ , $r$ , $z$ bands, along with forced photometry in the WISE $W1$ (3.4 $\mu$ m) infrared band. The target selection algorithm is anchored by color–magnitude and color–color cuts designed to isolate high-mass, old stellar population galaxies that exhibit the prominent 4000 Å break. A typical selection logic includes:

A “fiber magnitude” cut: $z_\text{fiber} < 21.6$ to ensure adequate spectral S/N.
A stellar rejection cut: $z - W1 > 0.8 \times (r - z) - 0.6$ .
Redshift-dependent color–magnitude cuts such as $(g - W1 > 2.9) \lor (r - W1 > 1.8)$ , refined with “sliding” boundaries to ensure a near-constant comoving number density across $0.4 < z < 0.8$.
Additional requirements for data quality (detections in all optical bands, positive inverse variances, masking for bright star or large galaxy proximity).

This yields an average target density of 605 deg $^{-2}$ for $0.4 < z < 0.8$ and maintains a constant comoving density of $n \approx 5 \times 10^{-4}\ h^{3}$ Mpc $^{-3}$ —surpassing legacy SDSS/BOSS LRG surveys in both density and reachable redshift. After applying bright star veto masks and stringent redshift quality cuts ( $\Delta\chi^2 > 15$ , $z_{\rm redrock} < 1.5$ , $ZWARN=0$ ), spectroscopic efficiency for LRGs exceeds 98.9%, with catastrophic failure rates of just 0.2% and stellar contamination of 0.5%. Redshift uncertainties for LRGs, as validated by repeated observations and visual inspection, have typical scatter of $\sigma_{\Delta z} \sim 40$ km/s (Zhou et al., 2022, Lan et al., 2022).

2. Imaging and Spectroscopic Systematics Control

The robustness of the LRG sample against systematic observational fluctuations has been extensively tested:

Imaging systematics associated with depth, seeing, Galactic extinction, and stellar density introduce $<5\%$ target density variations, further minimized with linear regression weights (Zhou et al., 2022).
Systematic variations in redshift success rate with spectroscopic conditions (TSNR2, fiber flux) are corrected with empirically derived “ $w_{\rm zfail}$ ” weights, ensuring uniformity in the final clustering catalog (Krolewski et al., 27 May 2024). Application of these weights alters BAO/RSD cosmological parameters by $<15\%$ of their statistical errors.
Forward modeling with the Obiwan simulation pipeline accurately predicts target density trends with depth and seeing, highlighting that faint LRGs near selection cutoffs are most sensitive to scattered flux in low-depth imaging (Kong et al., 25 May 2024). Discrepancies in Galactic extinction response, not reproduced by the image simulations, are traced to cosmic-infrared background contamination in the extinction maps, demonstrating the necessity for model-based systematics mitigation in clustering analyses.

3. Clustering Measurements and Halo Occupation Modeling

The clustering of the LRG sample is measured using advanced correlation function estimators tailored for photometric redshift uncertainty and spectroscopic completeness. In particular, projected two-point correlation functions $w_p(r_p)$ are computed using a “padded” auto-correlation approach:

$w_p(r_p) = 2\, \pi_{\rm max} \cdot \frac{D_1D_2 - D_1R_2 - D_2R_1 + R_1R_2}{R_1R_2}$

with $D_1$ , $D_2$ as data in narrow and padded redshift bins, and $R_1$ , $R_2$ as matched randoms (Zhou et al., 2020). This technique maximizes signal-to-noise by recovering pairs otherwise lost to photometric scattering. The projected function is integrated out to $\pi_{\rm max}$ up to 150 $h^{-1}$ Mpc.

Interpretation of clustering uses the five-parameter Halo Occupation Distribution (HOD) formalism, with central and satellite occupations:

$\langle N_{\rm cen}\rangle = \frac{1}{2}\left[1+\mathrm{erf}\left(\frac{\log M_{\rm vir}-\log M_{\rm min}}{\sigma_{\log M}}\right)\right]$

$\langle N_{\rm sat}\rangle = \left(\frac{M_{\rm vir}-M_0}{M_1}\right)^\alpha$

HOD parameter fits using MultiDark or AbacusSummit simulations reveal that for $0.4mass $\log_{10}\langle M_h\rangle \simeq 13.24$ –$13.4$, with linear bias rising from $b\simeq1.93$ to $2.08$ as redshift increases (Yuan et al., 2023). The inferred satellite fraction rises from $f_{\rm sat} \simeq 11\%$ to $14\%$ over this range, with declining mean halo mass at $z>0.8$ indicating selection incompleteness and the inclusion of lower-mass hosts at the high-redshift end.

4. Novel Approaches to Covariance, Survey Geometry, and Targeted Mock Generation

Because survey footprints are irregular, an algorithm that uses HEALPix pixelization and $k$ -means clustering partitions the area into $\sim$ 120 equal-area, compact subregions for robust jackknife resampling (Zhou et al., 2020). Covariance matrices for $w_p(r_p)$ and the power spectrum are produced using large suites of simulated mocks (e.g., 1000 GLAM or AbacusSummit realizations) (Hernández-Aguayo et al., 2020, Yuan et al., 2023).

Mock samples for LRG systematics and cosmological tests are generated by:

Direct HOD-based population of $N$ -body halos [both parametric and “digital twin” based on semi-analytic models],
Subhalo abundance and age-distribution matching, yielding catalogs that match observed luminosities, colors ( $r-z$ , $r-W1$ ), and clustering, and allowing studies of selection completeness—showing that IR-based LRG selection achieves $\gtrsim 90\%$ completeness across the principal $z$ bins (Berti et al., 2023).

Public access to all DESI-like LRG mocks enables reproducible cosmological inference [http://www.skiesanduniverses.org].

5. Large-Scale Structure, Cosmological Constraints, and Combination with Other Probes

LRGs serve as optimal tracers for large-scale structure due to high bias and density. Analyses using tomographic bins and cross-correlation with Planck CMB lensing convergence maps constrain the amplitude of structure at $0.4 < z < 1$, yielding $S_8 = 0.73 \pm 0.03$ , modestly lower than Planck $\Lambda$ CDM expectations (White et al., 2021).

Full-shape power spectrum and bispectrum analyses further disentangle growth rate $f(z)$ from clustering amplitude $\sigma_{s8}(z)$ : joint analyses measure

$f / f^{\rm fid} = \{0.888^{+0.186}_{-0.089}, 0.977^{+0.182}_{-0.220}, 1.030^{+0.368}_{-0.085}\}$

$\sigma_{s8}/\sigma^{\rm fid}_{s8} = \{1.224^{+0.091}_{-0.133}, 1.071^{+0.278}_{-0.163}, 1.000^{+0.088}_{-0.223}\}$

(cumulative constraints of 10.1% on $f$ and 8.4% on $\sigma_{s8}$ ), all consistent with Planck cosmology (Novell-Masot et al., 12 Mar 2025).

A key innovation is the combination of LRG and ELG samples in the overlapping $0.8 $9.1\sigma$

6. LRGs as Probes of the Galaxy–Halo Connection and Galaxy Evolution

Extensive simulation and empirical analyses reveal that the LRG–halo connection is non-trivial. HOD modeling and “digital twin” approaches show that even in the most massive halos, central LRG occupation fractions are significantly below unity, reflecting color–magnitude selection incompleteness rather than a simple mass threshold (Hernández-Aguayo et al., 2020, Berti et al., 2023). Hydrodynamical simulations (IllustrisTNG) support this, revealing non-standard satellite distributions, strong assembly bias (dependence on halo concentration and environment), and excess clustering relative to “vanilla” HOD predictions (Yuan et al., 2022). Clustering analyses with shuffling techniques quantify a 10–15% enhancement due to assembly bias.

On the evolution front, detailed stellar population analyses leveraging deep DESI validation spectra (median exposure $\sim$ 2.5 hr) demonstrate a rising fraction of recently quenched ( $f_\mathrm{1 Gyr}>0.1$ ) LRGs with redshift: from $<0.5\%$ at $z\sim0.4$ to $\sim3\%$ at $z\sim0.8$ , and even higher for weaker thresholds—implying rapid star formation shutdowns were more common at cosmic noon (Setton et al., 2022). Studies of the satellite galaxy population with deep imaging estimate that LRGs may gain up to $\sim15\%$ in stellar mass from $z{=}0.575$ to today via satellite accretion (Townsend et al., 2023).

7. Weak Lensing and Multi-Probe Cosmological Constraints

Galaxy–galaxy lensing (GGL) measurements, using DESI LRGs as massive lens samples and sources from major imaging surveys (HSC, KiDS, DES, SDSS), determine the excess surface mass density profile, $\Delta\Sigma(r_p)$ , and tangential shear, $\gamma_t$ , around LRGs. The relation $\Delta\Sigma(r_p) = \gamma_t(r_p) \Sigma_{\rm crit}$ underpins direct inference of halo matter profiles (Heydenreich et al., 26 Jun 2025). These measurements, robust against lens sample inhomogeneity and photometric redshift bias after calibration, are complemented by the projected galaxy correlation function $w_p(r_p)$ , further bolstering joint “3×2pt” constraints on structure growth and galaxy–halo connection.

Combining three-dimensional clustering, post-reconstruction BAO, angular clustering, and cross-correlations with CMB lensing from both Planck and ACT yields tightly constrained cosmological parameters for DESI DR1 LRGs: $\sigma_8 = 0.803 \pm 0.017, \quad S_8 = 0.808 \pm 0.017, \quad \Omega_m = 0.3037 \pm 0.0069$ with a $\sim$ 40% reduction in $\sigma_8$ uncertainty attributable to the inclusion of galaxy–lensing cross-correlations (Maus et al., 27 May 2025). Comparisons with BOSS LRG samples and extended parameter fits (evolving $w_0$ – $w_a$ dark energy, gravitational slip parameter $\gamma$ ) reinforce the robustness and scientific potential of the DESI LRG dataset.

In summary, the DESI DR1 LRG sample is defined by carefully engineered photometric and spectroscopic selection, validated by robust control of systematics, and underpinned by advanced mock catalog generation. It is delivering high-fidelity constraints on cosmic expansion (BAO), large-scale structure amplitude, and the galaxy–halo connection, and provides a foundation for multi-probe inference—positioning it as a flagship sample for precision cosmology and galaxy evolution studies in the DESI era.