DESI 2024 II: sample definitions, characteristics, and two-point clustering statistics

This DESI Collaboration paper addresses a practical but central question for precision cosmology: how to construct and validate large-scale structure (LSS) galaxy and quasar catalogs from DESI Data Release 1 (DR1) such that the measured two-point clustering statistics (correlation functions and power spectra) can be reliably compared to theoretical models. The question matters because raw observed number densities are modulated by many non-cosmological effects—survey geometry, fiber assignment incompleteness, imaging systematics, and spectroscopic success variations—each of which can imprint spurious correlations or bias the inferred cosmological parameters if not modeled correctly.

The paper’s contribution is methodological and infrastructural. It defines the DESI DR1 target samples (BGS, LRG, ELG, QSO), specifies the spectroscopic redshift selection criteria used to define “good” tracers, constructs the corresponding random catalogs that encode the survey footprint, and develops a weighting and correction framework to remove or marginalize known observational systematics. It also describes the measurement pipelines for two-point statistics in both configuration space and Fourier space, including the role of window functions, normalization constraints, and integral-constraint effects. Finally, it validates the resulting “raw” two-point measurements by comparing DESI DR1 data to mock catalogs that include realistic DESI fiber assignment.

Methodologically, the study is a large-scale survey data processing and validation effort rather than a controlled experiment. The data source is DESI DR1, using observations through June 14, 2022. The sample construction begins with photometric target selection from Legacy Surveys DR9 imaging, split into North (BASS/MzLS) and South (DECam/DECaLS) regions, with WISE W1/W2 used across the sky. The paper then adds spectroscopic information from the DESI “iron” reduction pipeline (Redrock redshifts, plus QSO classifiers such as QuasarNET and an MgII afterburner). A special reprocessing substitution is applied for data taken on Dec. 12, 2021 due to a calibration bug, affecting 8 dark and 9 bright tiles.

The final clustering samples are defined by tracer-specific spectroscopic success criteria and redshift cuts. For BGS, success requires ZWARN = 0 and $\Delta {\chi }^2>40$, with redshift selection $0.1<z<0.4$ and an absolute magnitude cut $M_r<-21.5$ (using Fastspecfit-based k-corrections and an evolution correction). This reduces the number of successful redshifts from 4,036,190 to 485,331 before the redshift cut, and then to 300,043 used in the final analysis. For LRG, success is ZWARN = 0 and $\Delta {\chi }^2>15$, with $0.4<z<1.1$ split into three bins. For ELG, success is ${\log }_{10}(S[\mathrm{OII}])+0.2{\log }_{10}(\Delta {\chi }^2)>0.9$ and $0.8<z<1.6$ split into two bins. For QSO, success is “not rejected by the quasar catalog,” using Redrock/MgII/QuasarNET identifications, with a broad $0.8<z<3.5$ selection but primary clustering using $0.8<z<2.1$.

The paper reports final sample sizes and key completeness metrics (Table 2). After vetoes and selection, the number of good redshifts are: BGS 300,043; LRG 2,138,627; ELG 2,432,072; and QSO 1,223,391 (with the primary QSO subset 856,831 in $0.8<z<2.1$). Spectroscopic success rates within the footprint are high for BGS (98.9%) and LRG (99.1%), moderate for ELG (72.7%), and lower for QSO (66.8%).

A major methodological component is the construction of random catalogs and the correction of selection-function variations. Randoms are generated at uniform angular density (2500 deg${}^{-2}$ per random file) over the DESI footprint defined by “reachable” targets under good hardware conditions. The paper applies multiple veto masks: hardware vetoes (bad fibers, low template signal-to-noise thresholds TSNR2, and instrument flags), a priority veto (e.g., QSO and rare strong-lens candidates remove area from lower-priority samples), and imaging vetoes (bright object masks and Healpix-based cuts on imaging property tails). The paper quantifies footprint losses; for example, hardware veto removes 3.1% of the dark-time footprint and 2.3% of the bright-time footprint. Priority veto removes 1666.7 deg${}^2$ (20.3%) for LRG & ELG and 38.5 deg${}^2$ (0.5%) for QSO.

Fiber assignment incompleteness is treated by defining assignment completeness $C_{\mathrm{assign}}$ and decomposing it into weights based on tile/fiber competition. The fiducial completeness weight is $w_{\mathrm{comp}}=1/f_{\mathrm{TLID}}$ (Eq. $5.2$), with additional handling of tile-group effects via $f_{\mathrm{tile}}$ applied to randoms. The paper emphasizes that this fiducial approach is not strictly unbiased at small angular scales because of physical fiber collision constraints; therefore, DESI’s default two-point analysis removes pairs with angular separation $\theta <0.05^{\circ }$ (“$\theta$-cut”) and incorporates the resulting bias through window matrices.

Imaging systematics are corrected using tracer-dependent regression methods. BGS uses linear regression with three maps (r-band depth, stellar density, HI column density). LRG uses linear regression with five maps in BASS/MzLS and one additional map in DECam regions depending on redshift bin. QSO uses a random-forest regression (Regressis). ELG uses a SYSNet neural-network regression. The paper validates these choices with null tests: it computes ${\chi }^2$ statistics of normalized projected density versus imaging-property bins, comparing data to uncontaminated mocks. It reports large improvements in the null ${\chi }^2$ after applying weights (e.g., for BGS, improvement close to a factor of 2 in DECam; for QSO, overall improvement greater than a factor of five in DECam). It also identifies residual concerns: for LRG, some residual trends in DECam are driven by CIB contamination components of $\Delta E(B-V)$, and for ELG the imaging systematic impact is the most severe.

Spectroscopic systematics are handled via redshift-failure weights $w_{z\mathrm{fail}}$, modeled as a function of TSNR2 (and for some tracers, fiberflux and redshift). The paper reports that despite significant trends in success rates with observing conditions, the impact on two-point clustering is negligible for DR1 when using these weights.

Two-point statistics are measured using Landy–Szalay estimators for correlation functions and FKP-based estimators for power spectra, with multipoles $\ell =0,2,4$. The paper describes the use of multiple random catalogs to reduce noise, the role of $\theta$-cut, and the computation of window matrices $W$ that map theoretical predictions to binned measurements. For power spectra, it also details corrections for radial integral constraint (RIC) and angular integral constraint (AIC) induced by imaging weights, using polynomial templates fit to differences measured in EZmocks and AbacusSummit cut-sky mocks.

The key validation results compare DESI DR1 “raw” two-point measurements to the mean of 25 “altmtl” mocks (mocks with realistic fiber assignment and the same LSS pipeline). The paper’s headline conclusion is that configuration- and Fourier-space two-point measurements are generally consistent to within about a 2% factor in the inferred real-space overdensity field. In the detailed ${\chi }^2$ comparisons (Table 9), BGS shows excellent configuration-space agreement (e.g., ${\chi }^2/dof=49.6/45$ for $\xi (s)$ over $20<s<200h^{-1}\mathrm{Mpc}$), while Fourier-space agreement is somewhat worse but improves when restricting to $k<0.2h{\mathrm{Mpc}}^{-1}$. LRG configuration-space agreement is generally strong; the largest ${\chi }^2/dof$ values occur in Fourier space for the highest redshift bin, but improve when restricting to $k<0.2h{\mathrm{Mpc}}^{-1}$ (e.g., LRG3 monopole ${\chi }^2/dof=37.7/39$ under $k<0.2$ with a bias scaling of 0.99). ELG exhibits the most notable tension: configuration-space ${\chi }^2/dof$ for ${\xi }_0+{\xi }_2$ in $0.8<z<1.1$ has PTE $=0.014$, and Fourier-space mismatches are largest at low $k$, consistent with residual imaging systematics. QSO mismatches are strongly scale dependent in Fourier space, with improved agreement when restricting to $k<0.2h{\mathrm{Mpc}}^{-1}$ (e.g., QSO monopole ${\chi }^2/dof=65.6/40$ for $k<0.2$ without scaling, improving to $49.3/39$ with a scaling factor 0.9882).

Limitations are inherent to the methodology. The paper’s validation uses a finite number of mocks (25 altmtl mocks for comparisons; 1000 EZmocks for covariance validation), and the mocks only approximately reproduce all aspects of the real data (notably fiber assignment realism and imaging systematics). It also acknowledges that the fiducial completeness weighting is not unbiased at small scales and therefore relies on the $\theta$-cut and window-matrix modeling. For small-scale clustering, the paper points to an alternative catalog version (v1.5pip) using PIP (pairwise inverse probability) weights and angular up-weighting, which is computationally more demanding and noisier on large scales.

Practically, the results matter for anyone performing DESI DR1 clustering analyses—BAO, full-shape RSD, and primordial non-Gaussianity studies—because they provide the public LSS catalogs, the recommended weights, and the measurement/correction pipeline needed to avoid systematic biases. The paper also provides guidance on robustness testing: analyses should assess sensitivity to imaging systematic weights (especially for ELG), spectroscopic success modeling, and residual integral-constraint effects. The intended audience includes DESI collaboration analysts and external researchers using DESI DR1 LSS products, as well as method developers interested in survey systematics modeling.

Overall, the paper’s core contribution is an end-to-end, validated framework for turning DESI DR1 observations into clustering-ready catalogs and two-point measurements, with explicit quantification of sample sizes, completeness, vetoed footprint fractions, weighting schemes, and the degree of agreement between data and realistic simulations.