Luminous Red Galaxy Sample (LRGS)

• LRGS is a spectroscopic or photometric sample of luminous, massive, red galaxies with prominent 4000 Å breaks, used as tracers of large-scale structure.
• Modern selections integrate optical and infrared color–magnitude criteria to distinguish passive, high-redshift galaxies across surveys like SDSS, eBOSS, and DESI.
• LRGS studies achieve high spectroscopic purity and redshift efficiency, enabling precise BAO, RSD, and galaxy evolution analyses critical for cosmological insights.

Searching arXiv for recent and foundational papers on Luminous Red Galaxy samples across SDSS, eBOSS, and DESI. Luminous Red Galaxy Sample, often abbreviated “LRGS” as a shorthand for a luminous red galaxy sample, denotes a spectroscopic or photometric galaxy sample built around luminous, massive, red, generally old stellar systems that are used as tracers of large-scale structure, targets for stellar-population analysis, and probes of the galaxy–halo connection. Across SDSS, BOSS, eBOSS, DESI, and related survey contexts, the term refers not to a single immutable catalog but to a family of survey-specific selections that share a common astrophysical target class: massive, passively evolving, highly biased galaxies with strong $4000$ Å breaks and, in modern selections, distinctive optical–infrared colors. The scientific role of LRGS selections ranges from baryon acoustic oscillation and redshift-space distortion measurements to tests of passive evolution, halo occupation, stellar-population fitting, and circumgalactic-medium studies (Zhou et al., 2020, Zhou et al., 2022, Bautista et al., 2020).

1. Definition and astrophysical basis

Luminous red galaxies are described in the survey literature as massive, passively evolving galaxies that inhabit highly biased structures and therefore exhibit strong clustering signals (Zhou et al., 2020). They are especially valuable because their spectra show a prominent $4000$ Å break, making redshift measurement comparatively easy and robust, and because they are bright enough that they can be selected with high uniformity over wide imaging footprints (Zhou et al., 2020). In high-redshift target-selection work, the target population is similarly described as very luminous, massive, generally old stellar systems, typically ellipticals with stellar masses of order $10^{11}-10^{12}\,M_\odot$ and luminosities $\gtrsim 3L^\star$ (Prakash et al., 2015).

The phrase “LRGS” is used in different papers in slightly different senses. In survey-targeting and clustering analyses, it denotes a survey-defined LRG sample, such as the SDSS/eBOSS LRG sample or the DESI LRG sample (Bautista et al., 2020, Zhou et al., 2022). In stellar-population studies, it can denote a more stringently filtered subset, for example a quiescent, high-$S/N$, emission-line-free SDSS DR7 sample intended for full-spectrum fitting (Liu et al., 2013). In specialized circumgalactic-medium work, it can denote a spectroscopic LRG sample assembled relative to QSO sightlines rather than a volume-limited cosmological catalog (Gauthier et al., 2011).

A recurrent misconception is that “LRGS” refers to a single standardized object class independent of survey methodology. The literature instead shows that each LRGS is defined operationally by a concrete target-selection algorithm, magnitude limits, masking rules, and redshift-performance requirements. This suggests that the common astrophysical identity of LRGs coexists with substantial survey-dependent selection complexity (Prakash et al., 2015, Zhou et al., 2022, Zhou et al., 2020).

2. Survey realizations of LRGS

The modern literature contains several major implementations of luminous red galaxy samples, each optimized for a distinct redshift regime and survey design.

Survey context	Redshift regime	Characteristic role
SDSS DR7 LRG samples	$0.0	Passive-evolution and stellar-population analyses
eBOSS / SDSS-IV LRG sample	$0.6	BAO and RSD at $z\sim0.7$
DESI LRG sample	$0.4<z\lesssim1.0$	Dense intermediate-redshift large-scale-structure tracer

In SDSS DR7 stellar-population work, one study analyzed 17,852 quiescent, Luminous Red Galaxies (LRGs) spanning $4000$0, after selecting from the SDSS DR7 spectroscopic database and imposing quiescence and quality requirements (Carson et al., 2010). Another SDSS DR7 study defined a final LRGS of 2,440 quiescent LRGs with $4000$1, after starting from the TARGET-GALAXY-RED flag, restricting to CUT I LRGs, and applying spectroscopic, morphological, and emission-line criteria (Liu et al., 2013). A separate SDSS DR7 evolution analysis used the complete sample of galaxies observed using the original SDSS LRG targeting algorithm over $4000$2, then constructed matched high- and low-redshift samples to test passive evolution (Tojeiro et al., 2010).

In eBOSS, the LRG program extended the SDSS/BOSS red-galaxy BAO program to higher redshift using SDSS optical plus WISE infrared photometry (Prakash et al., 2015). The final eBOSS DR16 cosmology sample analyzed in configuration space combined 174,816 eBOSS LRGs with 202,642 BOSS CMASS galaxies, and the paper explicitly states that the combined CMASS+LRG sample is simply referred to as the eBOSS LRG sample (Bautista et al., 2020). In an earlier BAO analysis, the DR14 eBOSS LRG spectroscopic sample contained 80,118 galaxies, and the BAO analysis sample grew to 126,557 galaxies after adding the $4000$3 tail of CMASS within the same footprint (Bautista et al., 2017).

In DESI, the LRG sample is the survey’s principal galaxy tracer over intermediate redshift, intended to deliver about 8 million redshifts over $4000$4 (Zhou et al., 2022). A preliminary selection note described a sample of more than 8 million candidate LRGs over $4000$5, with a uniform surface density of $4000$6 (Zhou et al., 2020). The validated DESI sample later reached a target density of 605 deg$4000$7 with comoving number density $4000$8 in $4000$9 (Zhou et al., 2022).

These survey realizations form a historical sequence. SDSS and BOSS selections relied primarily on optical color logic tied to the $10^{11}-10^{12}\,M_\odot$0 Å break, whereas eBOSS and DESI incorporated $10^{11}-10^{12}\,M_\odot$1 photometry to extend efficient LRG targeting to higher redshift and improve stellar rejection (Prakash et al., 2015, Zhou et al., 2020, Zhou et al., 2022).

3. Target selection methodology

Modern LRGS construction is fundamentally a color–magnitude selection problem in optical and infrared photometric space. The central methodological development is the move from optical-only selection to joint optical+infrared selection, motivated by the fact that optical-only selection works for lower-redshift red galaxies but becomes ineffective once the $10^{11}-10^{12}\,M_\odot$2 Å break moves beyond the relevant optical bands (Zhou et al., 2020, Prakash et al., 2015).

The physical reason $10^{11}-10^{12}\,M_\odot$3 is useful is the rest-frame $10^{11}-10^{12}\,M_\odot$4 bump in galaxy stellar populations. For galaxies at roughly $10^{11}-10^{12}\,M_\odot$5, this feature produces excess flux in the observed $10^{11}-10^{12}\,M_\odot$6 band, so optical–infrared colors separate high-redshift LRGs from stars and lower-redshift galaxies more effectively than optical colors alone (Zhou et al., 2020). In eBOSS, this logic was implemented through the cuts

$10^{11}-10^{12}\,M_\odot$7

together with magnitude cuts such as

$10^{11}-10^{12}\,M_\odot$8

using extinction-corrected AB magnitudes and unWISE forced photometry (Prakash et al., 2015). The eBOSS selection did not use explicit morphology; star–galaxy separation was performed by color alone (Prakash et al., 2015).

DESI adopted a denser and more infrared-centered selection. For the South, the final main selection is

$10^{11}-10^{12}\,M_\odot$9

$\gtrsim 3L^\star$0

$\gtrsim 3L^\star$1

$\gtrsim 3L^\star$2

with slightly modified coefficients in the North (Zhou et al., 2022). The paper identifies these components as a $\gtrsim 3L^\star$3 faint limit controlling spectroscopic success, a principal stellar-rejection cut using $\gtrsim 3L^\star$4 versus $\gtrsim 3L^\star$5, a low-redshift rejection cut, and a sliding $\gtrsim 3L^\star$6 versus $\gtrsim 3L^\star$7 luminosity cut that shapes the redshift distribution (Zhou et al., 2022). The preliminary DESI note used a related South selection with

$\gtrsim 3L^\star$8

$\gtrsim 3L^\star$9

$S/N$0

$S/N$1

again using extinction-corrected $S/N$2 photometry (Zhou et al., 2020).

The shift from optical to infrared-based luminosity selection also altered systematic sensitivity. DESI reports that a $S/N$3-based luminosity cut was favored over a $S/N$4-band-based alternative because the latter would have produced $S/N$5 RMS density fluctuations from photometric calibration uncertainty, whereas the adopted selection had a combined RMS density fluctuation of only $S/N$6 under the estimated zero-point uncertainties (Zhou et al., 2022).

This suggests that LRGS design is not solely about maximizing target yield or purity. It is also about choosing selection variables whose calibration properties preserve uniform angular density at the level required for precision clustering.

4. Validation, purity, and spectroscopic performance

LRGS validation generally combines photometric-redshift tests, spectroscopic commissioning or survey-validation data, and explicit audits of imaging-systematics sensitivity.

The DESI preliminary note stated that the sample had a uniform surface density of $S/N$7, low predicted stellar contamination, and high redshift success (Zhou et al., 2020). The validated DESI LRG sample sharpened this assessment: after applying a bright star veto mask, 98.9\% of observed LRG targets yielded confident redshifts, the catastrophic failure rate among accepted redshifts was 0.2\%, and only 0.5\% of LRG targets were stellar contamination (Zhou et al., 2022). A confident redshift was defined by

$S/N$8

The same work emphasizes that redshift efficiency depends primarily on $S/N$9-band fiber brightness and effective exposure time and provides a fitted failure model in those variables (Zhou et al., 2022).

Earlier eBOSS targeting achieved lower purity and redshift efficiency. The eBOSS target-selection paper reported that the spectra were of high enough signal-to-noise ratio that at least 89\% of the target sample yielded secure redshift measurements, with stellar contamination around 9\% in the visually inspected sample (Prakash et al., 2015). The fraction of all targets that were secure galaxies in $0.068–72\%, below the nominal 80% efficiency requirement, although the median redshift requirement was met and the target density in the desired redshift range was 41.0–43.1 deg$0.0 (Prakash et al., 2015).

The completed eBOSS DR16 clustering sample reported markedly improved spectroscopic performance at the sample level: 96.5\% of spectra yielded a confident redshift estimate, with <1\% catastrophic redshift failures (Bautista et al., 2020). In the BAO analysis of DR14, however, the average redshift efficiency of the eBOSS LRG sample was 90.5\%, and the paper developed a new random-subsampling correction because the failure rate of around 10% was too high for standard nearest-neighbor upweighting to remain unbiased for anisotropic clustering (Bautista et al., 2017).

Uniformity against imaging depth, seeing, extinction, and other survey properties is now treated as intrinsic to LRGS validity. The DESI validated sample found density deviations with imaging systematics “almost all within $0.0Zhou et al., 2022). A later forward-modeling study showed that faint DESI LRGs are the main source of depth-driven target-density fluctuations and that trends against Galactic extinction depend strongly on which extinction map is used, implying contamination in the maps themselves is likely part of the problem (Kong et al., 2024). A plausible implication is that imaging-systematics mitigation for LRGS cannot be reduced to a single position-dependent weight if the response also depends strongly on intrinsic galaxy brightness (Kong et al., 2024).

5. Cosmological applications

LRGS selections are a core observational substrate for BAO and RSD cosmology because LRGs are luminous, highly biased tracers of the matter density field over large cosmic volumes (Bautista et al., 2020, Zhou et al., 2022). Their clustering is used to infer geometric observables such as $0.0Bautista et al., 2020).

In the completed SDSS-IV eBOSS DR16 analysis, the combined eBOSS LRG plus $0.0

$0.0

The final consensus constraints after combining configuration-space and Fourier-space analyses were

$0.0

$0.15

$0.15

with an effective comoving volume of $0.15Bautista et al., 2020). These measurements were reported as consistent with flat $0.15Bautista et al., 2020).

An earlier DR14 BAO-only analysis used the eBOSS DR14 sample of 80,118 Luminous Red Galaxies, combined with the high-redshift tail of CMASS to form a 126,557-galaxy sample at effective redshift $0.15Bautista et al., 2017). After reconstruction, the main isotropic BAO result was

$0.15

a 2.6\% measurement with 2.8$0.15 significance (Bautista et al., 2017).

DESI was designed as a substantial advance in LRG density and redshift reach. The DESI LRG sample has target density 605 deg$0.15 and comoving number density $0.15Zhou et al., 2022). The preliminary DESI note described a roughly constant comoving density of $0.6Zhou et al., 2020). This suggests that the DESI LRGS is best understood as a denser successor to the eBOSS and CMASS high-redshift red-galaxy program rather than merely a reimplementation of older SDSS-style LRG targeting.

LRGS samples are also now being designed explicitly for cross-survey compatibility. The 4MOST-Cosmology Redshift Survey LRG sample was made intentionally DESI-like so that 4MOST and DESI could be combined into a much larger homogeneous spectroscopic sample, with the 4MOST LRG subsurvey targeting $0.6Verdier et al., 10 Aug 2025). This suggests that the concept of an LRGS increasingly includes interoperability between surveys, not just internal survey optimization.

6. Galaxy evolution, stellar populations, and halo occupation

Beyond cosmology, LRGS samples have become a central laboratory for studying stellar populations, passive evolution, and the galaxy–halo connection.

A quiescent SDSS DR7 sample of 2,440 LRGs analyzed with ULySS and STARLIGHT showed that the stellar populations of these galaxies are dominated by old, metal-rich populations, with old stellar populations contributing overwhelmingly to the mass budget (Liu et al., 2013). The study found that for sub-samples I–IV, STARLIGHT yielded mean ages of $0.6$z\sim0.7$0, and $z\sim0.7$1 Gyr, while ULySS yielded $z\sim0.7$2, $z\sim0.7$3, $z\sim0.7$4, and $z\sim0.7$5 Gyr; both methods showed that galaxies with larger velocity dispersion are older (Liu et al., 2013). The same paper reported that most LRGs are metal-rich, generally above solar metallicity, and that STARLIGHT was more robust than ULySS at low $z\sim0.7$6 because ULySS could become trapped in local minima (Liu et al., 2013).

A larger DR7 study of 17,852 quiescent LRGs analyzed with Lick indices found little evidence for evolution in metallicity or alpha-element abundance ratios over $z\sim0.7$7, while the stellar ages decreased by about 5 Gyrs across that redshift interval in a way consistent with cosmological lookback time (Carson et al., 2010). The same work concluded that the intermediate-mass samples were consistent with pure passive evolution and represented a homogeneous population over the redshift range studied (Carson et al., 2010). In a complementary DR7 analysis of LRG evolution over $z\sim0.7$8, the population was found to grow in luminosity by 1.5–6 % Gyr$z\sim0.7$9 depending on luminosity, with the brightest objects ($0.4<z\lesssim1.0$0) consistent with passive evolution but fainter LRGs showing growth inconsistent with a purely passive picture (Tojeiro et al., 2010).

The halo occupation of LRGS samples is similarly nontrivial. A direct cluster-based study of SDSS LRGs found that even in massive halos the asymptotic central occupation converges to about 0.95 rather than 1, and that at halo masses of $0.4<z\lesssim1.0$1, the central occupation is 0.73 rather than the 0.89 inferred from correlation studies (Hoshino et al., 2015). The same paper found $0.4<z\lesssim1.0$2, meaning the brightest cluster member is not always the central galaxy (Hoshino et al., 2015). An abundance-matching study of SDSS LRGs at $0.4<z\lesssim1.0$3 similarly found that about 10% of LRG-host halos contain satellite LRGs, and that in multiple-LRG halos the brightest LRG is central only $0.4<z\lesssim1.0$4 of the time (Masaki et al., 2012).

The same complexity carries into DESI. Forward modeling of DESI LRGs with subhalo abundance matching found that both the optical and infrared DESI LRG target selections yield populations with a non-trivial LRG–halo connection that does not reach unity for the most massive halos (Berti et al., 2023). In the preferred $0.4<z\lesssim1.0$5-band model, the IR selection achieved peak central occupation fractions of $0.4<z\lesssim1.0$6, $0.4<z\lesssim1.0$7, and $0.4<z\lesssim1.0$8 at $0.4<z\lesssim1.0$9, $4000$00, and $4000$01, while the optical selection achieved $4000$02, $4000$03, and $4000$04 (Berti et al., 2023). The paper concludes that the IR selection achieves $4000$05 completeness across all redshift bins studied, whereas the optical selection is somewhat less complete (Berti et al., 2023).

A common misconception is that luminous red galaxy samples can be modeled as simple halo-mass-threshold or central-galaxy-only populations. The SDSS cluster-counting work, the SDSS progenitor-tracking mock, and the DESI forward-modeling study all indicate that this is not the case [(Hoshino et al., 2015); (Masaki et al., 2012); (Berti et al., 2023)]. A plausible implication is that HOD analyses that hardwire $4000$06 at high mass or assume brightest-object centering without mis-centering terms may be adequate phenomenologically on some scales but can misrepresent the underlying LRGS selection physics.

7. Specialized and emerging uses

LRGS samples are increasingly used beyond traditional BAO and passive-evolution applications. One SDSS-based study assembled a spectroscopic sample of 37 LRGs at $4000$07 within $4000$08 of QSO sightlines to test the relation between LRGs and Mg II absorbers (Gauthier et al., 2011). Of these, 8 had associated Mg II absorbers with $4000$09, while 29 did not (Gauthier et al., 2011). The stacked spectra of absorbing and non-absorbing LRGs were both dominated by old stellar populations, and the covering fraction of cool gas in the unbiased subset was found to be

$4000$10

for absorbers with $4000$11 (Gauthier et al., 2011). This showed that cool gas can exist in halos of passive LRGs without implying active star formation in the hosts (Gauthier et al., 2011).

Another study used 1,823 BOSS LOWZ+CMASS LRGs in the $4000$12 DESI Legacy Imaging Surveys EDR footprint to measure the satellite populations around LRGs out to $4000$13 (Townsend et al., 2023). By statistical background subtraction and forward modeling, it constrained mean satellite counts within 600 kpc and inferred that LRGs can at most grow by about $4000$14 from $4000$15 to the present and $4000$16 from $4000$17 (Townsend et al., 2023). This suggests that LRGS studies are increasingly coupling deep imaging with spectroscopic host samples to probe faint satellite populations and late-time stellar-mass growth.

Marked-correlation work provides another emerging use. A study of BOSS DR12 NGC LOWZ and CMASS narrow redshift slices used projected marked correlation functions with density-dependent marks to test GR against Hu–Sawicki $4000$18 gravity (Armijo et al., 2023). The analysis found that current galaxy catalogues are too small to distinguish the tested $4000$19 model from GR once HOD uncertainty is included, but it explicitly identified future LRG surveys such as DESI as promising for such tests (Armijo et al., 2023). A plausible implication is that LRGS samples are becoming a general-purpose substrate for precision tests of structure formation, provided their galaxy–halo connection is modeled with sufficient realism.

Overall, the literature defines the Luminous Red Galaxy Sample not as a fixed catalog but as a technically evolving survey construct anchored to a stable astrophysical population. Its common features are massive red galaxies, strong large-scale-structure bias, and favorable spectroscopic properties. Its differences arise from the details of selection variables, calibration choices, masking, completeness, and intended scientific use. The concept has expanded from SDSS optical red-sequence targeting to optical+infrared high-redshift selections, from simple clustering tracers to benchmark samples for passive-evolution studies, and from phenomenological HOD inputs to systematics-sensitive forward-modeling targets (Prakash et al., 2015, Zhou et al., 2020, Zhou et al., 2022, Kong et al., 2024).