redMaGiC: Selecting Luminous Red Galaxies from the DES Science Verification Data

1 INTRODUCTION

• Photometric surveys without spectroscopic components motivate selection methods designed to minimize photometric redshift uncertainties.LRGs are luminous enough for relatively shallow exposures, and their 4000 Å break supports robust photo-z estimates when photometrically sampled.Source: §1 · p. 2
• Earlier LRG selection commonly used ad-hoc color-box cuts, while spectroscopic follow-up had made highly precise selection less necessary.Source: §1 · p. 2
• redMaGiC selects red galaxies by matching their colors to an empirical red-sequence template calibrated using sparse cluster spectroscopy.The method builds on redMaPPer infrastructure and aims to produce robust, well-controlled photo-zs with modest spectroscopic requirements.Source: §1 · p. 2
• The study characterizes DES SV redMaGiC photo-zs and also applies the algorithm to SDSS DR8 and Stripe 82 data.Source: §1 · p. 2

2.1 DES Science Verification Data

• DES SV coadd magnitudes and colors use SExtractor MAG AUTO, whose colors are noisier than model-fitting colors but more stable under coadd PSF discontinuities.The authors expect this choice to negatively affect results and plan to use full multi-epoch, multi-band color measurements in future work.Source: §2.1 · p. 3
• 148 deg2 of DES SV imaging are used, with ngmix-based star-galaxy separation and a z-band 10σ depth cut of mz > 22.The DES SV footprint has variable depth, and the catalog is restricted to z ∈ [0.2,0.8] for homogeneity; most spectroscopic training data lie in the supernova fields, limiting validation.Source: §2.1 · p. 3

2.2 SDSS DR8 Data

• SDSS DR8 imaging is reduced from ≈14,000 deg2 to ≈10,000 deg2 of contiguous high-quality observations using an extended mask.DR8 uses the SDSS star-galaxy separator and redMaPPer DR8 red-sequence model, with SDSS DR10 spectroscopy for training.Source: §2.2 · p. 3

2.3 SDSS Stripe 82 Data

• Stripe 82 supplies 275 deg2 of ugriz coadded imaging roughly two magnitudes deeper than single-pass SDSS; the selection uses griz photometry for most z ≳ 0.3 red galaxies.The analysis also considers the utility of u-band imaging at low redshift.Source: §2.3 · p. 3
• About 15% of S82 red cluster members have clearly incorrect magnitudes in at least one band, and the error origin and broader extent are unknown.The authors therefore do not release the S82 redMaPPer or redMaGiC catalogs, but retain the sample as a photo-z baseline against DES SV.Source: §2.3 · p. 4

3 THE redMaGiC SELECTION ALGORITHM

• redMaGiC fits each galaxy to a red-sequence color template, estimates its redshift and luminosity, and retains luminous galaxies with acceptable template-fit χ².The template models colors directly rather than converting through a spectrum.Source: §3 · p. 4

3.1 The redMaGiC Template

• The redMaGiC template uses an empirical red-sequence calibration from redMaPPer, with DES using z-band reference magnitudes and SDSS using i-band.The redMaPPer calibration fits the red-sequence color distribution of cluster galaxies as a function of redshift through an iterative likelihood procedure.Source: §3.1 · pp. 4–5

3.2 redMaGiC Photometric Redshfits

• The photo-z estimator finds the redshift maximizing a likelihood built from the galaxy’s colors and magnitude under a constant-density sample model.The redshift likelihood includes the red-sequence color model and photometric color-error covariance; the estimated redshift and fit χ² then inform luminosity and selection.Source: §3.2 · p. 5

3.3 Selection Cuts

• A redshift-dependent χ² threshold is chosen so the selected sample has constant comoving density, approximating passive evolution over relatively narrow redshift intervals.The authors note that galaxy merging means constant density is not exactly correct; the assumption also motivates P(z) ∝ |dV/dz| in the likelihood.Source: §3.3 · p. 6

3.4 Photo-z Afterburner

• The photo-z afterburner estimates redshift offsets from calibration galaxies and adjusts redshift errors with a spline-based scale factor.It uses redMaPPer cluster-member redshifts as calibration references when representative redMaGiC spectroscopy is unavailable; the small redshift perturbations improve photo-z performance.Source: §3.4 · p. 6

3.6 Selection Summary

• Only two redMaGiC selection parameters are free: the luminosity threshold and the target space density, while the color cuts are self-trained.Setting lmin too high can force selection of poor-fit galaxies to meet the target density, increasing photo-z outliers and making a flat density sample difficult to construct.Source: §3.6 · p. 7
• The fiducial cuts produce comoving densities close to flat across the samples, with low χ² thresholds, as desired.The example uses lmin = 0.5 and n̄ = 10^-3 h^3 Mpc^-3.Source: §3.6 · p. 7

4 PHOTO-Z PERFORMANCE

• The fiducial sample selects galaxies brighter than 0.5L* at n̄ = 10^-3 h^3 Mpc^-3; the comparison sample selects galaxies brighter than L* at 2 × 10^-4 h^3 Mpc^-3.The higher-luminosity, lower-density sample is intended for comparison with samples such as CMASS.Source: §4 · p. 7
• Three clumps of outlier points appear in DR8 and S82 but not DES SV, which the authors attribute to the paucity of DES spectra rather than improved performance.The authors caution that sparse spectra limit interpreting the apparent absence of DES outliers.Source: §4 · p. 7
• Observed redshift scatter agrees well with predicted photo-z uncertainty across all data sets, with peaks near z ≈0.35 and z ≈0.65 linked to filter transitions.The peaks correspond to the g-to-r and r-to-i transitions of the 4000 Å break.Source: §4 · p. 7
• DES has larger photometric redshift scatter than the SDSS data sets, with sparse redMaPPer training and noisier MAG AUTO colors cited as contributors.DES SV MAG AUTO colors are expected to be intrinsically noisier than SDSS MODEL MAG colors.Source: §4 · pp. 7–8
• Bias patterns are associated with non-representative spectroscopy: DR8 oversamples the reddest galaxies at z ≳0.3, and S82 does so from z ≈0.23.Offsets between spectroscopic-sample and full-sample color contours imply non-representative sampling.Source: §4 · p. 8
• At z ≈0.6 in S82, the photo-z bias is ≈−0.005 with SDSD spectroscopy but ≈0.009 with VIPERS, underscoring sensitivity to spectroscopic sampling.The paper notes that the difference between the two spectroscopic data sets affects conclusions.Source: §4 · p. 8
• DES SV bias origins are difficult to establish given sparse, non-representative training spectroscopy, its concentration in ≈30 deg² of SN fields, and MAG AUTO colors.The authors expect these difficulties to be ameliorated as DES images larger areas and data-reduction pipelines are updated.Source: §4 · p. 8

5.1 DR8 Comparisons

• The DR8 comparison used a high-luminosity redMaGiC sample over z ∈ [0.1,0.5], where spectroscopic sampling was less biased than at z ≥ 0.5.The comparison included SDSS photo-zs, RDF, and ANNZ.Source: §5.1 · p. 10
• 1.48% to 1.28% scatter: RDF improved on redMaGiC; SDSS photo-zs were slightly less biased but had nearly identical scatter to redMaGiC.All methods considered had comparable photo-z error tails.Source: §5.1 · pp. 10–11, Figure 7 · p. 12
• Fainter red-sequence galaxies beyond a machine-learning training set can have zphoto ≤ zspec; the cluster-redshift proxy test found bias around 0.02.At very high redshifts, the bias starts to decrease as redMaPPer’s luminosity threshold approaches the spectroscopic magnitude limit.Source: §5.1 · pp. 11–12

5.1 DR8 Comparisons; 5.2 DES Comparisons

• Across DR8 and DES SV, redMaGiC performed as well as the best machine-learning methods, without requiring representative spectroscopic training samples.The DES comparison also reports that redMaGiC scatter remains well characterized, unlike SkyNet and BPZ scatter.Source: §5.1 · p. 12, Figure 7 · p. 12, §5.2 · p. 13

5.2 DES Comparisons

• Nearly 12% of BPZ galaxies had normalized redshift error ≥ 0.08, compared with ≈1.4% for redMaGiC and SkyNet; SkyNet and redMaGiC performed equally well in bias and scatter.SkyNet predicted uncertainties were 3.5 times the observed errors, while BPZ uncertainties were overestimated by ≈6.Source: §5.2 · p. 12, Figure 8 · p. 13

• The samples are not perfectly matched: redMaGiC has comparable density but a lower luminosity threshold, and CMASS galaxies are about 0.3 magnitudes brighter.The authors say this added noise should degrade redMaGiC photo-z performance, making the comparison favorable to CMASS.Source: §6 · pp. 13–14, Table 3 · p. 14
• RedMaGiC has 1.5% photo-z scatter versus 2.1% for CMASS, and 1.4% versus 6.4% with |∆z|/(1 + z) ≥ 0.07.The comparison uses redMaGiC photo-zs for redMaGiC and SDSS photo-zs for CMASS; Figure 9 shows the spectroscopic-versus-photometric redshifts.Source: §6 · p. 13, Figure 9 · p. 14
• CMASS’s quoted scatter differs from Ross et al. (2011) partly because this section uses σz/(1+z) and median statistics to estimate σz.Ross et al. (2011) report σz and estimate it using ⟨zspec − zphoto⟩2, which is more sensitive to gross outliers than the MAD-based estimate.Source: §6 · p. 14
• CMASS galaxies with zspec ≲ 0.3 are particularly ill-behaved, and their inclusion in photometric-survey clustering could cause systematic errors.The authors contrast this with BOSS, where spectroscopic follow-up prevents these contaminants from entering cluster measurements near z ≈ 0.5.Source: §6 · p. 14

• A spectroscopic afterburner was tested on a validation half of the SDSS DR10 redMaGiC sample after training on the other half.The afterburner starts from the redMaGiC estimate and adjusts photo-zs and errors using spectroscopic information.Source: §7 · p. 14
• The validation results include a histogram of normalized photo-z residuals, with a zero-mean, unit-variance Gaussian shown as a reference rather than a fit.If estimates are Gaussian, unbiased, and have correctly estimated errors, the normalized residuals would follow that reference Gaussian.Source: §7 · pp. 14–15
• The authors withhold the spectroscopic afterburner by default because biased spectroscopic sampling can introduce unknown and uncontrolled photo-z biases.They defer adoption until a representative spectroscopic galaxy sample is available or data augmentation can extrapolate beyond training sets.Source: §7 · p. 15

8 UNDERSTANDING redMaGiC OUTLIERS

• The mean DR8 outlier fraction is about 0.7%, distributed among three clumps; outlier fractions also differ by dataset and luminosity sample.The authors report differences at low redshift between DR8 and S82/DES SV, and between fiducial and high-luminosity samples.Source: §8 · p. 15, Figure 11 · p. 16

8.1 Clump 1: Low Redshift Outliers

• Clump 1 outliers show excess blue light and Hα and [OII] emission, indicating residual star formation.Their spectra are largely consistent with non-outliers for wavelengths λ ≳ 5000 Å; Figure 12 shows the stacked spectra and their difference.Source: §8.1 · p. 15, Figure 12 · p. 15
• S82 and SV selections based only on griz admit more Clump 1 outliers than DR8, which also uses u-band; most S82 5σ outliers are unusually bright in u.The u-band is sensitive to Clump 1’s enhanced star formation, but it was excluded from S82 catalog construction because it caused problems with higher-redshift cluster calibration.Source: §8.1 · p. 15, Figure 13 · p. 17

8.2 Clump 2: Photo-z Biased High

• Clump 2 outliers show blue excess, Hα and [OII] emission, and a steeper continuum consistent with internal dust reddening of E(B−V) = 0.15.Near z ≈ 0.35, the reddening vector aligns with red-sequence color evolution, allowing dust to shift galaxies from zspec ∼ 0.3 to zphoto ∼ 0.4; reddening also dims galaxies and increases photometric errors.Source: §8.2 · pp. 15–16, Figure 14 · p. 17

8.3 Clump 3: Photo-z Biased Low

• Clump 3 outliers have residual-star-formation spectra qualitatively like Clump 1, but with significantly larger excess emission.The authors attribute the difference to larger photometric errors at higher redshifts in relatively shallow DR8 imaging.Source: §8.3 · p. 17, Figure 15 · p. 17
• Some outlier populations may be irreducible with available photometry; the authors expect DES Clump 1 outliers to be difficult to remove without u-band.If such populations cannot be removed, the authors say their P(z) distributions must be updated or the affected redshift regions excluded from high-precision LSS studies.Source: §8.3 · p. 17

• RedMaGiC targets photometric-redshift systematics in large-scale-structure studies by refining red-sequence selection; a complementary goal is a photo-z estimator for those galaxies.The paper frames photometric-redshift systematics as the primary challenge for large-scale-structure studies with photometric data.Source: §9 · pp. 17–18
• Across samples, redMaGiC photo-zs have bias ≲ 0.5%, scatter ≲ 1.6%, and catastrophic-outlier rates ⩽ 2%, with exact values depending on the sample.The paper reports superior performance to the standard color-cut selection used for SDSS CMASS, and scatter that is correctly estimated a priori.Source: §9 · p. 18
• RedMaGiC has minimal spectroscopic requirements and avoids the out-of-training-set bias expected for machine-learning algorithms without representative spectroscopy.The authors identify these as two advantages over machine-learning methods, especially for faint galaxies outside training samples.Source: §9 · p. 18
• Representative spectroscopic sampling of redMaGiC galaxies enables photo-z estimation unbiased at the 0.1% level, with well-characterized errors.The authors recommend pursuing machine-learning techniques if representative training sets become available.Source: §9 · p. 18
• The current photo-z estimates need extension to P(z) distributions to capture skewness and kurtosis, including near filter transitions.The paper identifies three distinct outlier classes: Clumps 1 and 3 are ellipticals or S0 galaxies with residual star formation, while Clump 2 galaxies are very dusty elliptical/S0 galaxies with E(B − V) ≈ 0.15.Source: §9 · p. 18

APPENDIX A: STAR-GALAXY SEPARATION

• The separator uses intrinsic size and size error to retain objects consistent with being extended sources within observational errors.The ngmix size estimates distinguish stellar and galaxy loci clearly at the bright end, but less well when faint-galaxy sizes approach the seeing.Source: Appendix A · pp. 20–21
• Cross-correlations with a known stellar sample estimate contamination, while comparing cuts with nmax = 5 estimates relative completeness.The approach treats a nonzero star–galaxy cross-correlation as evidence of stellar contamination and assumes δs = δ∗ when relating the correlations.Source: Appendix A · p. 21
• At n = 1, expected stellar contamination and galaxy incompleteness are each approximately 4%.The faintest fiducial redMaGiC galaxies fall between the two magnitude-bin curves used to set this cut.Source: Figure A2 · p. 21, Appendix A · p. 22
• The bright stellar reference sample gives difficult-to-interpret results, including completeness above unity and an estimated stellar fraction near 10%.The authors suggest δs = δ∗ may be incorrect, retain n = 1 for the selection, and leave a more accurate contamination estimate for future work.Source: Appendix A · p. 22
• In the redMaGiC catalog, stellar contamination is expected to be about 5% near z ≈ 0.7 and essentially absent at other redshifts.Red-sequence color selection suppresses the stellar fraction relative to the full catalog selected by the star–galaxy cut.Source: Appendix A · p. 22

APPENDIX B: DATA CATALOG FORMATS

• Catalog absolute magnitudes use kcorrect v4.2 with an LRG template band-shifted to z = 0.1.Source: Appendix B · p. 22
• The authors state that the SDSS catalogs will be available upon publication and plan to release DES redMaGiC catalogs publicly by January 2016.Source: Appendix B · p. 22
• The SDSS DR8 and DES SV catalog formats are summarized in Tables B1 and B2, respectively.Source: Table B1 · p. 23, Table B2 · p. 23