MagLim++: Enhanced Lens Galaxy Sample

• MagLim++ is defined using an evolving i-band magnitude cut and enhanced photometric redshift calibration, which increases statistical power for cosmological analyses.
• It achieves 2–3× more galaxies than redMaGiC at similar redshifts, balancing number density with broader photometric redshift distributions.
• Advanced SOM-based redshift calibration, uncertainty propagation, and systematics control reduce errors by 20–30% and improve dark energy parameter constraints by up to 40%.

The MagLim++ Lens Galaxy Sample is a photometrically selected galaxy sample optimized for precision cosmology, specifically galaxy clustering and galaxy–galaxy lensing (“3×2pt” analyses) in the Dark Energy Survey Year 6 (DES Y6) and future surveys. It is defined by an evolving $i$-band magnitude cut as a function of photometric redshift and employs advanced redshift calibration and uncertainty propagation methods. MagLim++ builds upon the DES Y3 MagLim sample, incorporating improved selection, redshift estimation, and systematics control to enhance statistical power and reduce systematic uncertainties.

1. Sample Definition and Photometric Selection

The MagLim++ lens galaxy sample is constructed through a redshift-dependent $i$-band magnitude cut of the form

$i < 4z_{\mathrm{phot}} + 18,$

with a lower bound of $i > 17.5$ to exclude bright stars and reduce stellar contamination (Porredon et al., 2020, Giannini et al., 9 Sep 2025). This selection is empirically motivated to maximize galaxy number density while maintaining acceptable photometric redshift (photo-$z$) accuracy. The approach balances the tradeoff between including fainter galaxies at higher redshift (to augment number density and statistical power) and enforcing stricter magnitude limits at low redshift (to retain galaxies with robust photo-$z$ determination).

Relative to traditional red sequence samples (e.g., redMaGiC), MagLim++ exhibits:

• 2–3$\times$ more galaxies than redMaGiC at comparable redshifts,
• $\sim30\%$ broader redshift distributions than redMaGiC,
• $\sim7\times$ fewer galaxies and $\sim20\%$ narrower redshift distributions than a strict flat flux–limited sample with $i < 22.2$ (Porredon et al., 2020).

These properties result in increased statistical power for two-point statistics at the expense of somewhat worsened redshift resolution.

2. Redshift Calibration and Uncertainty Propagation

Redshift calibration for MagLim++ employs a Self-Organizing Map-based algorithm (SOMPZ), leveraging deep-field multi-band photometry, Balrog synthetic source–injection simulations, and wide-field data (Giannini et al., 9 Sep 2025).

Key elements include:

• Deep SOM construction: Galaxy photometry in deep, multi-band (including non-standard bands) fields is clustered using SOMs. Empirical $p(z|c)$ redshift distributions are assigned using spectroscopic and high-quality photometric redshifts.
• Transfer function via Balrog: Balrog-injected galaxies, matched in deep and wide fields, enable the construction of $p(c|\hat{c})$, mapping deep-field SOM cells $c$ to wide-field cells $\hat{c}$.
• Noise-weighted SOM metric: Assignment distances in SOM space are weighted by signal-to-noise, leading to more robust cell assignments and reducing redshift outliers compared to Y3 calibrations.
• Uncertainty propagation: The calibration workflow integrates sources of error (sample variance, shot noise, photo-z sample biases, photometric zeropoint errors) using a hierarchical 3-step Dirichlet sampling (“3sDir”), generating ${\cal O}(10^8)$ $n(z)$ realizations per tomographic bin.
• Importance sampling with clustering-redshifts: Cross-correlation (“clustering-redshift”/WZ) measurements with spectroscopic references are used to importance-sample the SOMPZ $n(z)$ ensemble. This refinement typically reduces mean redshift uncertainties by $20$–$30\%$ over previous Y3 calibration.

A numerical decomposition compresses the final $n(z)$ ensemble into a small set of orthogonal modes, parameterizing the remaining uncertainty for efficient marginalization in cosmological parameter inference.

3. Cosmological Performance and Constraints

The MagLim++ sample is designed for combined galaxy clustering and galaxy–galaxy lensing ("2×2pt" or "3×2pt") analyses, optimizing the statistical power for key cosmological parameters:

• In wCDM and $\Lambda$CDM analyses, MagLim yields up to $40\%$ improvement in the figure of merit for parameter pairs $(\Omega_m, w)$ and $(\Omega_m, \sigma_8)$ over redMaGiC (Porredon et al., 2020, Faga et al., 18 Jun 2024).
• In the DES Y3 configuration-space analysis, the MagLim sample provided $S_8 = 0.778^{+0.037}_{-0.031}$ and $\Omega_m = 0.320^{+0.041}_{-0.034}$ in $\Lambda$CDM (Porredon et al., 2021).
• In harmonic space using DES Y3, MagLim yields $S_8 = 0.753 \pm 0.024$ with six tomographic bins and $S_8 = 0.779 \pm 0.028$ with four bins (Faga et al., 18 Jun 2024).
• Redshift calibration uncertainties, after the full propagation and clustering-redshift refinement, typically contribute $<1$–$2\%$ uncertainty in the mean redshift of each tomographic bin (Giannini et al., 9 Sep 2025).

These constraints demonstrate that MagLim++ achieves significant statistical power, with robust control of systematics, and parameter uncertainties competitive with or superior to previous lens samples.

4. Systematics Control: Galaxy Clustering and Lensing

Mitigating systematic errors in MagLim++ involves:

• Advanced systematics decontamination for clustering analyses, using iterative principal component analysis (PCA)–derived weights from a comprehensive library of survey property maps (Rodríguez-Monroy et al., 2021). The “ISD–PC$<$50” strategy, which restricts decontamination to the leading $\sim$50 PC maps, suppresses artificial clustering without removing true cosmological signal.
• Additive systematics are incorporated into the covariance matrices and marginalized over in the cosmology inference, with validation using log-normal mocks ensuring that clustering amplitude biases remain $<0.5\sigma$.
• For lensing, the estimator includes corrections for metacalibration shear response, random-point subtraction, boost factor correction (accounting for source–lens clustering), point-mass marginalization for small-scale systematics, and a TATT (tidal alignment and tidal torquing) model for intrinsic galaxy alignments (Prat et al., 2021).
• Harmonic-space analyses employ pseudo-$C_\ell$ estimators, analytic covariances including non-Gaussian and super-sample contributions, and stress tests with mock catalogs (Faga et al., 18 Jun 2024).

These systematics controls underpin the reliability of joint cosmological analyses using the MagLim++ sample.

5. Magnification Bias and Complex Sample Selection

For samples defined by complex selection functions like MagLim++, accurate modeling of lensing magnification bias is critical (Wietersheim-Kramsta et al., 2021, Elvin-Poole et al., 2022). Key procedures include:

• Direct calibration of the effective luminosity function slope, $\alpha_{\mathrm{obs}}$, using differential galaxy counts or mock simulations. The effective magnification response is measured, capturing both flux and size selection effects, using Balrog-injected image simulations (Elvin-Poole et al., 2022).
• Variations in the magnification bias amplitude are treated as nuisance parameters, informed by simulation-based priors or marginalized (with cross-bin clustering improving constraints).
• Neglect of these systematics can introduce $>1\sigma$ shifts in inferred $S_8$ for MagLim-like samples unless modeled and marginalized appropriately (Elvin-Poole et al., 2022).

The MagBEt codebase provides a publicly available implementation of these calibration protocols for samples with complex selection functions (Wietersheim-Kramsta et al., 2021).

6. Galaxy–Halo Connection and Physical Characterization

Small-scale lensing measurements using MagLim enable HOD (Halo Occupation Distribution) modeling of the galaxy–halo connection (Zacharegkas et al., 2021):

• For MagLim, the average host dark matter halo mass is $\log_{10}(M_h/M_\odot) \approx 13.3$–$13.5$, modestly lower than in redMaGiC due to the inclusion of a broader range of galaxy types.
• The linear galaxy bias is tightly constrained, typically in the range $1.54$–$2.01$, and agrees with large-scale clustering results but provides $\sim5\times$ improved precision due to small-scale information.
• The satellite fraction for MagLim is generally low ($\sim 10$–$20\%$), without strong redshift dependence.

Such physical constraints are essential for precise modeling of galaxy bias and for breaking degeneracies in multi-probe cosmological analyses.

7. Sample Selection Optimization and Future Implications

Sample selection and tomographic bin definition critically impact cosmological constraining power (Alemany-Gotor et al., 24 Jul 2025):

• Automated pipelines using SOMs for photo-$z$ estimation and iterative optimization of redshift bin edges can increase the figure of merit for the dark energy equation of state by a factor $\sim2$, equivalent to a $\sim4\times$ effective area increase vs. standard binning.
• Optimizing lens and source bin configurations separately allows strategic allocation of narrower bins at low–mid redshift (for lens samples) and broader bins at high redshift (where photo-$z$ uncertainties dominate) to maximize Fisher information from 3×2pt analyses.
• These methodologies are directly applicable to MagLim++ and will be integral to forthcoming DES Y6 and next-generation surveys (e.g., LSST, Euclid).

This approach, coupled with improved data and calibration infrastructure, positions MagLim++ as a competitive and robust lens sample for precision cosmology in current and future photometric surveys.