Dark Energy Survey Year 6 Results: Clustering-redshifts and importance sampling of Self-Organised-Maps $n(z)$ realizations for $3\times2$pt samples

TL;DR

This work enhances DES Y6 3×2pt analyses by combining SOMPZ-derived redshift distributions with clustering-z (WZ) constraints from BOSS/eBOSS galaxies and eBOSS QSOs. It formulates an analytically marginalizable WZ likelihood, incorporates magnification and a flexible systematic-bias model, and marginalizes photometric uncertainties via importance sampling and mode compression. Using Cardinal mocks to calibrate priors and validate scale choices (1.5–5 Mpc), the study shows WZ can tighten n(z) posteriors and improve $S_8$ by about 10% for both cosmic shear and 3×2pt analyses, with only modest shifts in mean redshift for most bins. The results demonstrate that a hybrid SOMPZ+WZ approach yields more accurate redshift calibration and stronger cosmological constraints, a methodology readily extensible to upcoming LSST, Euclid, and Roman analyses.

Abstract

This work is part of a series establishing the redshift framework for the $3\times2$pt analysis of the Dark Energy Survey Year 6 (DES Y6). For DES Y6, photometric redshift distributions are estimated using self-organizing maps (SOMs), calibrated with spectroscopic and many-band photometric data. To overcome limitations from color-redshift degeneracies and incomplete spectroscopic coverage, we enhance this approach by incorporating clustering-based redshift constraints (clustering-z, or WZ) from angular cross-correlations with BOSS and eBOSS galaxies, and eBOSS quasar samples. We define a WZ likelihood and apply importance sampling to a large ensemble of SOM-derived $n(z)$ realizations, selecting those consistent with the clustering measurements to produce a posterior sample for each lens and source bin. The analysis uses angular scales of 1.5-5 Mpc to optimize signal-to-noise while mitigating modeling uncertainties, and marginalizes over redshift-dependent galaxy bias and other systematics informed by the N-body simulation Cardinal. While a sparser spectroscopic reference sample limits WZ constraining power at $z>1.1$, particularly for source bins, we demonstrate that combining SOMPZ with WZ improves redshift accuracy and enhances the overall cosmological constraining power of DES Y6. We estimate an improvement in $S_8$ of approximately 10\% for cosmic shear and $3\times2$pt analysis, primarily due to the WZ calibration of the source samples.

Figures (22)

• Figure 1: Flowchart summarizing the DES Y6 3$\times$2pt redshift calibration pipeline. Photometric data for targeted subsets of the DES Y6 galaxy catalog are placed into Self-Organizing Maps (SOMs), with the redshift distributions of each SOM cell estimated from better-observed galaxies in DES deep fields, along with an observational 'transfer function' from deep to wide observational properties derived from the 'Balrog' source injection simulations. Sampling over the associated uncertainties produces a set of realizations, $n_i^{\rm SOMPZ}(z)$. The constraints on $n(z)$ implied by clustering information (WZ), described in this work, are realized by importance sampling the $n_i^{\rm SOMPZ}(z)$ to yield $n_i^{\rm SOMPZ+WZ}(z)$ realizations. These are then projected onto a small number modes that capture all of the cosmologically relevant variation, enabling a more accurate marginalization over the redshift distribution in cosmological inference. Note that for weak-lensing source galaxies, there is an additional step of correction for image blending, applied after the mode projection. y6-sompz-metadetect and y6-sompz-maglim contain longer descriptions of the full redshift pipeline.
• Figure 2: Illustration of the clustering and magnification for 8 sawtooth distributions cross-correlated with 8 rectangle reference bins, both with $\Delta z=0.1$. Clustering matrix $A$ and magnification matrices $D$ are then $8\times 8$. The orange values are one order of magnitude smaller than the red, and the blue, two orders of magnitude. Matrix coefficients in white are exactly 0. Please note that $D_{{\rm r}_i j}$ and $D_{j{\rm r}_i}$ are very similar but not exactly equal because for this calculation we have taken similar $\Delta z$ binning but with sawtooth kernels for the unknowns ${\rm u}$ and rectangular (boxcar) kernels for the references ${\rm r}.$
• Figure 3: Redshift distributions of the data (top panel) and cardinal mocks (bottom panel) are shown for Maglim++ (lenses, left panel), Metadetect (sources, middle panel), and BOSS-eBOSS (reference, right panel). Spectroscopic data are presented as a function of spectroscopic redshift. Maglim++ bins are generated with photo-$z$ cuts, and we plot the photo-$z$ histograms of every bin, along with the corresponding SOM estimate of the $n(z)$ for the data. For Metadetect data, only the SOM estimate of the $n(z)$ is shown. The true redshift distributions are provided for all simulated DES samples. Simulated data do not reproduce properly the $z>1.5$ distribution of the data.
• Figure 4: Impact of systematics on WZ for the Cardinal-simulated Maglim++ samples. Left: redshift distributions inferred from the no-systematics mock catalog, WZ estimate (points) compared to the true $n(z)$ (solid lines). Middle-left: Same as left but with the all-systematics mock catalog that uses only information available in the real data. Middle-right: Corresponding systematic function $w/\hat{w}$, for the no-systematic analysis, consistent with no deviation from a normalization constant. Right: Systematic function $w(z)/\hat{w}(z)$ in the presence of systematics, where deviations from unity $S_{{\rm ur}_i}$ are fitted using a Legendre polynomial basis (black lines). The gray lines plot some realizations of $S_{{\rm ur}_i}$ from the derived prior on its $s_{\rm uk}$ coefficients.
• Figure 5: Impact of systematics on WZ for the Cardinal-simulated Metadetect samples. Left: redshift distributions inferred from the no-systematics mock catalog, WZ estimate (points) compared to the true $n(z)$ (solid lines). Middle-left: Same as left but with the all-systematics mock catalog that uses only information available in the real data. Middle: Corresponding systematic function $w/\hat{w}$, for the no-systematic analysis, consistent with no deviation from a normalization constant. Middle right and right: Systematic function $w(z)/\hat{w}(z)$ in the presence of systematics, where deviations from unity $S_{{\rm ur}_i}$ are fitted using a Legendre polynomial basis (black lines). The gray lines plot some realizations of $S_{{\rm ur}_i}$ from the derived prior on its $s_{\rm uk}$ coefficients.