A Unified Photometric Redshift Calibration for Weak Lensing Surveys using the Dark Energy Spectroscopic Instrument

TL;DR

This paper introduces a unified photometric redshift calibration framework for weak lensing surveys by leveraging high-quality DESI redshifts and neural-network-based importance weights to derive accurate redshift distributions $n(z)$ for DES, HSC, and KiDS. It combines a direct calibration approach with robust incompleteness and lensing weight corrections, producing $σ_{\bar z}$ on the order of $0.01$ and validating results against existing fiducial calibrations. The analysis finds strong agreement with DES Y3 and HSC Y1, with notable KiDS-1000 differences traced to COSMOS-field photometric properties and SOM-related biases; these do not substantially alter cosmic-structure growth inferences. The work demonstrates DESI's potential to calibrate large fractions of weak lensing samples and discusses implications for future stage-IV surveys, including the Rubin Observatory, while highlighting the importance of deep-field coverage and footprint alignment. Overall, the method provides a cross-check against previous calibrations and offers a scalable path toward precise redshift calibration in upcoming cosmology experiments, addressing current tensions in cosmological parameters.

Abstract

The effective redshift distribution $n(z)$ of galaxies is a critical component in the study of weak gravitational lensing. Here, we introduce a new method for determining $n(z)$ for weak lensing surveys based on high-quality redshifts and neural network-based importance weights. Additionally, we present the first unified photometric redshift calibration of the three leading stage-III weak lensing surveys, the Dark Energy Survey (DES), the Hyper Suprime-Cam (HSC) survey and the Kilo-Degree Survey (KiDS), with state-of-the-art spectroscopic data from the Dark Energy Spectroscopic Instrument (DESI). We verify our method using a new, data-driven approach and obtain $n(z)$ constraints with statistical uncertainties of order $σ_{\bar z} \sim 0.01$ and smaller. Our analysis is largely independent of previous photometric redshift calibrations and, thus, provides an important cross-check in light of recent cosmological tensions. Overall, we find excellent agreement with previously published results on the DES Y3 and HSC Y1 data sets while there are some differences on the mean redshift with respect to the previously published KiDS-1000 results. We attribute the latter to mismatches in photometric noise properties in the COSMOS field compared to the wider KiDS SOM-gold catalog. At the same time, the new $n(z)$ estimates for KiDS do not significantly change estimates of cosmic structure growth from cosmic shear. Finally, we discuss how our method can be applied to future weak lensing calibrations with DESI data.

Figures (9)

• Figure 1: Approximate footprints of the different data sets used in this work in the COSMOS area.
• Figure 2: Properties of the calibration sample. From left to right, we show distributions in the COSMOS2020 redshifts $z_\mathrm{C20}$, the $i$ magnitude, the $g-z$ colors, and fiber probability $p_\mathrm{f}$ (right). In this figure, we limit our analysis to targets with $i < 24.5$. In all cases, we show the distribution of the COSMOS2020 parent sample as the blue line and the unweighted calibration sample as a red line. Finally, the colored histogram represents the weighted calibration sample and is divided in different target classes. These include targets with successful redshifts that are part of the BGS, LRG, ELG, and QSO samples (DESI-LSS), targets with DESI redshifts from other programs (DESI-Other), targets that received fibers from DESI but did not received a high-confidence redshift (DESI-Fail), and objects never targeted by DESI (COSMOS2020). Note that the $y$-axes of the middle and right histograms are partially logarithmic, i.e., beyond $0.1$ and $1.0$ for the middle and right histograms, respectively.
• Figure 3: Visual check of the accuracy of our machine learning model of the fiber fraction $p_\mathrm{f}$. We show galaxies in the DES (top row) and KiDS (bottom row) COSMOS sample projected onto the DES and KiDS SOM, respectively. The left panel shows the fraction of galaxies in each SOM cell observed by DESI. The middle panel shows the predicted fraction in each cell, i.e., the mean predicted fiber fraction of all galaxies in each cell. Finally, the right panel shows the difference between the left and middle panel. Overall, our machine learning model for $p_\mathrm{f}$ reproduces the trends as a function of DES and KiDS photometry seen in the data. Grey cells indicate SOM cells not present in the final weak lensing catalogs.
• Figure 4: Impact of the choice of $p_\mathrm{f, min}$ on the fraction of the weak lensing sample calibrated with DESI redshifts and shot noise. Each column corresponds to one of the three weak lensing samples: DES, HSC, and KiDS. Upper panels show the weighted fraction of galaxies in the calibration sample with successful redshifts from DESI. Note that galaxies observed with DESI but without a successful redshift are counted as not having a DESI redshift, i.e., they will drive $f_\mathrm{DESI}$ down. The lower panel shows the inverse square root of the effective sample size, a measure of the shot noise uncertainty in the sample. The grey vertical line in the upper panels indicate our default choice, $p_\mathrm{f, min} = 0.10$.
• Figure 5: Verification of the importance weighting method with COSMOS2020 photometric redshifts. We show the difference in the weighted-average COSMOS2020 redshift as a function of $p_\mathrm{f, min}$ with respect to $p_\mathrm{f, min} = 100 \%$. As disussed in the text, $p_\mathrm{f, min} = 100 \%$ corresponds to an unweighted sample of all galaxies in the COSMOS2020 catalog. Each column corresponds to one of the three weak lensing samples: DES, HSC, and KiDS. Upper panels show the absolute difference whereas lower panels shows an estimate of the significance of the difference after accounting for shot noise.