The DECADE cosmic shear project II: photometric redshift calibration of the source galaxy sample

TL;DR

This paper tackles the challenge of calibrating the redshift distributions for the DECADE weak-lensing source sample by employing Self-Organizing Maps Photo-z (SOMPZ) with a deep-field transfer function learned through Balrog injections, and cross-validating with clustering redshifts (WZ). It introduces a four-bin tomographic framework and provides a comprehensive uncertainty budget that includes sample variance, zeropoint offsets, and redshift biases, finding $\sigma_{\langle z \rangle} \approx 0.01$ for the mean redshifts. The study demonstrates consistency between SOMPZ and WZ across redshift, reinforcing the reliability of the $n(z)$ used in cosmological analyses, and presents a forward-modeling approach to combine both sources of redshift information. The work also establishes a data-driven transfer function for DECADE, utilizes a robust Balrog-based validation, and offers a scalable methodology applicable to future surveys with heterogeneous imaging depths.

Abstract

We present the photometric redshift characterization and calibration for the Dark Energy Camera All Data Everywhere (DECADE) weak lensing dataset: a catalog of 107 million galaxies observed by the Dark Energy Camera (DECam) in the northern Galactic cap. The redshifts are estimated from a combination of wide-field photometry, deep-field photometry with associated redshift estimates, and a transfer function between the wide field and deep field that is estimated using a source injection catalog. We construct four tomographic bins for the galaxy catalog, and estimate the redshift distribution, $n(z)$, within each one using the Self-organizing Map Photo-Z (SOMPZ) methodology. Our estimates include the contributions from sample variance, zeropoint calibration uncertainties, and redshift biases, as quantified for the deep-field dataset. The total uncertainties on the mean redshifts are $σ_{\langle z \rangle} \approx 0.01$. The SOMPZ estimates are then compared to those from the clustering redshift method, obtained by cross-correlating our source galaxies with galaxies in spectroscopic surveys, and are shown to be consistent with each other.

Figures (11)

• Figure 1: The weighted (top) and raw (bottom) counts of galaxies in the redshift sample, split by the source of their redshift information. The numbers on the right are the percentage contribution of a given sample to the total redshift sample. Cosmos and Paus are photometric estimates (from 30 bands, and 66 bands, respectively) while the rest are spectroscopic samples. The distributions were smoothed with a narrow Gaussian kernel for visualization purposes. Our fiducial redshift estimates (which use weights) are primarily informed by the spectroscopic samples and the Paus plus Cosmos sample.
• Figure 2: The distribution of the reference sample, across the sky (top) and across redshift (bottom). The reference sample has an overlap of around $3,\!000 \deg^2$ with the source-galaxy sample. We show the DECADE footprint in gray for comparison. The inhomogeneity in number counts of the reference sample is due to the different samples (denoted in legend of bottom panel) spanning different areas on the sky. The number counts in the bottom panel have been smoothed by a narrow Gaussian kernel for visualization purposes.
• Figure 3: The properties of the deep SOM, which has $48\times48$ cells. We show the number counts of galaxies per cell, the average $i$-band magnitude, the average colors, and the average redshift per cell. There is clear spatial structure in the 2D maps of different properties, as is expected from using a SOM to classify galaxy photometry into phenotypes.
• Figure 4: The properties of galaxies in the wide SOM, which has $32\times32$ cells. We show the number counts of galaxies per cell, the average $i$-band magnitude, the average colors, the average redshift per cell, the dispersion in the redshift per cell, and the tomographic bin assignment per wide cell. We also show one version of the average redshift estimated using only spectroscopic redshifts. Both versions of $\langle z\rangle$ are obtained by computing the mean redshift of Balrog sample galaxies in a given $\hat{c}$ cell. The cells with faint magnitudes are frequently assigned to tomographic bins 3 and 4.
• Figure 5: The median redshift bias as a function of magnitude for the two photometric redshift samples used in this work. The baseline sample is a curated list of high-quality spectroscopic redshifts, consisting of Zcosmos and C3R2. This follows the choices in Sanchez:2023:highzY3. The bias of Paus plus Cosmos is within $0.001(1 + z)$, while that of Cosmos is slightly higher for the brightest/faintest objects. The errors are estimated through a simple bootstrap and therefore only account for shot noise and not sample variance.