Clustering redshift distribution calibration of weak lensing surveys using the DESI-DR1 spectroscopic dataset

TL;DR

This study demonstrates clustering-based redshift (clustering-$z$) calibration of weak-lensing source distributions by cross-correlating DESI-DR1 spectroscopic samples (BGS, LRG, ELG) with DES, KiDS, and HSC imaging data. By explicitly modelling magnification biases and marginalising over source-bias evolution using Buzzard mock catalogues, the authors validate that the clustering-$z$ signal reliably recovers the bias-weighted redshift distribution $b_u(z_r)p_u(z_r)$, which agrees with self-organising map calibrations within uncertainties across surveys and tomographic bins. Applying the method to DES-Y3, KiDS-1000, HSC-Y1, and HSC-Y3, they find magnification effects become non-negligible for $z_r\,\gtrsim\,1$, particularly for deep ELG-based references, and they show consistency with fiducial redshift distributions while accounting for magnification and source-bias evolution. The work provides a robust, independent redshift calibration pathway for current and future Stage-III/IV lensing surveys and informs joint $3\times2$-pt analyses for DESI-DR2 and beyond, with implications for LSST and Euclid.

Abstract

We estimate the source redshift distribution of current weak lensing surveys by applying the clustering-based redshift calibration technique, using the galaxy redshift sample provided by the Dark Energy Spectroscopic Instrument Data Release 1 (DESI-DR1). We cross-correlate the Bright Galaxy Survey (BGS), Luminous Red Galaxies (LRGs) and Emission Line Galaxies (ELGs) from DESI, within the redshift range $0.1 < z < 1.6$, with overlapping tomographic source samples from the Dark Energy Survey (DES), Kilo-Degree Survey (KiDS), and Hyper Suprime-Cam (HSC) survey. Using realistic mock catalogues, we test the stability of the clustering-redshift signal to fitting scale, reference-sample choice, and the evolution of source galaxy bias, and we explicitly model and marginalise over magnification contributions, which become non-negligible at $z \gtrsim 1$ due to the depth of the DESI ELG sample. We then compare the resulting bias-weighted redshift distributions to those calibrated using self-organising map (SOM) techniques, finding agreement within uncertainties for all surveys and tomographic bins. Our results demonstrate that clustering redshifts enabled by DESI's unprecedented spectroscopic sample provides a robust, complementary, and independent constraint capable of reducing one of the dominant systematic uncertainties in weak lensing cosmology.

Figures (10)

• Figure 1: Angular auto-correlation function $w_{rr}(\theta)$ measurements for the DESI-DR1 spectroscopic sample, shown in representative redshift bins corresponding to the three tracer populations: BGS (top row), LRG (middle row), and ELG (bottom row). The top panel shows BGS at low redshift, with bins centred at $\bar{z} = 0.125,0.275,0.375$; the middle panel shows LRGs at intermediate redshift, at $\bar{z} = 0.525,0.825,0.925$; and the bottom panel shows ELGs at high redshift, at $\bar{z} = 1.225,1.425,1.575$. The points show the measurements with jackknife-derived errors; the solid line indicates the best-fitting model $A_{rr}\,w_m(\theta)$.
• Figure 2: Angular cross-correlation function $w_{ur}(\theta)$ measurements between DES-Y3 source galaxies and the DESI spectroscopic reference sample. The rows show the first three DES-Y3 tomographic source bins, and the columns show tracer populations at their middle spectroscopic bin: BGS ($\bar{z} = 0.275$), LRG ($\bar{z} = 0.725$), and ELG ($\bar{z} = 1.325$). The points are measurements with jackknife errors; the black line is the best-fitting model $A_{ur}w_m + p\,w^{\rm mag}_{ru} + q\,w^{\rm mag}_{ur}$.
• Figure 3: Component decomposition of the angular cross-correlation $w_{ur}(\theta)$ between DES-Y3 source galaxies and the DESI spectroscopic reference sample. The rows corresponds to the first three DES-Y3 tomographic bins. Within each row, the three columns show representative spectroscopic bins from the three DESI tracer regimes: BGS at $\bar{z} = 0.325$, LRG at $\bar{z} = 0.725$, and ELG at $\bar{z} = 1.475$. The markers show the measured correlations with jackknife uncertainties. The curves show the best-fit clustering term $A_{ur} w_{m}(\theta)$ (the orange lines), the magnification contributions $p\, w_{ru}^{\mathrm{mag}}(\theta)$ (the green lines) and $q\, w_{ur}^{\mathrm{mag}}(\theta)$ (the red lines), and their sum (the black lines).
• Figure 4: The evolution of the source bias $b_u(z_r)$ across surveys, as determined from the Buzzard mock catalogues for each imaging survey. The blue curve corresponds to DES-Y3, the orange curve to KiDS-1000, and the green curve to HSC-Y1. For each survey, the solid line represents the average over the ten mock regions, and the shaded band indicates the region-to-region scatter.
• Figure 5: Clustering-$z$ validation using mock catalogues for DESI and DES-Y3. The panels show the recovery of the source redshift distribution in the four DES-Y3 tomographic bins. The solid black line shows the true bias-weighted redshift distribution $b_u(z_r)\,p_u(z_r)$ from the simulation, while the dashed black line shows the true underlying source distribution $p_u(z_r)$ alone. The red points show the raw clustering-based estimate of $b_u(z_r)\,p_u(z_r)$, measured from $w_{ur}(\theta)$ in discrete redshift slices. The shaded coloured band shows the final clustering-$z$ estimate after smoothing, together with the propagated uncertainty from jackknife resampling and after marginalization over the magnification nuisance parameters. The reasonable agreement between the points and the solid black curve demonstrates that the method accurately recovers the source bias–weighted distribution when applied to realistic mock data.