KiDS-Legacy: Redshift distributions and their calibration

TL;DR

The KiDS-Legacy study tackles the critical challenge of calibrating the mean redshift distributions for cosmic shear analyses by employing two complementary approaches: a colour-based SOM method and clustering redshifts, validated with two sophisticated simulations (SKiLLS and MICE2). It introduces tomographic-SOMs per bin, gold weighting, and prior-volume corrections to tightly constrain N(z) biases, achieving percent-level precision in the mean redshifts. The work demonstrates strong cross-validation between methods and simulations, showing residual biases at the 0.01 level and outlining priors for cosmological inference that approach Euclid-like requirements. The results establish a robust, redundant calibration framework and delineate clear paths for further reducing systematic floors in future stage-IV surveys.

Abstract

We present the redshift calibration methodology and bias estimates for the cosmic shear analysis of the fifth and final data release (DR5) of the Kilo-Degree Survey (KiDS). KiDS-DR5 includes a greatly expanded compilation of calibrating spectra, drawn from $27$ square degrees of dedicated optical and near-IR imaging taken over deep spectroscopic fields. The redshift distribution calibration leverages a range of new methods and updated simulations to produce the most precise $N(z)$ bias estimates used by KiDS to date. Improvements to our colour-based redshift distribution measurement method (SOM) mean that we are able to use many more sources per tomographic bin for our cosmological analyses, and better estimate the representation of our source sample given the available spec-$z$. We validate our colour-based redshift distribution estimates with spectroscopic cross-correlations (CC). We find that improvements to our cross-correlation redshift distribution measurement methods mean that redshift distribution biases estimated between the SOM and CC methods are fully consistent on simulations, and the data calibration is consistent to better than $2σ$ in all tomographic bins.

Figures (18)

• Figure 1: Redshift distribution of the calibration data used for KiDS-Legacy. The top panel displays the full KiDZ data in grey and the proportion of it that enters each tomographic bin after calibrating the fiducial SOM, shown as a stacked histogram. The bin edges are indicated by the vertical dashed lines. The bottom panel shows the spectroscopic surveys used as calibration samples for the clustering redshift measurements (also stacked).
• Figure 2: Footprint of the spectroscopic surveys overlapping KiDS used for the clustering redshift measurements. VIPERS is exclusive to the KiDZ fields, which are not shown here.
• Figure 3: Comparison between gold-class and gold-weight definitions. Here, a SOM trained on tomographic bin one in our SKiLLS simulation is coloured by the true mean redshift of each cell ( left), the gold-class definition of each cell under a single realisation ( centre), and the gold weight of each cell after ten realisations. In the gold-weight panel, the cells, which are assigned a (highly stochastic) zero gold class in our single realisation, are highlighted with an orange border. These cells are assigned a wide range of final gold-weights, highlighting the stochasticity of the gold-class definition and the superiority of the gold-weights. In each colour bar, the PDF of cell values is shown.
• Figure 4: Distributions of gold weight per tomographic bin for our fiducial SKiLLS simulations. Individual lines show the scatter in the gold-weight PDFs under different realisations of our spectroscopic calibration samples. The tomographic bins show qualitatively similar behaviour: many sources are consistently classed as gold under all realisations of the SOM ($w_{\rm gold}=1$), and very few sources are consistently classed as not-gold under all realisations ($w_{\rm gold}=0$).
• Figure 5: Model parameters and the resulting analytic $N(z)$ for samples defined as magnitude-limited (in the $r$ band) from our noiseless SURFS+Shark light cone. The left and centre panels show the free parameters from Eq. \ref{['eq:analyticnz']}, as a function of the $r$-band magnitude limit, including polynomial fits. The right panel shows the analytically estimated $N(z)$ for each of the models parameters in the other two panels.