KiDS-1000 catalogue: Redshift distributions and their calibration

TL;DR

This paper addresses the need for precise redshift distributions in KiDS-1000 weak lensing analyses. It implements a colour-based redshift calibration using a self-organising map (SOM) to map high-dimensional photometric space to a robust, gold subset, achieving mean redshift biases around 0.01 with ~0.01–0.02 uncertainties when complemented by clustering redshifts. An independent clustering-z approach validates the SOM results and provides an alternative n(z) calibration that remains competitive, especially when including SOM uncertainties. The study demonstrates that combining SOM with CZ yields robust, high-fidelity redshift distributions for five tomographic bins, enabling KiDS-1000 cosmology to exploit its statistical power while controlling systematic errors; the methodology also outlines pathways to meet stage-IV redshift calibration demands with future spectroscopic and modelling advances.

Abstract

We present redshift distribution estimates of galaxies selected from the fourth data release of the Kilo-Degree Survey over an area of $\sim1000$ deg$^2$ (KiDS-1000). These redshift distributions represent one of the crucial ingredients for weak gravitational lensing measurements with the KiDS-1000 data. The primary estimate is based on deep spectroscopic reference catalogues that are re-weighted with the help of a self-organising map (SOM) to closely resemble the KiDS-1000 sources, split into five tomographic redshift bins in the photometric redshift range $0.1<z_\mathrm{B}\le1.2$. Sources are selected such that they only occupy that volume of nine-dimensional magnitude-space that is also covered by the reference samples (`gold' selection). Residual biases in the mean redshifts determined from this calibration are estimated from mock catalogues to be $\lesssim0.01$ for all five bins with uncertainties of $\sim 0.01$. This primary SOM estimate of the KiDS-1000 redshift distributions is complemented with an independent clustering redshift approach. After validation of the clustering-$z$ on the same mock catalogues and a careful assessment of systematic errors, we find no significant bias of the SOM redshift distributions with respect to the clustering-$z$ measurements. The SOM redshift distributions re-calibrated by the clustering-$z$ represent an alternative calibration of the redshift distributions with only slightly larger uncertainties in the mean redshifts of $\sim 0.01-0.02$ to be used in KiDS-1000 cosmological weak lensing analyses. As this includes the SOM uncertainty, clustering-$z$ are shown to be fully competitive on KiDS-1000 data.

Figures (7)

• Figure 1: Redshift distributions for the five tomographic redshift bins used in the KiDS-1000 cosmological analyses estimated with the SOM method of wright/etal:2019. The grey vertical bands indicate the photo-$z$ cuts defining the bins. Solid red lines show the estimate from the KiDS-1000 data whereas the dotted blue lines and their confidence intervals represent the average and standard deviation of all lines-of-sight of the MICE mocks. The dashed orange lines show one representative (in terms of its mean redshifts) line-of-sight (number 39 in our list) that is used in Sect. \ref{['sec:CZ_res_MICE']}.
• Figure 2: Correlation matrix of the uncertainties of the $\Delta \langle z\rangle^{\rm SOM}_i$ from the SOM analysis of the MICE mocks reported in column 2 of Table \ref{['tab:results']}.
• Figure 3: Correlation matrix of CZ measurements from the MICE mocks using an idealised reference sample with high number density. There are six blocks in a line, each $30$ pixels wide corresponding to 30 redshift bins in the range $0<z<1.4$ (with the first and last redshift bin containing no galaxies due to the redshift limits of MICE and shown white here). The first five blocks correspond to the five tomographic bins and the sixth block to the combined sample. The latter one is obviously correlated with all other samples as it shares target galaxies with the other bins.
• Figure 4: Clustering-$z$ measurements on the MICE mocks with the fiducial setup, i.e. using the wide fields and scales of $100\,{\rm kpc}<r<1\,{\rm Mpc}$ for the first three tomographic bins (top row) and the deep fields and scales of $30\,{\rm kpc}<r<300\,{\rm kpc}$ for the upper two tomographic bins (bottom row). The original SOM redshift distributions from a representative line-of-sight are shown in solid red and the best-fit model is shown in dashed blue. The true redshift distributions are shown in dotted orange for comparison.
• Figure 5: Same as Fig. \ref{['fig:res_MICE']} but for the KiDS-1000 data.