Z-Sequence: Photometric redshift predictions for galaxy clusters with sequential random k-nearest neighbours

Abstract

We introduce Z-Sequence, a novel empirical model that utilises photometric measurements of observed galaxies within a specified search radius to estimate the photometric redshift of galaxy clusters. Z-Sequence itself is composed of a machine learning ensemble based on the k-nearest neighbours algorithm. We implement an automated feature selection strategy that iteratively determines appropriate combinations of filters and colours to minimise photometric redshift prediction error. We intend for Z-Sequence to be a standalone technique but it can be combined with cluster finders that do not intrinsically predict redshift, such as our own DEEP-CEE. In this proof-of-concept study we train, fine-tune and test Z-Sequence on publicly available cluster catalogues derived from the Sloan Digital Sky Survey. We determine the photometric redshift prediction error of Z-Sequence via the median value of $|\Delta z|/(1+z)$ (across a photometric redshift range of $0.05\le \text{z}\le 0.6$) to be $\sim 0.01$ when applying a small search radius. The photometric redshift prediction error for test samples increases by 30-50 per cent when the search radius is enlarged, likely due to line-of-sight interloping galaxies. Eventually, we aim to apply Z-Sequence to upcoming imaging surveys such as the Legacy Survey of Space and Time to provide photometric redshift estimates for large samples of as yet undiscovered and distant clusters.

Accepted to MNRAS on 16th March 2021; pp. 1-21. Supplementary material is included; pp. 22-164

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