Self-consistent redshift estimation using correlation functions without a spectroscopic reference sample

Abstract

We present a new method to estimate redshift distributions and galaxy-dark matter bias parameters using correlation functions in a fully data driven and self-consistent manner. Unlike other machine learning, template, or correlation redshift methods, this approach does not require a reference sample with known redshifts. By measuring the projected cross- and auto- correlations of different galaxy sub-samples, e.g., as chosen by simple cells in color-magnitude space, we are able to estimate the galaxy-dark matter bias model parameters, and the shape of the redshift distributions of each sub-sample. This method fully marginalises over a flexible parameterisation of the redshift distribution and galaxy-dark matter bias parameters of sub-samples of galaxies, and thus provides a general Bayesian framework to incorporate redshift uncertainty into the cosmological analysis in a data-driven, consistent, and reproducible manner. This result is improved by an order of magnitude by including cross-correlations with the CMB and with galaxy-galaxy lensing. We showcase how this method could be applied to real galaxies. By using idealised data vectors, in which all galaxy-dark matter model parameters and redshift distributions are known, this method is demonstrated to recover unbiased estimates on important quantities, such as the offset ${\Delta }_z$ between the mean of the true and estimated redshift distribution and the 68\% and 95\% and 99.5\% widths of the redshift distribution to an accuracy required by current and future surveys.

20pages, 11 figures, text revised for clarification, version accepted by journal, conclusions unchanged

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Cited by in corpus (6)

• Weak Lensing Tomographic Redshift Distribution Inference for the Hyper Suprime-Cam Subaru Strategic Program three-year shape catalogue
• Galaxy-Galaxy Lensing in HSC: Validation Tests and the Impact of Heterogeneous Spectroscopic Training Sets
• Self-calibration and robust propagation of photometric redshift distribution uncertainties in weak gravitational lensing
• A Composite Likelihood Approach for Inference under Photometric Redshift Uncertainty
• Estimating redshift distributions using Hierarchical Logistic Gaussian processes
• Effects of Redshift Uncertainty on Cross-Correlations of CMB Lensing and Galaxy Surveys