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

TL;DR

This paper introduces a novel, fully data-driven method for estimating galaxy redshift distributions and bias parameters using correlation functions without relying on spectroscopic reference samples, enhancing accuracy and self-consistency.

Contribution

The method uniquely estimates redshift distributions and bias parameters solely from correlation data, avoiding the need for spectroscopic reference samples, and incorporates redshift uncertainties into cosmological analyses.

Findings

Successfully recovers unbiased redshift distribution parameters

Achieves an order of magnitude improvement with CMB and lensing cross-correlations

Meets accuracy requirements for current and future galaxy surveys

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.