Redshift tomography of the kinematic matter dipole

TL;DR

This paper develops a formalism to compute the kinematic matter dipole in redshift bins, accounting for redshift selection, measurement uncertainties, and variable cuts, revealing potential significant corrections in cosmological surveys.

Contribution

It introduces a comprehensive method to calculate the matter dipole considering redshift-dependent effects and selection biases, enhancing the analysis of cosmological anisotropies.

Findings

Correction terms can significantly alter the dipole direction.

Redshift measurement uncertainties impact dipole estimates.

Selection cuts can induce additional correction effects.

Abstract

The dipole anisotropy induced by our peculiar motion in the sky distribution of cosmologically distant sources is an important consistency test of the standard FLRW cosmology. In this work, we formalize how to compute the kinematic matter dipole in redshift bins. Apart from the usual terms arising from angular aberration and flux boosting, there is a contribution from the boosting of the redshifts that becomes important when considering a sample selected on observed redshift, leading to non-vanishing correction terms. We discuss examples and provide expressions to incorporate arbitrary redshift selection functions. We also discuss the effect of redshift measurement uncertainties in this context, in particular in upcoming surveys for which we provide estimates of the correction terms. Depending on the shape of a sample's redshift distribution and on the applied redshift cuts, the correction terms can become substantial, even to the degree that the direction of the dipole is reversed. Lastly, we discuss how cuts on variables correlated with observed redshift, such as color, can induce additional correction terms.