Statistical effects of the observer's peculiar velocity on source number counts

TL;DR

This paper investigates how the observer's peculiar velocity affects source number count correlations, proposing an unbiased estimator to measure the velocity and assessing its potential for precise future measurements.

Contribution

It introduces a new unbiased estimator for the kinetic dipole amplitude in source counts and evaluates its effectiveness for upcoming experiments.

Findings

Estimator can achieve better than 5% velocity constraints.

Peculiar velocity significantly impacts source count correlations.

Potential for improved measurements of observer velocity in future surveys.

Abstract

The velocity of the Sun with respect to the cosmic microwave background (CMB) can be extracted from the CMB dipole, provided its intrinsic dipole is assumed to be small in comparison. This interpretation is consistent, within fairly large error bars, with the measurement of the correlations between neighboring CMB multipoles induced by the velocity of the observer, which effectively breaks isotropy. In contrast, the source number count dipole was reported to privilege a velocity of the observer with an amplitude which is about twice as large as the one extracted from the entirely kinematic interpretation of the CMB dipole, with error bars which indicate a more and more significant tension. In this work, we study the effect of the peculiar velocity of the observer on correlations of nearby multipoles in the source number counts. We provide an unbiased estimator for the kinetic dipole amplitude, which is proportional to the peculiar velocity of the observer and we compute the expected signal to noise ratio. Near future experiments can achieve better than 5$\%$ constraints on the velocity of the Sun with our estimator.