Determining our peculiar velocity from the aberration in the cosmic microwave background

TL;DR

This paper explores a novel method using scalar measures derived from covariant derivatives of the CMB temperature field to detect aberration effects caused by our solar system's velocity, aiming to distinguish Doppler and intrinsic dipole contributions.

Contribution

It introduces the use of eigenvalues of the Hessian matrix of the CMB temperature field as invariant measures to detect aberration effects at high multipoles, providing an independent velocity determination method.

Findings

Eigenvalues of the Hessian matrix effectively detect aberration distortions.

The method can potentially disentangle Doppler and intrinsic dipole contributions.

Provides a new approach for measuring our peculiar velocity relative to the CMB.

Abstract

The motion of our solar system relative to the CMB rest frame leads to subtle distortions in the observed CMB sky map due to the aberration effect. Usually the corresponding peculiar velocity is determined from the CMB dipole but neglecting intrinsic dipole contributions. Here it is investigated whether certain invariant scalar measures, which are derived from first and second order covariant derivatives on the sphere, can detect the distortions caused by the aberration effect at high multipoles. This would in principle allow to disentangle the Doppler from intrinsic dipole contributions providing an independent method for the determination of our peculiar velocity. It is found that the eigenvalues of the Hessian matrix of the temperature field are well suited for that task.