Note on pulsar timing array correlation functions induced by peculiar velocities

TL;DR

This paper confirms recent findings on how our peculiar velocity affects pulsar timing array correlation functions using harmonic-space calculations, also enabling easier derivation of related correlations.

Contribution

It provides a harmonic-space calculation that verifies previous results and simplifies obtaining ORFs for spin-1 GWs and astrometry correlations.

Findings

Harmonic-space calculation confirms previous results

Simplifies derivation of ORFs for spin-1 GWs

Enables easier computation of astrometry correlations

Abstract

Several papers have recently calculated the contribution to pulsar timing array overlap reduction functions (ORFs) induced by our peculiar velocity with respect to the rest frame of the stochastic gravitational-wave background. Here we show that a harmonic-space calculation confirms the most recent result. We note that, with the harmonic-space calculation, the ORFs for spin-1 GWs and the correlations with astrometry measurements are also easily obtained.