Kinematic Anisotropies in PTA Observations: Analytical Toolkit

TL;DR

This paper develops an analytical toolkit to describe kinematic anisotropies in pulsar timing array observations of the gravitational-wave background, improving understanding of anisotropic signals and aiding data analysis.

Contribution

It introduces a novel analytical framework for kinematic anisotropies in PTA data, including new formulas differing from previous work at the quadrupole order.

Findings

Derived analytical expressions for kinematic anisotropies affecting overlap reduction functions.

Provided formulas for auto-correlation functions with both infinite and finite pulsar distances.

Results can be integrated into forecasting and Bayesian analysis pipelines.

Abstract

The reported evidence for an isotropic gravitational-wave background (GWB) from pulsar timing array (PTA) collaborations has motivated searches for extrinsic and intrinsic anisotropies. Kinematic anisotropies may arise as a consequence of a boosted observer moving with respect to the frame in which the GWB appears isotropic. In this work, we present an analytical toolbox to describe the effects of kinematic anisotropies on the overlap reduction function. Our analytical results differ from previous findings at the quadrupole order and are detailed in three appendices. For the first time, we also derive the corresponding auto-correlation using two approaches, taking the pulsar distances to be infinite or finite, respectively. Our formulas can be used in forecasts or Bayesian analysis pipelines.