Characterising gravitational wave stochastic background anisotropy with Pulsar Timing Arrays

TL;DR

This paper extends Pulsar Timing Array analysis methods to characterize anisotropic gravitational wave backgrounds by decomposing angular power into multipoles and introducing generalized overlap reduction functions.

Contribution

It generalizes the standard isotropic background analysis to include anisotropy, enabling detailed characterization of gravitational wave power distribution on the sky.

Findings

Derived generalized overlap reduction functions for anisotropic backgrounds.

Provided estimates of anisotropy levels from super-massive black hole binaries.

Demonstrated the method's applicability to Pulsar Timing Array configurations.

Abstract

Detecting a stochastic gravitational wave background, particularly radiation from individually unresolvable super-massive black hole binary systems, is one of the primary targets for Pulsar Timing Arrays. Increasingly more stringent upper limits are being set on these signals under the assumption that the background radiation is isotropic. However, some level of anisotropy may be present and the characterisation of the power at different angular scales carries important information. We show that the standard analysis for isotropic backgrounds can be generalised in a conceptually straightforward way to the case of generic anisotropic background radiation by decomposing the angular distribution of the gravitational wave power on the sky into multipole moments. We introduce the concept of generalised overlap reduction functions which characterise the effect of the anisotropy multipoles on the correlation of the timing residuals from the pulsars timed by a Pulsar Timing Array. In a search for a signal characterised by a generic anisotropy, the generalised overlap reduction functions play the role of the so-called Hellings and Downs curve used for isotropic radiation. We compute the generalised overlap reduction functions for a generic level of anisotropy and Pulsar Timing Array configuration. We also provide an order of magnitude estimate of the level of anisotropy that can be expected in the background generated by super-massive black hole binary systems.