Fisher formalism for anisotropic gravitational-wave background searches with pulsar timing arrays

TL;DR

This paper develops a Fisher formalism to forecast and optimize anisotropic gravitational-wave background searches with pulsar timing arrays, enhancing the potential to extract astrophysical and cosmological information.

Contribution

It introduces a realistic Fisher formalism for anisotropic SGWB searches with PTAs, accommodating realistic properties and enabling accurate forecasts.

Findings

Formalism can accommodate realistic PTA properties

Allows simple and accurate forecasts for anisotropic SGWB searches

Illustrated with an idealized PTA model

Abstract

Pulsar timing arrays (PTAs) are currently the only experiments directly sensitive to gravitational waves with decade-long periods. Within the next five to ten years, PTAs are expected to detect the stochastic gravitational-wave background (SGWB) collectively sourced by inspiralling supermassive black hole binaries. It is expected that this background is mostly isotropic, and current searches focus on the monopole part of the SGWB. Looking ahead, anisotropies in the SGWB may provide a trove of additional information both on known and unknown astrophysical and cosmological sources. In this paper, we build a simple yet realistic Fisher formalism for anisotropic SGWB searches with PTAs. Our formalism is able to accommodate realistic properties of PTAs, and allows simple and accurate forecasts. We illustrate our approach with an idealized PTA consisting of identical, isotropically distributed pulsars. In a companion paper, we apply our formalism to current PTAs and show that it can be a powerful tool to guide and optimize real data analysis.