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

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.

Version accepted for publication in PRD after minor changes. Follow-up paper on applications: arXiv:2010.13958

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• Pulsar-timing measurement of the circular polarization of the stochastic gravitational-wave background
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• Dissecting the Stochastic Gravitational Wave Background with Astrometry
• Anisotropy of phase transition gravitational wave and its implication for primordial seeds of the Universe
• The MeerKAT Pulsar Timing Array: Maps of the gravitational-wave sky with the 4.5 year data release
• Timing-residual power spectrum of a polarized stochastic gravitational-wave background in pulsar-timing-array observation
• How to Detect an Astrophysical Nanohertz Gravitational-Wave Background
• Measuring kinematic anisotropies with pulsar timing arrays
• Harmonic analysis for pulsar timing arrays
• Probing Parity Violation in the Stochastic Gravitational Wave Background with Astrometry
• Separating deterministic and stochastic gravitational wave signals in realistic pulsar timing array datasets
• A novel probe of graviton dispersion relations at nano-Hertz frequencies
• Astrometry meets Pulsar Timing Arrays: Synergies for Gravitational Wave Detection
• Mitigating cosmic variance in the Hellings-Downs curve: a Cosmic Microwave Background analogy
• Exploring realistic nanohertz gravitational-wave backgrounds
• Cosmology with the SZ spectrum: measuring the Universe's temperature with galaxy clusters
• Observation of polarized stochastic gravitational-wave background in pulsar-timing-array experiments