Characterising gravitational wave stochastic background anisotropy with Pulsar Timing Arrays

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.

12 pages plus 5 page Appendix. Accepted to PRD

References in corpus (13)

• The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays
• The North American Nanohertz Observatory for Gravitational Waves
• Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects
• Gravitational waves from resolvable massive black hole binary systems and observations with Pulsar Timing Arrays
• The stochastic background: scaling laws and time to detection for pulsar timing arrays
• On measuring the gravitational-wave background using Pulsar Timing Arrays
• Measuring the parameters of massive black hole binary systems with Pulsar Timing Array observations of gravitational waves
• Black Hole Growth in Hierarchical Galaxy Formation
• Searching For Anisotropic Gravitational-wave Backgrounds Using Pulsar Timing Arrays
• Detecting a Stochastic Gravitational-Wave Background: The Overlap Reduction Function
• Constraint on the early Universe by relic gravitational waves: From pulsar timing observations
• The Most Massive Black Holes in the Universe: Effects of Mergers in Massive Galaxy Clusters
• Accelerating pulsar timing data analysis

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