Insights into searches for anisotropies in the nanohertz gravitational-wave background

Abstract

Within the next several years pulsar timing arrays (PTAs) are positioned to detect the stochastic gravitational-wave background (GWB) likely produced by the collection of inspiralling super-massive black holes binaries, and potentially constrain some exotic physics. So far most of the pulsar timing data analysis has focused on the monopole of the GWB, assuming it is perfectly isotropic. The natural next step is to search for anisotropies in the GWB. In this paper, we use the recently developed PTA Fisher matrix to gain insights into optimal search strategies for GWB anisotropies. For concreteness, we apply our results to EPTA data, using realistic noise characteristics of its pulsars. We project the detectability of a GWB whose angular dependence is assumed to be a linear combination of predetermined maps, such as spherical harmonics or coarse pixels. We find that the GWB monopole is always statistically correlated with these maps, implying a loss of sensitivity to the monopole when searching simultaneously for anisotropies. We then derive the angular distributions of the GWB intensity to which a PTA is most sensitive, and illustrate how one may use these "principal maps" to approximately reconstruct the angular dependence of the GWB. Since the principal maps are neither perfectly anisotropic nor uncorrelated with the monopole, we also develop a frequentist criterion to specifically search for anisotropies in the GWB without any prior knowledge about their angular distribution. Lastly, we show how to recover existing EPTA results with our Fisher formalism, and clarify their meaning. The tools presented here will be valuable in guiding and optimizing the computationally demanding analyses of pulsar timing data.

21 pages, 14 figures. Version accepted for publication in PRD after minor changes

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• Imprints of Supermassive Black Hole Evolution on the Spectral and Spatial Anisotropy of Nano-Hertz Stochastic Gravitational-Wave Background
• 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
• Unraveling Cosmological Anisotropies within Stochastic Gravitational Wave Backgrounds
• Timing-residual power spectrum of a polarized stochastic gravitational-wave background in pulsar-timing-array observation
• Measuring kinematic anisotropies with pulsar timing arrays
• Probing Parity Violation in the Stochastic Gravitational Wave Background with Astrometry
• Parameter-Estimation Biases for Eccentric Supermassive Binary Black Holes in Pulsar Timing Arrays: Biases Caused by Ignored Pulsar Terms
• A novel probe of graviton dispersion relations at nano-Hertz frequencies
• Seeing the gravitational wave universe
• Astrometry meets Pulsar Timing Arrays: Synergies for Gravitational Wave Detection
• Mitigating cosmic variance in the Hellings-Downs curve: a Cosmic Microwave Background analogy
• Searching for Anisotropy in the Gravitational Wave Background Using the Parkes Pulsar Timing Array
• Observation of polarized stochastic gravitational-wave background in pulsar-timing-array experiments