Directional Anisotropic Sensitivity Curves for Pulsar Timing Arrays
Abstract
After two decades of observations, pulsar timing array collaborations have reported strong evidence for a stochastic gravitational wave background, most likely sourced by an inspiraling population of supermassive black hole binaries. Because that population is finite, anisotropy in the background is inevitable, producing hotspots on the sky that track the loudest binaries. Building on the Fisher formalism for anisotropic backgrounds, we recast the directional Fisher information as effective sensitivity curves on the sky, distinguishing the radiometer and full-Fisher estimators, along with a sky-weighted curve that reduces the anisotropic sky to a single spectrum and recovers the standard isotropic curve in the isotropic limit. We implement five sky-decomposition bases: pixel, spherical harmonic, square-root spherical harmonic, radiometer, and principal-map. We demonstrate the framework on an IPTA-like pulsar timing array: characterizing the angular response, analyzing the Fisher structure, recovering injected anisotropic hotspots, and forecasting future-array sensitivity. The framework is released as an extension to the sensitivity software package hasasia.
Versions
Related
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BibTeX
@misc{oliver2026directional,
title = {{Directional Anisotropic Sensitivity Curves for Pulsar Timing Arrays}},
author = {Daniel J. Oliver and Jeffrey S. Hazboun and Martine Maggi and Jeremy G. Baier and Kyle E. Gourlie},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.00250},
eprint = {2608.00250},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00250},
}
RIS
TY - UNPB
TI - Directional Anisotropic Sensitivity Curves for Pulsar Timing Arrays
AU - Daniel J. Oliver
AU - Jeffrey S. Hazboun
AU - Martine Maggi
AU - Jeremy G. Baier
AU - Kyle E. Gourlie
PY - 2026
DA - 2026/08/01
PB - arXiv
DO - 10.48550/arxiv.2608.00250
UR - https://arxiv.org/abs/2608.00250
AB - After two decades of observations, pulsar timing array collaborations have reported strong evidence for a stochastic gravitational wave background, most likely sourced by an inspiraling population of supermassive black hole binaries. Because that population is finite, anisotropy in the background is inevitable, producing hotspots on the sky that track the loudest binaries. Building on the Fisher formalism for anisotropic backgrounds, we recast the directional Fisher information as effective sensitivity curves on the sky, distinguishing the radiometer and full-Fisher estimators, along with a sky-weighted curve that reduces the anisotropic sky to a single spectrum and recovers the standard isotropic curve in the isotropic limit. We implement five sky-decomposition bases: pixel, spherical harmonic, square-root spherical harmonic, radiometer, and principal-map. We demonstrate the framework on an IPTA-like pulsar timing array: characterizing the angular response, analyzing the Fisher structure, recovering injected anisotropic hotspots, and forecasting future-array sensitivity. The framework is released as an extension to the sensitivity software package hasasia.
ER -