Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Resolution Operational Regimes
Abstract
Pulsar timing arrays (PTAs) are usually analyzed in the Earth-term approximation, although the exact response of an Earth--pulsar baseline contains additional angular structure through the pulsar term. We develop a tensor-spherical-harmonic framework for PTA sky mapping of a deterministic, band-limited gravitational-wave strain field, retaining the full Earth--pulsar response. The single-baseline response is reduced to a compact analytical closed form involving two spherical Bessel functions. Its asymptotic analysis reveals four regimes: Earth-term dominance, transition, pulsar-term dominance, and an effective diffraction cutoff at lcut≃ωL. This scale characterizes the intrinsic exponential suppression of an individual baseline, while the practical angular resolution of a PTA is primarily governed by the finite number, sky distribution and timing noise of the pulsars. Formulating PTA sky mapping as a linear inverse problem; we derive the associated Fisher information matrix and construct an singular-value-decomposition-based reconstruction framework that explicitly separates observable and poorly constrained sky modes. The analysis clarifies the relationship between intrinsic detector resolution and array-sampling limitations and provides a quantitative assessment of the circumstances under which coherent pulsar-term information becomes relevant for full-sky reconstruction. Idealized scaling arguments suggest that exploiting the transition/pulsar-term-dominated regime in global sky mapping imposes a severe ∼ l4 penalty on the array size required to maintain uniform reconstruction fidelity at high multipoles. The formalism extends naturally to anisotropic stochastic backgrounds and provides a unified framework for deterministic field reconstruction and angular-power anisotropy inference.
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BibTeX
@misc{andrianov2026gravitationalwave,
title = {{Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Resolution Operational Regimes}},
author = {S. A. Andrianov and S. M. Kopeikin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.19329},
eprint = {2607.19329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.19329},
}
RIS
TY - UNPB
TI - Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Resolution Operational Regimes
AU - S. A. Andrianov
AU - S. M. Kopeikin
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2607.19329
UR - https://arxiv.org/abs/2607.19329
AB - Pulsar timing arrays (PTAs) are usually analyzed in the Earth-term approximation, although the exact response of an Earth--pulsar baseline contains additional angular structure through the pulsar term. We develop a tensor-spherical-harmonic framework for PTA sky mapping of a deterministic, band-limited gravitational-wave strain field, retaining the full Earth--pulsar response. The single-baseline response is reduced to a compact analytical closed form involving two spherical Bessel functions. Its asymptotic analysis reveals four regimes: Earth-term dominance, transition, pulsar-term dominance, and an effective diffraction cutoff at l_cut≃ωL. This scale characterizes the intrinsic exponential suppression of an individual baseline, while the practical angular resolution of a PTA is primarily governed by the finite number, sky distribution and timing noise of the pulsars. Formulating PTA sky mapping as a linear inverse problem; we derive the associated Fisher information matrix and construct an singular-value-decomposition-based reconstruction framework that explicitly separates observable and poorly constrained sky modes. The analysis clarifies the relationship between intrinsic detector resolution and array-sampling limitations and provides a quantitative assessment of the circumstances under which coherent pulsar-term information becomes relevant for full-sky reconstruction. Idealized scaling arguments suggest that exploiting the transition/pulsar-term-dominated regime in global sky mapping imposes a severe ∼ l^4 penalty on the array size required to maintain uniform reconstruction fidelity at high multipoles. The formalism extends naturally to anisotropic stochastic backgrounds and provides a unified framework for deterministic field reconstruction and angular-power anisotropy inference.
ER -