{
  "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 $l_\\mathrm{cut}\\simeqωL$. 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 $\\sim l^4$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.19329",
  "author_total": 2,
  "authors": [
    {
      "name": "S. A. Andrianov"
    },
    {
      "name": "S. M. Kopeikin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/djpmfhksnmz0j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.19329",
  "fulltext_url": null,
  "id": "djpmfhksnmz0j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.19329",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.HE"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7170060077",
  "pdf_url": "https://arxiv.org/pdf/2607.19329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/djpmfhksnmz0j.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2607.19329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.19329"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.HE",
      "subfield": "high-energy-astrophysics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Resolution Operational Regimes",
  "title_text": "Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Resolution Operational Regimes",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/djpmfhksnmz0j",
  "venue": "arXiv",
  "versions": []
}