{
  "abstract": "Recent high-precision cosmological observations have revealed several anomalies in the cosmic microwave background (CMB), indicating possible violations of statistical isotropy (SI)—rotational invariance of statistical measures of a random skymap. The bipolar spherical harmonic (BipoSH) formalism, a widely used complete representation of both the SI and statistical anisotropy (nSI) components of a random skymap, is defined and implemented in the spherical harmonic space. In this work we probe the rotational symmetry violation of the correlation function using weighted rotational averages, providing a geometric interpretation of BipoSH as a real-space operation. We establish that the BipoSH measures are related to averages of the correlation function over all rotated configurations weighted by Wigner matrices. As a demonstration, we consider a phenomenological dipole modulation model and numerically implement the rotational average measures and show their agreement with their harmonic space counterparts. The real-space approach could be advantageous in formulating BipoSH like nSI measures on a partial sky. We envisage broader applications of this framework to the studies of primordial non-Gaussianity, CMB polarisation, weak gravitational lensing and the characterization of general random fields on a sphere.",
  "abstract_shown": true,
  "affiliations": [
    "Raman Research Institute",
    "Inter University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune-411007,"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Vaishali R",
      "orcid": "0009-0004-7856-9587"
    },
    {
      "affs": [
        0
      ],
      "name": "Dipayan Mukherjee",
      "orcid": "0000-0002-5267-1944"
    },
    {
      "affs": [
        0
      ],
      "name": "Akshank Tyagi",
      "orcid": "0009-0002-2757-1957"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Tarun Souradeep",
      "orcid": "0000-0003-3764-8102"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/97t7ye7devf6f.bib",
  "cited_by": 0,
  "doi": "10.3847/1538-4357/aeaf53",
  "fulltext_url": null,
  "id": "97t7ye7devf6f",
  "issns": [
    "1538-4357",
    "0004-637X"
  ],
  "landing_url": "https://iopscience.iop.org/article/10.3847/1538-4357/aeaf53",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "feed-journal",
      "astronomy/general"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://iopscience.iop.org/article/10.3847/1538-4357/aeaf53/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": "American Astronomical Society",
  "ris": "https://research.draconitic.com/paper/97t7ye7devf6f.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:20:44Z",
      "native_id": "10.3847/1538-4357/aeaf53",
      "source": "feed-iop",
      "url": "https://iopscience.iop.org/article/10.3847/1538-4357/aeaf53"
    },
    {
      "first_seen": "2026-11-04T12:20:54Z",
      "native_id": "10.3847/1538-4357/aeaf53",
      "source": "crossref",
      "url": "https://iopscience.iop.org/article/10.3847/1538-4357/aeaf53"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "journal-openalex:3103|Stellar, planetary, and galactic studies",
      "subfield": "stellar"
    }
  ],
  "title": "Capturing Statistical Isotropy Violation with Rotational Averages",
  "title_text": "Capturing Statistical Isotropy Violation with Rotational Averages",
  "type": "peer-reviewed",
  "updated_at": "2026-11-04T12:20:54Z",
  "url": "https://research.draconitic.com/paper/97t7ye7devf6f",
  "venue": "The Astrophysical Journal",
  "versions": []
}