{
  "abstract": "Least-squares deconvolution (LSD) is the standard technique for measuring stellar magnetic fields from circular polarisation spectra. It rests on the weak-field approximation and yields the longitudinal field alone. We aim to extend LSD beyond the weak-field limit and interpret departures from a linear field response in terms of the field modulus. The Stokes V absorption coefficient is expanded in odd wavelength derivatives of the intensity profile, with coefficients given by the Zeeman pattern moments. Truncation after two terms gives every line a second weight, formed from the third moment of its splitting pattern, and two mean Stokes V profiles follow from multiprofile LSD. This description was tested with polarised spectrum synthesis and applied to archival spectra of two Ap stars and two active M dwarfs. The second mean profile is proportional to the second derivative of the first, with a coefficient measuring the mean square field modulus weighted by the longitudinal flux. This observable separates field strength from the area it covers. Simulations at realistic signal-to-noise ratios show that the second component is reliably detected from about 500 G and constrains the field modulus up to several kG. Applying this methodology to the Ap stars, we found the modulus consistent with their known field strengths, whereas for the M dwarfs it was close to the Zeeman-broadening measurements and far above the large-scale fields from Zeeman-Doppler imaging. Second-order LSD turns the breakdown of the weak-field approximation from a source of error into a new magnetic observable, revealing for the first time the field strength in the regions emitting circular polarisation. It applies to any star with a detectable Stokes V signature and bridges the gap between polarimetry and Zeeman broadening, most promisingly for cool active stars in the infrared.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07148",
  "author_total": 1,
  "authors": [
    {
      "name": "Oleg Kochukhov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78b6m00s9rcrp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07148",
  "fulltext_url": null,
  "id": "78b6m00s9rcrp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07148",
  "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.SR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.07148",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78b6m00s9rcrp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07148",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07148"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.SR",
      "subfield": "stellar"
    }
  ],
  "title": "Unlocking new information in stellar circular polarisation with second-order least-squares deconvolution",
  "title_text": "Unlocking new information in stellar circular polarisation with second-order least-squares deconvolution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/78b6m00s9rcrp",
  "venue": "arXiv",
  "versions": []
}