Unlocking new information in stellar circular polarisation with second-order least-squares deconvolution
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.
Related
- Reading Between the Lines: How Much Information Remains After Fitting a Stellar Spectrum?
- A cross-calibration approach for polarisation-sensitive detectors in CMB experiments: application to LiteBIRD's polarisation angle calibration
- Full Characterisation of the Polarisation Primary Beam of the GRAO 32-m Telescope
- ViCTORIA project: A pilot study of the M49 region in the Virgo cluster in polarisation
- Validation of harmonic-space likelihood methods for LiteBIRD B-mode polarisation analysis
BibTeX
@misc{kochukhov2026unlocking,
title = {{Unlocking new information in stellar circular polarisation with second-order least-squares deconvolution}},
author = {Oleg Kochukhov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07148},
eprint = {2610.07148},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07148},
}
RIS
TY - UNPB
TI - Unlocking new information in stellar circular polarisation with second-order least-squares deconvolution
AU - Oleg Kochukhov
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07148
UR - https://arxiv.org/abs/2610.07148
AB - 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.
ER -