How to interpret near-infrared polarisation spectra of active M dwarfs?

Analyses of global magnetic fields in M dwarfs rely on many approximations regarding the derivation of average line profiles from spectropolarimetric data, interpreting them with analytical functions and modelling them using Zeeman Doppler imaging (ZDI). These assumptions have not been systematically tested. We assessed the accuracy of standard treatments of average polarisation profiles in M dwarfs and their interpretation with ZDI. We focused on the filling-factor approach, which attempts to represent coexisting global and small-scale fields. We performed polarised radiative transfer calculations across the near-infrared spectrum of a typical M dwarf. From these theoretical spectra, we derived mean Stokes profiles and approximated them with different line-synthesis methods. To test the recovery of global fields, we performed ZDI inversions using simulated Stokes V observations for low- and high-activity cases. The analytical approximation of mean polarisation profiles reproduces Stokes I and V only for fields up to ~1 kG and fails for linear polarisation. ZDI with single-line analytical Stokes V profiles is adequate for weakly magnetic M dwarfs with fields below a few hundred gauss. However, combined with the filling-factor formalism, this traditional modelling approach produces unphysical local fields and distorted global geometries for active M dwarfs with multi-kilogauss fields. These issues are mitigated using a new mapping technique based on theoretical Stokes profiles that account for both global and randomly distributed small-scale fields. Our study reveals fundamental limitations of current ZDI analyses of active M dwarfs and questions the reliability of some published maps. (abridged)

💡 Research Summary

This paper presents a systematic evaluation of the methodological foundations underlying near‑infrared (NIR) spectropolarimetric analyses of M‑dwarf stars, focusing on the widely used Least‑Squares Deconvolution (LSD) technique, the weak‑field approximation, and the filling‑factor formalism that attempts to account for coexisting large‑scale (global) and small‑scale magnetic fields. The authors construct a controlled synthetic experiment: they generate high‑resolution Stokes I, V, Q, and U spectra for a typical mid‑M dwarf (T_eff = 3500 K, log g = 5.0) using the polarized radiative‑transfer code SYNMast. The line list includes ~3 200 atomic transitions with full Zeeman splitting patterns and an extensive molecular opacity database (~1.35 × 10⁸ lines from 17 species) pre‑computed with a dedicated non‑magnetic code (Fast‑Spec).

To mimic realistic stellar magnetic topologies, they superimpose a simple oblique dipole (global field B_d) with an isotropic random field (small‑scale component B_s). The random component is generated on a surface grid of ~10⁵ elements, each with the same magnitude but random orientation, optionally weighted to represent multi‑component small‑scale distributions inferred from Zeeman‑broadening studies. This composite model reproduces the observed dichotomy: the mean longitudinal field ⟨B_z⟩ remains essentially unchanged while the mean field modulus ⟨B⟩ increases dramatically as B_s grows.

From the synthetic spectra they derive LSD profiles using a standard atomic‑line mask (≈ 3 200 lines) covering the SPIRou wavelength range (950–2500 nm). They then compare these LSD profiles with analytical single‑line Stokes solutions based on the weak‑field approximation. The comparison shows that for magnetic strengths up to ~1 kG the analytical profiles reproduce Stokes I and V reasonably well, but they completely miss linear polarisation (Q, U) and become inaccurate for stronger fields. The λ² scaling of Zeeman splitting in the NIR exacerbates these discrepancies.

The core of the study is a series of Zeeman Doppler Imaging (ZDI) inversions. Two activity regimes are considered: a low‑activity case with a global field of a few hundred gauss, and a high‑activity case with a dipole of ~2 kG. In the low‑activity scenario, traditional ZDI (single‑line analytical Stokes V combined with a filling‑factor parameter) recovers the input dipole geometry with acceptable fidelity. In the high‑activity scenario, however, the filling‑factor approach leads to unphysical local field strengths (several kilogauss) and severely distorted global topologies. The reason is that the small‑scale component inflates ⟨B⟩ without affecting ⟨B_z⟩, so the inversion compensates by artificially boosting the large‑scale field to match the observed Stokes V amplitude.

To overcome these limitations, the authors propose a new “multi‑scale Stokes mapping” technique. Instead of using a simplified analytical line, they pre‑compute a library of realistic Stokes profiles that already incorporate both the global dipole and the random small‑scale field for a range of field strengths. During ZDI, the observed time‑series of LSD profiles is fitted directly against this library, allowing the inversion to adjust the relative contributions of the two scales rather than forcing a single‑line representation. Tests show that this method accurately recovers both the geometry and the strength of the global field even when the total surface field exceeds 2–3 kG, and it yields realistic local field distributions without the spurious amplification seen with the filling‑factor model.

The paper concludes that current ZDI practices are reliable only for weakly magnetic M dwarfs (B ≲ few × 10² G). For active, kilogauss‑level stars, the standard approximations break down, casting doubt on many published magnetic maps that rely on them. The newly introduced multi‑scale mapping framework offers a physically consistent alternative, paving the way for more accurate magnetic diagnostics in the era of high‑resolution NIR spectropolarimetry (e.g., SPIRou, CRIRES+, NIRPS). The authors also suggest that past results should be revisited in light of these findings, especially when comparing ZDI‑derived fields with those obtained from Zeeman broadening analyses.