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

Context. 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, especially for near-infrared observations that require a more accurate treatment of the Zeeman effect. Aims. 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. Methods. We performed polarised radiative transfer calculations across the near-infrared spectrum of a typical M dwarf, including atomic and molecular opacities. 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. Results. 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. Conclusions. Our study reveals fundamental limitations of current ZDI analyses of active M dwarfs and questions the reliability of some published maps. The new computational framework proposed here enables a more accurate and physically consistent interpretation of high-resolution polarimetric spectra, representing a step towards multi-scale magnetic diagnostics of low-mass stars.