M dwarfs are known to host strong magnetic fields, which can be measured through several complementary techniques. However, the impact of key methodological choices on Zeeman broadening diagnostics has not been systematically quantified. Here we aim to assess the reliability of different approaches for inferring magnetic fields of M dwarfs and to identify strategies that yield the most accurate magnetic measurements. We combined state-of-the-art three-dimensional magnetohydrodynamic simulations of fully convective M dwarfs with MARCS model atmospheres to generate synthetic Stokes I spectra of a set of lines. Synthetic observations were produced for different surface magnetic field strengths, projected rotational velocities, and inclination angles. Zeeman broadening and intensification were analysed using polarised radiative transfer calculations coupled with Markov chain Monte Carlo inference. We evaluated several statistical criteria (BIC, AIC, and WAIC) to determine the number of magnetic filling factors and compared two alternative strategies for treating line strengths. Ti i The inferred surface-averaged magnetic field is sensitive to the number of magnetic components. In most cases, BIC, AIC, and WAIC favoured the same number of components. In a few tests corresponding to more active and faster rotating stars, BIC and AIC favoured models with fewer components producing lower field estimates, while WAIC selected more complex models, which, generally, yielded a closer agreement with the input field strengths. Treating the intensity of each spectral line as a free parameter in the fitting process resulted in an underestimation of the field strength by 30–50%, while fitting a joint element abundance along with continuum scaling recovered the input field more reliably. Moreover, we showed that the latter inference methodology adequately recovers the binned strength distribution of the magnetic field on the visible hemisphere. Zeeman broadening diagnostics can robustly recover magnetic fields in M dwarfs, but their accuracy strongly depends on methodological choices. Using quantitative statistical criteria for model selection and fitting continuum scaling factors together with element abundance provides reliable results and should be preferred in applications to observational data.
Amateis et al. (Tue,) studied this question.