Testing the reliability of magnetic field strength measurements for M dwarfs

TL;DR

This study systematically evaluates the reliability of different methods for measuring magnetic fields in M dwarfs using synthetic spectra, highlighting how methodological choices impact accuracy.

Contribution

It provides a comprehensive assessment of Zeeman broadening diagnostics and compares statistical criteria for inferring magnetic field properties in M dwarfs.

Findings

WAIC yields more accurate magnetic field estimates for active, rapidly rotating M dwarfs.

Treating line strengths as free parameters underestimates magnetic fields by 30-50%.

Joint fitting of element abundance and continuum improves field recovery.

Abstract

M dwarfs host strong magnetic fields that can be measured using several complementary techniques. However, the impact of key methodological choices on Zeeman broadening diagnostics has not been systematically quantified. We assess the reliability of different approaches for inferring magnetic fields in M dwarfs using synthetic Stokes $I$ spectra of Ti I lines generated from three-dimensional magnetohydrodynamic simulations combined with MARCS model atmospheres. 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) for selecting the number of magnetic filling factors and compared alternative strategies for treating line strengths. In most cases, BIC, AIC, and WAIC favoured the same number of components. For some active and rapidly rotating models, BIC and AIC selected fewer components and yielded lower field estimates, while WAIC generally produced closer agreement with the input field strengths. Treating individual line strengths as free parameters underestimated the field strength by 30--50%, whereas fitting a joint element abundance together with continuum scaling recovered the input field more reliably. Our results show that Zeeman broadening diagnostics can robustly recover magnetic fields in M dwarfs, but their accuracy depends strongly on methodological choices.