Modelling the molecular Zeeman effect in M-dwarfs: methods and first results

We present first quantitative results of the surface magnetic field measurements in selected M-dwarfs based on detailed spectra synthesis conducted simultaneously in atomic and molecular lines of the FeH Wing-Ford $F^4,Delta-X^4,Delta$ transitions. A modified version of the Molecular Zeeman Library (MZL) was used to compute Lande g-factors for FeH lines in different Hunds cases. Magnetic spectra synthesis was performed with the Synmast code. We show that the implementation of different Hunds case for FeH states depending on their quantum numbers allows us to achieve a good fit to the majority of lines in a sunspot spectrum in an automatic regime. Strong magnetic fields are confirmed via the modelling of atomic and FeH lines for three M-dwarfs YZ~CMi, EV~Lac, and AD~Leo, but their mean intensities are found to be systematically lower than previously reported. A much weaker field ($1.7-2$~kG against $2.7$~kG) is required to fit FeH lines in the spectra of GJ~1224. Our method allows us to measure average magnetic fields in very low-mass stars from polarized radiative transfer. The obtained results indicate that the fields reported in earlier works were probably overestimated by about $15-30$%. Higher quality observations are needed for more definite results.