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Exploring the magnetic field complexity in M dwarfs at the boundary to full convection

Based on detailed spectral synthesis we carry out quantitative measurements of the strength and complexity of surface magnetic fields in the four well-known M-dwarfs GJ 388, GJ 729, GJ 285, and GJ 406 populating the mass regime around the boundary between partially and fully convective stars. Very high resolution R=100000, high signal-to-noise (up to 400) near-infrared Stokes I spectra were obtained with CRIRES at ESO's Very Large Telescope covering regions of the FeH Wing-Ford transitions at 1mum. The field distributions in all four stars are characterized by three distinct groups of field components, the data are neither consistent with a smooth distribution of different field strengths, nor with one average field strength covering the full star. We find evidence of a subtle difference in the field distribution of GJ 285 compared to the other three targets. GJ 285 also has the highest average field of 3.5kG and the strongest maximum field component of 7-7.5kG. The maximum local field strengths in our sample seem to be correlated with rotation rate. While the average field strength is saturated, the maximum local field strengths in our sample show no evidence for saturation. We find no difference between the field distributions of partially and fully convective stars. The one star with evidence for a field distribution different to the other three is the most active star (i.e. with largest x-ray luminosity and mean surface magnetic field) rotating relatively fast. A possible explanation is that rotation determines the distribution of surface magnetic fields, and that local field strengths grow with rotation even in stars in which the average field is already saturated.