The stable magnetic field of the fully convective star V374 Peg

We report in this paper phase-resolved spectropolarimetric observations of the rapidly rotating fully convective M4 dwarf V374 Peg, on which a strong, mainly axisymmetric, large-scale poloidal magnetic field was recently detected. In addition to the original data set secured in 2005 August, we present here new data collected in 2005 September and 2006 August. From the rotational modulation of unpolarized line profiles, we conclude that star-spots are present at the surface of the star, but their contrast and fractional coverage are much lower than those of non-fully convective active stars with similar rotation rate. Applying tomographic imaging on each set of circularly polarized profiles separately, we find that the large-scale magnetic topology is remarkably stable on a time-scale of 1 yr; repeating the analysis on the complete data set suggests that the magnetic configuration is sheared by very weak differential rotation (about 1/10th of the solar surface shear) and only slightly distorted by intrinsic variability. This result is at odds with various theoretical predictions, suggesting that dynamo fields of fully convective stars should be mostly non-axisymmetric unless they succeed at triggering significant differential rotation.