Magnetic Doppler imaging of α2 Canum Venaticorum in all four Stokes parameters Unveiling the hidden complexity of stellar magnetic fields

Context. Strong organized magnetic fields have been studied in the upper main sequence chemically peculiar stars for more than half a century. However, only recently have observational methods and numerical techniques become sufficiently mature to allow us to record and interpret high-resolution four Stokes parameter spectra, leading to the first assumption-free magnetic field models of these stars. Aims. Here we present a detailed magnetic Doppler imaging analysis of the spectropolarimetric observations of the prototypical magnetic Ap star alpha(2) CVn. This is the second star for which the magnetic field topology and horizontal chemical abundance inhomogeneities have been inferred directly from phase-resolved observations of line profiles in all four Stokes parameters, free from the traditional assumption of a low-order multipolar field geometry. Methods. We interpret the rotational modulation of the circular and linear polarization profiles of the strong Fe II and Cr II lines in the spectra of alpha 2 CVn recorded with the MuSiCoS spectropolarimeter. The surface abundance distributions of the two chemical elements and a full vector map of the stellar magnetic field are reconstructed in a self-consistent inversion using our state-of-the-art magnetic Doppler imaging code INVERS10. Results. We succeeded in reproducing most of the details of the available spectropolarimetric observations of alpha 2 CVn with a magnetic map which combines a global dipolar-like field topology with localized spots of higher field intensity. We demonstrate that these small-scale magnetic structures are inevitably required to fit the linear polarization spectra; however, their presence cannot be inferred from the Stokes I and V observations alone. We also found high-contrast surface distributions of Fe and Cr, with both elements showing abundance minima in the region of weaker and topologically simpler magnetic field. Conclusions. Our magnetic Doppler imaging analysis of alpha 2 CVn and previous results for 53 Cam support the view that the upper main sequence stars can harbour fairly complex surface magnetic fields which resemble oblique dipoles only at the largest spatial scales. Spectra in all four Stokes parameters are absolutely essential to unveil and meaningfully characterize this field complexity in Ap stars. We therefore suggest that understanding magnetism of stars in other parts of the H-R diagram is similarly incomplete without investigation of their linear polarization spectra.