Magnetic field structure in single late-type giants: the effectively single giant V390 Aurigae

Aims. We have studied the active giant V390 Aur using spectropolarimetry to obtain direct and simultaneous measurements of the magnetic field and the activity indicators to obtain a precise insight of its activity. Methods. We used the spectropolarimeter NARVAL at the Bernard Lyot Telescope (Observatoire du Pic du Midi, France) to obtain a series of Stokes I and Stokes V profiles. Using the least-squares deconvolution (LSD) technique we were able to detect the Zeeman signature of the magnetic field in each of our 13 observations and to measure its longitudinal component. Using the wide wavelength range of the spectra we were able to monitor the CaII K&H and IR triplet, as well as the Hα lines, which are activity indicators. To reconstruct the magnetic field geometry of V390 Aur on the basis of modelling the Stokes V profiles, we applied the Zeeman Doppler imaging (ZDI) inversion method and present a map for the magnetic field. Based on the obtained spectra, we also refined the fundamental parameters of the star and the Li abundance using MARCS model atmospheres. Results. The ZDI revealed a structure in the radial magnetic field consisting of a polar magnetic spot of positive polarity and several negative spots at lower latitude. A high latitude belt is present on the azimuthal field map, indicative of a toroidal field close to the surface. Similar features are observed in some RS CVn and FK Com -type stars. It was found that the photometric period cannot fit the behaviour of the activity indicators formed in the chromosphere. Their behaviour suggests slower rotation compared to the photosphere, but our dataset is too short for us to be able to estimate their exact periods. All these results can be explained in terms of an α − ω dynamo operation, taking into account the stellar structure and rotation properties of V390 Aur that we studied with up-to-date stellar models computed at solar metallicity with the code STAREVOL. The calculated Rossby number also points to a very efficient dynamo