EK Eridani: the tip of the iceberg of giants which have evolved from magnetic Ap stars

Aims. We observe the slowly-rotating, active, single giant, EK Eri, to study and infer the nature of its magnetic field directly. Methods. We used the spectropolarimeter NARVAL at the Telescope Bernard Lyot, Pic du Midi Observatory, and the Least Square Deconvolution method to create high signal-to-noise ratio Stokes V profiles. We fitted the Stokes V profiles with a model of the large-scale magnetic field. We studied the classical activity indicators, the Ca II H and K lines, the Ca II infrared triplet, and Ha line. Results. We detected the Stokes V signal of EK Eri securely and measured the longitudinal magnetic field B(1) for seven individual dates spanning 60% of the rotational period. The measured longitudinal magnetic field of EK Eri reached about 100 G and was as strong as fields observed in RSCVn or FK Com type stars: this was found to be extraordinary when compared with the weak fields observed at the surfaces of slowly-rotating MS stars or any single red giant previously observed with NARVAL. From our modeling, we infer that the mean surface magnetic field is about 270 G, and that the large scale magnetic field is dominated by a poloidal component. This is compatible with expectations for the descendant of a strongly magnetic Ap star.