Three-dimensional magnetic and abundance mapping of the cool Ap star HD 24712 II. Two-dimensional magnetic Doppler imaging in all four Stokes parameters

Aims. We present a magnetic Doppler imaging study from all Stokes parameters of the cool, chemically peculiar star HD24712. This is the very first such analysis performed at a resolving power exceeding 105. Methods. The analysis is performed on the basis of phase-resolved observations of line profiles in all four Stokes parameters obtained with the HARPSpol instrument attached at the 3.6 m ESO telescope. We used the magnetic Doppler imaging code INVERS 10, which allowed us to derive the magnetic field geometry and surface chemical abundance distributions simultaneously. Results. We report magnetic maps of HD24712 recovered from a selection of Fe I, Fe II, Nd III, and Na i lines with strong polarization signals in all Stokes parameters. Our magnetic maps successfully reproduce most of the details available from our observation data. We used these magnetic field maps to produce abundance distribution map of Ca. This new analysis shows that the surface magnetic field of HD24712 has a dominant dipolar component with a weak contribution from higher-order harmonics. The surface abundance distributions of Fe and Ca show enhancements near the magnetic equator with an underabundant patch at the visible (positive) magnetic pole; Nd is highly abundant around the positive magnetic pole. The Na abundance map shows a high overabundance around the negative magnetic pole. Conclusions. Based on our investigation and similar recent magnetic mapping studies that used four Stokes parameters, we present tentative evidence for the hypothesis that Ap stars with dipole-like fields are older than stars with magnetic fields that have more small-scale structures. We find that our abundance maps are inconsistent with recent theoretical calculations of atomic diffusion in presence of magnetic fields.