Modelling element distributions in the atmospheres of magnetic Ap stars

Context. In recent papers convincing evidence has been presented for chemical stratification in Ap star atmospheres, and surface abundance maps have been shown to correlate with the magnetic field direction. Radiatively driven diffusion, which is known to be sensitive to the magnetic field strength and direction, is among the processes responsible for these inhomogeneities. Aims. Here we explore the hypothesis that equilibrium stratifications - such that the diffusive particle flux is close to zero throughout the atmosphere - can, in a number of cases, explain the observed abundance maps and vertical distributions of the various elements. Methods. An iterative scheme adjusts the abundances in such a way as to achieve either zero particle flux or zero effective acceleration throughout the atmosphere, taking strength and direction of the magnetic field into account. Results. The investigation of equilibrium stratifications in stellar atmospheres with temperatures from 8500 to 12 000 K and fields up to 10 kG reveals considerable variations in the vertical distribution of the 5 elements studied (Mg, Si, Ca, Ti, Fe), often with zones of large over- or under-abundances and with indications of other competing processes (such as mass loss). Horizontal magnetic fields can be very efficient in helping the accumulation of elements in higher layers. Conclusions. A comparison between our calculations and the vertical abundance profiles and surface maps derived by magnetic Doppler imaging reveals that equilibrium stratifications are in a number of cases consistent with the main trends inferred from observed spectra. However, it is not clear whether such equilibrium solutions will ever be reached during the evolution of an Ap star.