Time-dependent atomic diffusion in magnetic ApBp stars

Numerical modelling of surface abundance distributions in ApBp star atmospheres constitutes a challenging astrophysical problem. This paper is intended to deepen our understanding of how atomic diffusion affects the atmospheric structure of magnetic ApBp stars, and in particular how time-dependent calculations may be compared to the alternative method of estimating equilibrium stratifications. Our numerical calculations – with the stellar atmosphere adjusted self-consistently to the abundance profiles – show that final stationary solutions of the time-dependent diffusion problem (constant particle flux throughout the stellar atmosphere) are seemingly at variance with equilibrium stratifications (zero particle flux). In this work, we will provide some understanding of the origin of these differences and try to elucidate the as yet little explored behaviour of time-dependent atomic diffusion. To this purpose, we assess the influence of the boundary condition at the bottom of the atmosphere, we investigate how the stratifications depend on magnetic field angle and strength, and we have a look at possible interactions between different chemical elements. Based on a grid of atmospheric models and stratifications reflecting dipolar magnetic geometries, we also present predicted line profiles for different oblique rotator models. Finally, we shortly discuss the consequences of our findings for the interpretation of abundance maps of magnetic ApBp stars.