Abstract. With the aim of establishing a benchmark for the detailed calculation of the polarised line profiles of magnetic stars, we describe an intercomparison of LTE Stokes profiles calculated using three independent, stateof-the-art magnetic spectrum synthesis codes: Cossam, Invers10 and Zeeman2. We find, upon establishing a homogeneous basis for the calculations (identical definitions of the Stokes parameters and the magnetic and stellar reference frames, identical input model stellar atmosphere, identical input atomic data, and identical chemical element abundances and magnetic field distributions), that local and disc-integrated Stokes IQUV profiles of Fe II λ4923.9 calculated using the three codes agree very well. For the illustrative case of disc-integrated profiles calculated for abundance log nFe/ntot = −4.60, dipole magnetic field intensity B d = 5 kG, and projected rotational velocity ve sin i = 20 km s −1 , Stokes I profiles (depth ∼40% of the continuum flux Ic) agree to within about 0.05% rms of Ic, Stokes V profiles (full amplitude ∼10%) to within about 0.02% rms of Ic, and Stokes Q and U profiles (full amplitudes ∼2%) at the sub-0.01% rms level. These differences are sufficiently small so as to allow for congruent interpretation of the best spectropolarimetric data available, as well as for any data likely to become available during the near future. This indicates that uncertainties in modeling Stokes profiles result overwhelmingly from uncertainties in input atomic and physical data, especially the state and structure of model stellar atmospheres.

Context. Theoretical modelling of abundance stratifications and surface distributions of chemical elements in Ap stars constitutes a major challenge. The atomic diffusion model provides the most appropriate framework in which to understand these abundance anomalies.Aims. We present theoretical 2D stratifications of 16 metals in upper main sequence chemically peculiar stars, with and without magnetic fields to provide a reference point for further theoretical and observational studies. Methods. We used our code CaratStrat to compute a large grid of stratifications (equilibrium solutions in LTE) for plane-parallel T eff = 8500, 10 000, 12 000, and 14 000 K stellar atmospheres. By interpolation, we constructed bi-dimensional cuts through these stellar atmospheres, which are permeated by a dipolar magnetic field of strength 20 kG at the magnetic pole. We also provide vertical (1D) stratifications of metals in non-magnetic stars (HgMn).Results. We present a large number of 2D and 1D stratifications, mostly as online material. We discuss in detail the case of Fe for the T eff = 8500 K model in the printed version, and compare it with stratifications derived from observed spectra.

Abstract. We present a comparison of observed and calculated Stokes IQUV spectra of two well-known magnetic chemically peculiar stars, β Coronae Borealis and 53 Camelopardalis. The observed Stokes spectra were recently described by Wade et al. (2000a), and have been complemented with additional circularly polarized spectra obtained at the Special Astrophysical Observatory. The calculated spectra represent the predictions of new and previously published magnetic field models derived from the analysis of some surface averaged field estimates (e.g., longitudinal field, magnetic field modulus, etc.). We find that these magnetic models are not sufficient to account fully for the observed Stokes profiles -particularly remarkable is the disagreement between the predicted and observed Stokes Q and U profiles of 53 Cam. We suggest that this should be interpreted in terms of magnetic morphologies which are significantly more complex than the second-order multipolar expansions assumed in the models. However, it is clear that some of our inability to reproduce the detailed shapes of the Stokes IQUV profiles is unrelated to the magnetic models. For many metallic ions, for both stars, we found it impossible to account for the strengths and shapes of the observed spectral line profiles when we adopted a unique value for the individual ion abundance. We suggest that this results from strongly non-uniform distributions of these ions as a function of optical depth (i.e., chemical stratification), a hypothesis that is supported by comparison with simple chemically stratified models.

The chemical peculiarities of Ap stars are due to abundance stratifications produced by atomic diffusion in their outer layers. Theoretical models can predict such stratifications, but so far only provide equilibrium solutions which correspond to the maximum depth‐dependent abundances for each element that can be supported by the radiation field. However, these stratifications are actually built up through a non‐linear, time‐dependent process which has never been modelled for realistic stellar atmospheres. Here, we present the first numerical simulations of time‐dependent diffusion. We solve the continuity equation after having computed, as accurately as possible, atomic diffusion velocities (with and without a magnetic field) for a simplified fictitious – but still realistic – chemical element: cloudium. The direct comparison with existing observations is not the immediate aim of this work but rather a general understanding of how the stratification build‐up proceeds in time and space. Our results raise serious questions as to the relevance of equilibrium solutions and reinforce the suspicion that certain accumulations of chemical elements might prove unstable.