Doppler imaging of chemical spots on magnetic Ap/Bp stars. Numerical tests and assessment of systematic errors

Doppler imaging (DI) is a powerful spectroscopic inversion technique that enables conversion of a line profile time series into a two-dimensional map of the stellar surface inhomogeneities. In this paper we investigate the accuracy of chemical abundance DI of Ap/Bp stars and assess the impact of several different systematic errors on the reconstructed spot maps. We simulate spectroscopic observational data for different spot distributions in the presence of a moderately strong dipolar magnetic field. We then reconstruct chemical maps using different sets of spectral lines and making different assumptions about line formation in the inversion calculations. Our numerical experiments demonstrate that a modern DI code successfully recovers the input chemical spot distributions comprised of multiple circular spots at different latitudes or an element overabundance belt at the magnetic equator. For the optimal reconstruction the average reconstruction errors do not exceed ~0.10 dex. The errors increase to about 0.15 dex when abundance distributions are recovered from a few and/or blended spectral lines. Ignoring a 2.5 kG dipolar magnetic field in chemical abundance DI leads to an average relative error of 0.2 dex and maximum errors of 0.3 dex. Similar errors are encountered if a DI inversion is carried out neglecting a non-uniform continuum brightness distribution and variation of the local atmospheric structure. This series of numerical DI simulations proves that inversions with simplifying assumptions of the non-magnetic radiative transfer and a single model atmosphere are generally reliable. We assess magnetic field strengths of several dozen Ap/Bp stars previously studied with DI methods, concluding that the vast majority of the published chemical spot maps are unaffected by the systematic errors addressed in this paper. (Abridged)