We present a detailed analysis of the reliability of abundance and magnetic
maps of Ap stars obtained by Zeeman Doppler mapping (ZDM). It is shown how they
can be adversely affected by the assumption of a mean stellar atmosphere
instead of appropriate "local" atmospheres corresponding to the actual
abundances in a given region. The essenceof the difficulties was already shown
by Chandrasekhar's picket-fence model. The results obtained with a suite of
Stokes codes written in the Ada programming language and based on modern
line-blanketed atmospheres are described in detail. We demonstrate that the
high metallicity values claimed to have been found in chemically inhomogeneous
Ap star atmospheres would lead to local temperature structures, continuum and
line intensities, and line shapes that differ significantly from those
predicted by a mean stellar atmosphere. Unfortunately, past applications of ZDM
have consistently overlooked the intricate aspects of metallicity with their
all-pervading effects. The erroneous assumption of a mean atmosphere for a
spotted star can lead to phase-dependent errors of uncomfortably large
proportions at varying wavelengths both in the Stokes I and V profiles, making
precise mapping of abundances and magnetic field vectors largely impossible.
The relation between core and wings of the H_beta line changes, too, with
possible repercussions on the determination of gravity and effective
temperature. Finally, a ZDM analysis of the synthetic Stokes spectra of a
spotted star reveals the disturbing differences between the respective
abundance maps based on a mean atmosphere on the one hand, and on appropriate
"local" atmospheres on the other. We then discuss what this all means for
published ZDMresults. Our discussion makes it clear that realistic local
atmospheres must be used, especially if credible small-scale structures are to
be obtained.Comment: Accepted for publication in MNRA
