  Zeeman-Doppler imaging (ZDI) is used to reconstruct the surface magnetic
field of late-type stars from high resolution spectropolarimetric observations.
The results are usually described in terms of characteristics of the field
topology, i.e. poloidality vs. toroidality and axi-symmetry vs. non-axisymmetry
in addition to the field strength. We want to test how well these
characteristics are preserved when applying the ZDI method on simulated data,
i.e. how accurately the field topology is preserved and to what extent stellar
parameters influence the reconstruction. We use published magnetic field data
from direct numerical MHD simulations. These have variable rotation rates, and
hence represent different levels of activity, of an otherwise Sun-like setup.
Our ZDI reconstruction is based on spherical harmonics expansion. By comparing
the original values to those of the reconstructed images, we study the ability
to reconstruct the surface magnetic field in terms of various characteristics
of the field. The main large-scale features are reasonably well recovered, but
the strength of the recovered magnetic field is just a fraction of the original
input. The quality of the reconstruction shows clear correlations with the data
quality. Furthermore, there are some spurious dependencies between stellar
parameters and the characteristics of the field. Our study uncovers some limits
of ZDI. Firstly, the recovered field strength will generally be lower than the
"real" value as smaller structures with opposite polarities will be blurred in
the inversion. Secondly, the axisymmetry is overestimated. The poloidality vs.
toroidality is better recovered. The reconstruction works better for a stronger
field and faster rotation velocity. Still, the ZDI method works surprisingly
well even for a weaker field and slow rotation, provided the data has a high
signal-to-noise and good rotation phase coverage.
