  Aims: The goal of this study is to perform numerical tests of Zeeman Doppler
Imaging (ZDI) to asses whether correct reconstruction of magnetic fields is at
all possible without taking temperature into account for stars in which
magnetic and temperature inhomogeneities are spatially correlated. Methods: We
used a modern ZDI code employing a physically realistic treatment of the
polarized radiative transfer in all four Stokes parameters. We generated
artificial observations of isolated magnetic spots and of magnetic features
coinciding with cool temperature spots and then reconstructed magnetic and
temperature distributions from these data. Results: Using Stokes I and V for
simultaneous magnetic and temperature mapping for the star with a homogeneous
temperature distribution yields magnetic field strengths underestimated by
typically 10-15% relative to their true values. When temperature is kept
constant and Stokes I is not used for magnetic mapping, the underestimation is
30-60%. At the same time, the strength of magnetic field inside cool spots is
underestimated by as much as 80-95% and the spot geometry is also poorly
reconstructed when temperature variations are ignored. On the other hand, the
inversion quality is greatly improved when temperature variations are accounted
for in magnetic mapping. When using all four Stokes parameters the
reconstructed field strength inside cool spots is underestimated by 30-40% but
the spot geometry can be recovered very accurately compared to the experiments
with circular polarization alone. Conclusions: Reliable magnetic field
reconstruction for a star with high-contrast temperature spots is essentially
impossible if temperature inhomogeneities are ignored. A physically realistic
line profile modeling method, which simultaneously accounts for both types of
inhomogeneities, is required for meaningful ZDI of cool active stars.

Solar and Stellar Astrophysics