Zeeman Doppler maps. II: the perils of eschewing physics

For the observational modeling of horizontal abundance distributions and of magnetic geometries in chemically peculiar (CP) stars, Zeeman Doppler mapping (ZDM) has become the method of choice. Comparisons between abundance maps obtained for CP stars and predictions from numerical simulations of atomic diffusion have always proved unsatisfactory, with the blame routinely put on theory. Expanding a previous study aimed at clarifying the question of the uniqueness of ZDM maps, this paper inverts the roles between observational modeling and time-dependent diffusion results, casting a cold eye on essential assumptions and algorithms underlying ZDM, in particular the Tikhonov-style regularization functionals, from 1D to 3D. We show that these have been established solely for mathematical convenience, but that they in no way reflect the physical reality in the atmospheres of magnetic CP stars. Recognizing that the observed strong magnetic fields in most well-mapped stars require the field geometry to be force-free, we demonstrate that many published maps do not meet this condition. There follows a discussion of the frequent changes in magnetic and abundance maps of well observed stars and a caveat concerning the use of least squares deconvolution in ZDM analyses. It emerges that because of the complexity and non-linearity of the field-dependent chemical stratifications, Tikhonov based ZDM inversions cannot recover the true abundance and magnetic geometries. As our findings additionally show, there is no way to define a physically meaningful 3D regularization functional instead. ZDM remains dysfunctional and does not provide any observational constraints for the modeling of atomic diffusion.