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Zeeman Doppler mapping deconstructed

M. J. Stift, F. Leone

TL;DR

Zeeman Doppler mapping (ZDM) maps for chemically peculiar stars are widely used to test diffusion theories, but this study shows that ZDM inversions are non-unique and can produce physically non-viable magnetic topologies that still fit Stokes IQUV data. By inter-comparing multiple published maps for five well-studied CP stars, the authors demonstrate substantial and systematic discrepancies in both magnetic field topologies and chemical abundances across maps derived from the same data set or within the same methodological framework. They argue that many recovered maps violate force-free or divergence-free constraints, and that existing numerical tests of ZDM accuracy are inadequate for ruling out spurious solutions. The findings imply that current ZDM results cannot reliably constrain atomic diffusion theories, and they call for more stringent, physically consistent validation of ZDM inversions.

Abstract

Aims. Magnetic and abundance maps of chemically peculiar (CP) stars, derived with the help of Zeeman Doppler mapping, have invariably been used as arguments against theories, in particular atomic diffusion theory. We intend to expose the fallacy of these claims. Methods. We have identified in the literature those (5) CP stars for which multiple maps have been published, all based on the same Zeeman Doppler mapping strategy. For each of these stars we have then carried out inter comparisons between the recovered distributions of magnetic field and of abundances. Results. Agreement between maps often turns out to be quite poor in regard to both abundances, field topology and absolute field strengths. Maps based on the same set of observations can differ considerably, even when they are coming from the same authors. Conclusions. It becomes clear that Zeeman Doppler mapping cannot be guaranteed to yield unique results. When a number of physically impossible magnetic geometries all provide good fits to the observed Stokes $IQUV$ profiles, these solutions must necessarily be spurious and cannot be used as constraints to diffusion theory.

Zeeman Doppler mapping deconstructed

TL;DR

Zeeman Doppler mapping (ZDM) maps for chemically peculiar stars are widely used to test diffusion theories, but this study shows that ZDM inversions are non-unique and can produce physically non-viable magnetic topologies that still fit Stokes IQUV data. By inter-comparing multiple published maps for five well-studied CP stars, the authors demonstrate substantial and systematic discrepancies in both magnetic field topologies and chemical abundances across maps derived from the same data set or within the same methodological framework. They argue that many recovered maps violate force-free or divergence-free constraints, and that existing numerical tests of ZDM accuracy are inadequate for ruling out spurious solutions. The findings imply that current ZDM results cannot reliably constrain atomic diffusion theories, and they call for more stringent, physically consistent validation of ZDM inversions.

Abstract

Aims. Magnetic and abundance maps of chemically peculiar (CP) stars, derived with the help of Zeeman Doppler mapping, have invariably been used as arguments against theories, in particular atomic diffusion theory. We intend to expose the fallacy of these claims. Methods. We have identified in the literature those (5) CP stars for which multiple maps have been published, all based on the same Zeeman Doppler mapping strategy. For each of these stars we have then carried out inter comparisons between the recovered distributions of magnetic field and of abundances. Results. Agreement between maps often turns out to be quite poor in regard to both abundances, field topology and absolute field strengths. Maps based on the same set of observations can differ considerably, even when they are coming from the same authors. Conclusions. It becomes clear that Zeeman Doppler mapping cannot be guaranteed to yield unique results. When a number of physically impossible magnetic geometries all provide good fits to the observed Stokes profiles, these solutions must necessarily be spurious and cannot be used as constraints to diffusion theory.

Paper Structure

This paper contains 15 sections, 13 figures.

Table of Contents

  1. Introduction
  2. The (Zeeman) Doppler mapping approach
  3. Constructing an artificial paradise
  4. Controversial claims
  5. More idealisations, more claims
  6. Outdated and skewed numerical tests
  7. Assessing published, ZDM based maps
  8. Data extraction and its caveats
  9. A detailed discussion of 5 stars
  10. $\alpha^2$ CVn (HD 112413)
  11. 49 Cam (HD 62140)
  12. 53 Cam (HD 65339)
  13. HD 24712
  14. HD 3980
  15. Conclusions

Figures (13)

  • Figure 1: Abundance differences between the original 2002 3-spot map and the recovered map.
  • Figure 2: Hammer projection of the recovered abundance map for the K17 4-spot test case, based on all 4 Stokes parameters at 20 phases, 20 mÅ spectral resolution and 2034 pixel spatial grid. Top: Unsmoothed ZDM output. Bottom: Difference map original minus inverted.
  • Figure 3: Same as before, but now based on all 4 Stokes parameters at 10 phases, 25 mÅ spectral resolution and 10310 pixel spatial grid. Top: Unsmoothed ZDM output. Bottom: Difference map original minus inverted; the excluded pixels are displayed in white.
  • Figure 4: ( top 3) $\alpha^2$ CVn : Absolute magnetic field strengths at 5 equidistant phases, recovered from 3 articles. ( bottom 3) Differences in field strengths at 5 equidistant phases for combinations between 5 maps.
  • Figure 5: ( top 3) $\alpha^2$ CVn : Cr abundance at 5 equidistant phases and abundance differences for combinations between 3 maps. ( bottom 3) Same as before, but for Fe abundances.
  • ...and 8 more figures