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Keywords:

  • atomic processes;
  • line: profiles;
  • magnetic fields;
  • stars: chemically peculiar;
  • stars: individual: HD 318107;
  • stars: magnetic field

ABSTRACT

Modelling of the spectra of magnetic A and B main-sequence stars is generally done assuming that all the lines are split by the magnetic field according to the Zeeman effect. However, a number of prominent spectral lines are produced by closely spaced doublets or triplets. Such lines should be treated using the theory of the partial Paschen–Back (PPB) effect. Depending on the strength and orientation of magnetic field, the PPB effect can result in the Stokes I and V profiles of a spectral line that differ significantly from those predicted by the Zeeman effect theory. It is important to understand the size and types of errors that are introduced into magnetic spectrum synthesis by treating such lines with the usual Zeeman splitting theory rather than using the correct theoretical treatment of line splitting. To estimate the error introduced by the use of the Zeeman approximation, numerical simulations have been performed for spectral lines of the element silicon, for which a number of important lines are actually in the PPB regime, assuming an oblique rotator model, for various silicon abundances and V sin i values. A comparative analysis of the Stokes I and V profiles calculated assuming the PPB and Zeeman splitting has been carried out for a number of both strong and weak Si ii and Si iii lines. The analysis indicates that for high precision studies of some spectral lines the PPB approach should be used if the field strength at the magnetic poles is Bp > 10 kG. In the case of the Si ii line 5041 Å, the difference between the two simulated profiles is caused by a significant contribution from a so-called ‘ghost’ line. The Stokes I and V profiles of this particular line simulated taking into account PPB splitting provide a significantly better fit to the observed profiles in the spectrum of the magnetic Ap star HD 318107 than the profiles calculated with Zeeman splitting. Employing the PPB approach, the Si ii 5041 Å line can become a useful tool for abundance mapping and reconstruction of magnetic field configuration due to its sensitivity to the silicon abundance and to the magnetic field strength.