Submitted to be published in: 2006, Magnetic stars, Proc. Internat. Conf. SAO, Nizhnij Arkhyz, 28 August - 1 September 2006:

Calculation of the integral magnetic field

of a star

accounting for the surface distribution

of elements

Ewald Gerth and Yurij V. Glagolevskij

Abstract

The observable magnetic field of a star is the result of integration over its visible hemisphere, related to the information transferring medium: the spectral line profile. The hitherto practised simple integration of the magnetic field strength neglects the spotty face of the star and is physically wrong. Because of the topographically distributed line-generating elements in the stellar atmosphere, the contribution of all parts of the surface to the integration is different. For an effective computation, both the magnetic field and the element distribution are transformed from globes to Mercator maps and arranged as right-angled matrices. The numerical evaluation is performed by a special computer program, which uses matrices and vector algebra. The theory is based on the mathematical derivation of convolution integrals for the rotation of the star and the line profiles formed in its atmosphere, whereby the radiation from all surface areas in direction to the observer is integrated, accounting for the geometrical and radiation transfer conditions of the disk-like visible hemisphere and the element distribution of chemically peculiar (CP) stars. The computation starts from a given magnetic field structure on the surface of a star and progresses straightforward over convolution integrals to the phase curves of the integral magnetic field strength. In consideration of other approaches to the problem of field structure analysis, also the inversion of the convolution is discussed.

Keywords: CP stars, magnetic field, element distribution, line profile