Ten years magnetic modelling of stars
by field sources - a review

E. Gerth,
D-14471 Potsdam, Gontardstr 130, Germany.
e-mail: ewald-gerth@t-online.de
Yu.V. Glagolevskij, Special Astrophysical Observatory of Russian AS, Nizhnij Arkhyz 369167, Russia.
e-mail: glagol@sao.ru

Preliminary abstract
Since Babcock's epoch-making work half a century ago an enormous quantity of observational data on magnetic stars has been compiled, waiting for analysis and interpretation. Arranging the data in phase curves, one could hope to discover at least a rough topographic structure of the magnetic surface field by an inverse procedure. This has been done by Khokhlova, Piskunov, Kochukhov. Bagnulo et al. modelled the surface field by spherical harmonics with the poles as parameters. Ten years ago Glagolevskij and Gerth proposed a modelling method to construct the magnetic field out of its sources and vortices by a straightforward calculation. After a theorem of the potential theory, the sources and vortices are the constituents of any vector field. In analogy to electric fields there were formally introduced "magnetic charges", which allow to use a standard algorithm for the point-like source, relating to a minimum of physically significant parameters. The sources can be positioned inside and/or outside the star, filling by their superposed fields the entire space - the magneto-sensitive atmosphere included. The program has been developed to a useful multivalent tool for controlling the inverse derivation of the surface field but, above all, to construct the field on a synthetic way, hereby fitting the calculation to the observational facts.

(This is a summary of a lecture held by E. Gerth at the CP#AP WORKSHOP in Vienna, Austria, 10.-14. September 2007)