On generating and derived magnitudes of stellar magnetic fields

The structure of the stellar surface magnetic field is covered from direct observation by many mixing processes. The discovery of the topographic surface structure requires an inversion procedure but does not reveal the origin of the magnetic field. Modelling of magnetic stars, however, has to start from the generating magnitudes and is a matter of construction by a strategy of forward calculation. The model of the star is fitted to the observed appearance of the real object by variation of parameters and optimizing. The magnetic field strength on the surface of the star -- including the magnetic poles -- is a derived magnitude, which should not be taken as a parameter for modeling. At the present time two versions of magnetic modeling are discussed: 1) expansion of spherical harmonics, 2) magnetic charge distribution. Both methods claim for the application of parameters, which determine the magnetic field. In this paper the question is investigated, what the generating and the derived magnitudes of the magnetic field are. Tracing back the observed spherical distribution of the magnetic field to its origin, one is led to the eigen values as the solution of Legendre's differential equation. We regard the eigen values as the generating magnitudes of the magnetic field, the physical quantities of which are the constituents of any vector field, namely the sources and vortices, from which the field originates. This interpretation is substantiated by graphical representations of magnetic maps with topographical features like poles -- derived from the field-generating sources: the virtual magnetic charges.