2000A&A...358..929B

The most common techniques for detecting magnetic fields of chemically peculiar (CP) stars are based on the determination of some quantities related to the magnetic morphology, which are obtained through the analysis of Stokes I and V profiles, and on observations of frequency integrated Stokes Q and U. In previous papers of this series we set up a formalism aimed at describing the magnetic field of CP stars in terms of a superposition of a dipole and a quadrupole field, and we proposed a method to recover the magnetic morphology from the combined analysis of those observable quantities which can simply be expressed by means of analytical formulas, namely: the mean longitudinal field, the crossover, and the mean square field. Here we extend this method in order to include those quantities for which numerical integrations are required, i.e., the mean field modulus and the broadband linear polarisation. Estimates of stellar radius and projected equatorial velocity are also explicitly taken into account. We present an application to the well-known CP star β CrB, the only star for which all kinds of magnetic data are available. We find that β CrB, like most CP stars, exhibits a complex magnetic structure, which may not be fully accounted for even by a second-order multipolar expansion. However, we are able to suggest two models which are compatible with all the magnetic data.