Zeeman tomography of magnetic white dwarfs, I. Reconstruction of the field geometry from synthetic spectra

We have computed optical Zeeman spectra of magnetic white dwarfs for field strengths between 10 and 200MG and effective temperatures between 8000 and 40000K. They form a database containing 20628 sets of flux and circular polarization spectra. A least-squares optimization code based on an evolutionary strategy can recover relatively complex magnetic field topologies from phase-resolved synthetic Zeeman spectra of rotating magnetic white dwarfs. We consider dipole and quadrupole components which are non-aligned and shifted off-centre. The model geometries include stars with a single high-field spot and with two spots separated by approx. 90 degrees. The accuracy of the recovered field structure increases with the signal-to-noise ratio of the input spectra and is significantly improved if circular polarization spectra are included in addition to flux spectra. We discuss the strategies proposed so far to unravel the field geometries of magnetic white dwarfs.