Successful spectral synthesis of Zeeman-split molecular bands in sunspot spectra

We present the first spectral synthesis of Zeeman- split Stokes profiles of the MgH A 2 -X 2 green system and TiO -system. The calculations involve different regimes of the molecular Zeeman effect, up to the complete Paschen-Back effect for individual lines. The synthetic spectra are compared with observations of Stokes I and V in sunspot umbrae. We find that although the Stokes I spectra are reasonably reproduced, some lines are obviously still missing from the employed line lists. The Stokes V spectra turn out to be much cleaner since the missing lines do not appear to be Zeeman-split. We thus pro- vide the first good fit to Zeeman-split molecular lines, including profiles with unconventional Stokes V shapes, determined by the Paschen-Back effect.