Inclinations of small quiet-Sun magnetic features based on a new geometric approach

Context. High levels of horizontal magnetic flux have been reported in the quiet-Sun internetwork, often based on Stokes profile inversions. Aims. Here we introduce a new method for deducing the inclination of magnetic elements and use it to test magnetic field inclinations from inversions. Methods. We determine accurate positions of a set of small, bright magnetic elements in high spatial resolution images sampling different photospheric heights obtained by the Sunrise balloon-borne solar observatory. Together with estimates of the formation heights of the employed spectral bands, these provide us with the inclinations of the magnetic features. We also compute the magnetic inclination angle of the same magnetic features from the inversion of simultaneously recorded Stokes parameters. Results. Our new, geometric method returns nearly vertical fields (average inclination of around 14° with a relatively narrow distribution having a standard deviation of 6°). In strong contrast to this, the traditionally used inversions give almost horizontal fields (average inclination of 75 ± 8°) for the same small magnetic features, whose linearly polarised Stokes profiles are adversely affected by noise. We show that for such magnetic features inversions overestimate the flux in horizontal magnetic fields by an order of magnitude. Conclusions. The almost vertical field of bright magnetic features from our geometric method is clearly incompatible with the nearly horizontal magnetic fields obtained from the inversions. This indicates that the amount of magnetic flux in horizontal fields deduced from inversions is overestimated in the presence of weak Stokes signals, in particular if Stokes Q and U are close to or under the noise level. Inversions should be used with great caution when applied to data with no clear Stokes Q and no U signal. By combining the proposed method with inversions we are not just improving the inclination, but also the field strength. This technique allows us to analyse features that are not reliably treated by inversions, thus greatly extending our capability to study the complete magnetic field of the quiet Sun.