Astronomy Astrophysics

Abstract. We have analysed two-dimensional spectro-polarimetric data taken with the MSDP observing mode of THEMIS in the Na I D1 line to investigate the height variation of the magnetic eld in sunspot umbrae. From the Zeeman-induced circular polarization measured at individual MSDP channels within the line prole, maps of the longitudinal magnetic eld have been computed. A method based on Response Functions has been developed to estimate the depth in the atmosphere at which the Zeeman measurements are originated, thus providing the line-of-sight eld at dierent altitudes in the photosphere. The magnetogram corresponding to the deepest level has served as a boundary condition to perform the potential eld extrapolation into the corona. We have found that the spatial distribution of vertical eld gradient contours predicted from extrapolation is in qualitatively good agreement with that inferred from observations. Quantitatively, however, the longitudinal eld gradients obtained with both methods dier about one order of magnitude, being larger for observations. The origin of this discrepancy has been discussed with respect to possible observation biases, as well as to idealizations used for eld extrapolation. This is a crucial problem to be addressed in future work, and may have important implications for the physics of how the magnetic eld evolves through sunspots and how the flux is distributed in the corona. Key words. sunspots { Sun: magnetic elds 1