Vertical structure of sunspots from THEMIS observations

We have analysed two-dimensional spectro-polarimetric data taken with the MSDP observing mode of THEMIS in the Na I D-1 line to investigate the height variation of the magnetic field in sunspot umbrae. From the Zeeman-induced circular polarization measured at individual MSDP channels within the line profile, maps of the longitudinal magnetic field 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 field at different altitudes in the photosphere. The magnetogram corresponding to the deepest level has served as a boundary condition to perform the potential field extrapolation into the corona. We have found that the spatial distribution of vertical field gradient contours predicted from extrapolation is in qualitatively good agreement with that inferred from observations. Quantitatively, however, the longitudinal field gradients obtained with both methods differ 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 field extrapolation. This is a crucial problem to be addressed in future work, and may have important implications for the physics of how the magnetic field evolves through sunspots and how the flux is distributed in the corona.