The three-dimensional structure of the magnetic field of a sunspot

Spectro-polarimetric observations in several spectral lines allow to determine the height variation of the magnetic field of a small sunspot throughout the solar photosphere. The full Stokes-vector is measured with high spatial resolution. From these data we derive the magnetic field vector. The magnetic field strength decreases with height everywhere in the spot, even in the outer penumbra where some other authors have reported the opposite. The precise value of this decrease depends on the exact position in the spot. Values vary between 0.5 and 2.2 G km⁻¹ when they are determined from an iron and a silicon line in the near infrared. The magnetic field is less inclined in the higher layers where the silicon line is formed. Once the magnetic vector field is known, it is straight forward to determine current densities and helicities. Current densities exhibit a radial structure in the penumbra, although it is still difficult to correlate this with the structure seen in the intensity continuum. In spite of this, current densities have a potential to serve as diagnostic tools to understand the penumbra, at least with the spatial resolution of the upcoming telescopes. The mean infered helicity is negative, as expected for a spot in the northern hemisphere. Nevertheless, there are locations inside the spot with positive helicity.