The three-dimensional structure of sunspots

Abstract

Aims. We investigate the height dependence of the magnetic field of a sunspot, which has been until now a controversial issue. Methods. Full-Stokes profiles of a sunspot, derived from infrared spectro-polarimetric measurements, were investigated. The magnetic field strength, inclination and azimuth were obtained using an inversion code. The results from two different spectral lines deliver the height dependence of the magnetic vector field. Vertical current densities and helicities as well as the vertical derivative of the vertical component of the magnetic field strength are calculated using Maxwell’s equations. Results. Inside the spot, the total magnetic field strength decreases with height, even in the outer penumbra, where the opposite trend was reported by other investigators. Outside the spot, the field strength increases with height apart from at a few small locations. This result is interpreted in terms of magnetic canopies. Magnetic field lines are less inclined in higher layers everywhere in the field of view. In the umbra, the vertical component of the magnetic field decreases by values in the range 0.5–2.2 G km −1 , depending on the applied method. Mean values in the inner penumbra are smaller than in the umbra. In the outer penumbra, the vertical magnetic component increases independently of the local intensity distribution. A pore close to the spot exhibits a more rapid decrease with height than the spot itself. The electric current densities and helicities depend on the fine structure of the sunspots. Typical values of the current densities vary in the range ±40 mA m −2 . The mean values are −11 mA m −1 for the umbra and − 2m A m −1 for the penumbra, respectively, but the propagated errors are of the same order as the mean values. There are indications that the radial structure of the penumbra is related to enhanced current densities, but at the present resolution we are unable to establish a correlation with local intensity fluctuations. Conclusions. If the spatial resolution is sufficiently high, electric current densities and helicities could be applied as reliable diagnostic tools for understanding penumbral fine structure.