Thermal-magnetic relation in a sunspot and a map of its Wilson depression

We present relations between thermal and magnetic quantities in a simple, isolated sunspot, as deduced from the inversion of 1.56 μm spectropolarimetric data. We used a combination of two infrared $\ion{Fe}{i}$ lines at 15 648.5 Åand 15 652.8 Å in the inversions. Due to the high Zeeman sensitivity of these lines, we can study this relationship in the entire sunspot. The relevant parameters were derived both as a function of location within the sunspot and of height in the atmosphere using an inversion technique based on response functions. In this paper we relate the magnetic vector with temperature. We find a non-linear relationship between the various components of the magnetic vector and temperature, which confirm the results from earlier investigations. We also computed the Wilson depression and the plasma β for the observed sunspot and compare our results with earlier findings.