Abstract
Context. In sunspots, the geometric height of continuum optical depth unity is depressed compared to the quiet Sun. This so-called Wilson depression is caused by the Lorentz force of the strong magnetic field inside the spots. However, it is not understood in detail yet how the Wilson depression is related to the strength and geometry of the magnetic field or to other properties of the sunspot. Aims. We aim to study the dependence of the Wilson depression on the properties of the magnetic field of the sunspots and how exactly the magnetic field contributes to balancing the Wilson depression with respect to the gas pressure of the surroundings of the spots. Methods. Our study is based on 24 spectropolarimetric scans of 12 individual sunspots performed with Hinode. We derived the Wilson depression for each spot using both a recently developed method that is based on minimizing the divergence of the magnetic field and an approach that was developed earlier, which enforces an equilibrium between the gas pressure and the magnetic pressure inside the spot and the gas pressure in the quiet Sun, thus neglecting the influence of the curvature force. We then performed a statistical analysis by comparing the Wilson depression resulting from the two techniques with each other and by relating them to various parameters of the sunspots, such as their size or the strength of the magnetic field. Results. We find that the Wilson depression becomes larger for spots with a stronger magnetic field, but not as much as one would expect from the increased magnetic pressure. This suggests that the curvature integral provides an important contribution to the Wilson depression, particularly for spots with a weak magnetic field. Our results indicate that the geometry of the magnetic field in the penumbra is different between spots with different strengths of the average umbral magnetic field.
Highlights
The Wilson depression zW (Wilson & Maskelyne 1774) is the difference in height of unity optical depth between a sunspot and the quiet Sun
We aim to study the dependence of the Wilson depression on the properties of the magnetic field of the sunspots and how exactly the magnetic field contributes to balancing the Wilson depression with respect to the gas pressure of the surroundings of the spots
We derived the Wilson depression for each spot using both a recently developed method that is based on minimizing the divergence of the magnetic field and an approach that was developed earlier, which enforces an equilibrium between the gas pressure and the magnetic pressure inside the spot and the gas pressure in the quiet Sun, neglecting the influence of the curvature force
Summary
The Wilson depression zW (Wilson & Maskelyne 1774) is the difference in height of unity optical depth between a sunspot and the quiet Sun. The Wilson depression zW (Wilson & Maskelyne 1774) is the difference in height of unity optical depth between a sunspot and the quiet Sun This depression is caused by the strong magnetic field of the spot. The magnetic field quenches the convection, leading to a less effective heat transport, and to a lower temperature and to a lower opacity within the spot. The Wilson depression should strongly depend on the strength and the geometry of the magnetic field. The properties of the magnetic field of a sunspot depend, to a large extent, on its size. Larger spots exhibit a stronger magnetic field and a lower temperature in the umbra
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