Connecting the Wilson depression to the magnetic field of sunspots

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 developed earlier that 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.

16 pages, 8 figures. Accepted for publication in Astronomy and Astrophysics

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• The Solar Optical Telescope for the Hinode Mission: An Overview
• The Polarimetric and Helioseismic Imager on Solar Orbiter
• Stokes Inversion based on Convolutional Neural Networks
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• FIRTEZ-dz: A Forward and Inverse solver of the polarized Radiative Transfer Equation under Zeeman regime in geometrical scale
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• On the Collective Magnetic Field Strength and Vector Structure of Dark Umbral Cores Measured by the Hinode Spectropolarimeter
• Measuring the Wilson depression of sunspots using the divergence-free condition of the magnetic field vector
• Vertical magnetic field gradient in the photospheric layers of sunspots
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Cited by in corpus (4)

• Combining magneto-hydrostatic constraints with Stokes profile inversions. II. Application to Hinode/SP observations
• The magnetic topology of the inverse Evershed flow
• The impact of unresolved magnetic spots on high precision radial velocity measurements
• The MODEST catalog of depth-dependent spatially coupled inversions of sunspots observed by Hinode/SOT-SP