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Magnetic field reconstruction based on sunspot oscillations

The magnetic field of a sunspot guides magnetohydrodynamic waves toward higher atmospheric layers. In the upper photosphere and lower chromosphere, wave modes with periods longer than the acoustic cut-off period become evanescent. The cut-off period essentially changes due to the atmospheric properties, e.g., increases for larger zenith inclinations of the magnetic field. In this work, we aim at introducing a novel technique of reconstructing the magnetic field inclination on the basis of the dominating wave periods in the sunspot chromosphere and upper photosphere. On 2013 August 21st, we observed an isolated, circular sunspot (NOAA11823) for 58 min in a purely spectroscopic multi-wavelength mode with the Interferometric Bidimensional Spectro-polarimeter (IBIS) at the Dunn Solar Telescope. By means of a wavelet power analysis, we retrieved the dominating wave periods and reconstructed the zenith inclinations in the chromosphere and upper photosphere. The results are in good agreement with the lower photospheric HMI magnetograms. The sunspot's magnetic field in the chromosphere inclines from almost vertical (0$^{\circ}$) in the umbra to around 60$^{\circ}$ in the outer penumbra. With increasing altitude in the sunspot atmosphere, the magnetic field of the penumbra becomes less inclined. We conclude that the reconstruction of the magnetic field topology on the basis of sunspot oscillations yields consistent and conclusive results. The technique opens up a new possibility to infer the magnetic field inclination in the solar chromosphere.