Multi-height observations of magnetoacoustic cut-off frequency in a sunspot atmosphere

Context. The cut-off frequency of magnetoacoustic gravity (MAG) waves could be decreased by the inclined magnetic field, and therefore, low-frequency waves could penetrate into the upper atmosphere. Aims. We observe the distribution of the cut-off frequency of compressive waves at various heights and reconstruct the magnetic field inclination, according to the MAG wave theory in a stratified atmosphere permeated by a uniform magnetic field. Methods. We analysed the emission intensity oscillations of sunspot AR11131 (08 Dec. 2010) observed at the 1700 angstrom, 1600 angstrom, and 304 angstrom bandpasses of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO), and computed the narrow-band power maps with the pixelised wavelet filtering method. The distribution of the cut-off frequency was defined as the median contour in the azimuthally-averaged oscillation power. The magnetic field inclination was estimated with the local cut-off frequency according to the MAG wave theory in the low-beta limit and was compared to the potential field extrapolation. Results. Shorter period oscillations dominate in the sunspot umbra, while longer period oscillations form an annular shape approximately concentric with the sunspot. Oscillations with longer periods are distributed further away from the sunspot centre. The 5 min oscillations appear to originate at or lower than the photosphere. The magnetic field inclinations determined with the cut-off frequency theory are about 30-40% larger than the values obtained by the potential field extrapolation. Conclusions. The oscillation power distribution in a sunspot atmosphere reflects its magnetic and thermal structure. The cut-off frequency could be used to probe the magnetic field inclination, however, other factors have to be included to fully understand this phenomenon. The existence of return magnetic flux at the outer penumbra was evidenced by the cut-off frequency distribution.