The Frequency-dependent Damping of Slow Magnetoacoustic Waves in a Sunspot Umbral Atmosphere

High spatial and temporal resolution images of a sunspot, obtainedsimultaneously in multiple optical and UV wavelengths, are employed tostudy the propagation and damping characteristics of slowmagnetoacoustic waves up to transition region heights. Power spectra aregenerated from intensity oscillations in sunspot umbra, across multipleatmospheric heights, for frequencies up to a few hundred mHz. It isobserved that the power spectra display a power-law dependence over theentire frequency range, with a significant enhancement around 5.5 mHzfound for the chromospheric channels. The phase difference spectrareveal a cutoff frequency near 3 mHz, up to which the oscillations areevanescent, while those with higher frequencies propagate upward. Thepower-law index appears to increase with atmospheric height. Also,shorter damping lengths are observed for oscillations with higherfrequencies suggesting frequency-dependent damping. Using the relativeamplitudes of the 5.5 mHz (3 minute) oscillations, we estimate theenergy flux at different heights, which seems to decay gradually fromthe photosphere, in agreement with recent numerical simulations.Furthermore, a comparison of power spectra across the umbral radiushighlights an enhancement of high-frequency waves near the umbralcenter, which does not seem to be related to magnetic field inclination angle effects.