Observed Dispersive Properties of the Slow Magnetoacoustic Waves Propagating in Coronal Fan Loops above Sunspots

Recurrent and propagating intensity perturbations are frequently observed in extreme ultraviolet (EUV) channels along coronal fan loops above sunspots, and these perturbations are suggested to be slow magnetoacoustic waves. Numerous studies have been conducted to investigate their propagation speeds, damping, and excitation sources; however, there have been limited observational analyses on whether these waves are dispersive despite some theoretical studies. In this study, we apply cross-correlation analysis in the Fourier domain on slow magnetoacoustic waves using three different datasets: EUV intensity observed by SDO/AIA, differential emission measure (DEM) temperature maps, and Doppler velocities from Hinode/EIS spectrometer observations. The apparent phase velocities of the waves, which are the plane-of-sky component of the waves' phase velocities, are derived as functions of frequency for all the three datasets. It is found that the phase velocities show clear frequency dependency, with a general trend of increase with frequency, ranging from approximately 30 km/s around 3 mHz to about 80 km/s around 10 mHz. The frequency dependency of the phase velocities demonstrates that the slow magnetoacoustic waves in the coronal loops are dispersive. The dispersiveness of these waves can provide a useful tool for the diagnosis of physical conditions inside the coronal loops along which these waves travel.