Dispersion of Slow Magnetoacoustic Waves in Coronal Fan Loops Rooting at Sunspots

Recurrent and propagating intensity perturbations are frequently observed in coronal fan loops in EUV channels, and these perturbations are believed to be slow-mode magnetoacoustic waves. Numerous studies have been conducted to investigate their propagation speeds, damping, and sources; however, there has been limited observational studies on whether these waves exhibit dispersion, despite some theoretical suggestions. This study is focused on propagating disturbances in a fan loop associated with a large sunspot observed in EUV emissions using SDO/AIA and in Doppler velocities using Hinode/EIS. We analyze the phase speeds of the waves as a function of oscillatory frequency and find that these magnetoacoustic waves exhibit significant dispersion, with the plane-of-sky phase speed approximately 30 km/s around the frequency of 2 mHz and up to 80 km/s around 15 mHz. This dispersion relation in the magnetoacoustic waves can provide a useful tool for diagnosing the nonuniform structure in the coronal loops and understanding the related heating/cooling processes.