Analysis of the Helioseismic Power-Spectrum Diagram of a Sunspot

The continuous high spatial resolution Doppler observation of the Sun by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager allows us to compute a helioseismic k–ω power-spectrum diagram using only oscillations inside a sunspot. Individual modal ridges can be clearly seen with reduced power in the k–ω diagram that is constructed from a 40-hour observation of a stable and round sunspot. Comparing this with the k–ω diagram obtained from a quiet-Sun region, one sees that inside the sunspot the f-mode ridge is more reduced in power than the p-mode ridges, especially at high wavenumbers. The p-mode ridges all shift toward lower wavenumber (or higher frequency) for a given frequency (or wavenumber), implying an increase of phase velocity beneath the sunspot. This is probably because the acoustic waves travel across the inclined magnetic field of the sunspot penumbra. Line-profile asymmetries exhibited in the p-mode ridges are more significant in the sunspot than in the quiet Sun. Convection inside the sunspot is also highly suppressed, and its characteristic spatial scale is substantially larger than the typical convection scale of the quiet Sun. These observational facts demand a better understanding of magnetoconvection and interactions of helioseismic waves with magnetic field.