$f$-mode interaction with models of sunspot : near-field scattering and multi-frequency effects

Abstract

We use numerical simulations to investigate the interaction of an $f$-mode wave packet with small and large models of a sunspot in a stratified atmosphere. While a loose cluster model has been largely studied before, we focus in this study on the scattering from an ensemble of tightly compact tubes. We showed that the small compact cluster produces a slight distorted scattered wave field in the transverse direction, which can be attributed to the simultaneous oscillations of the pairs of tubes within the cluster aligned in a perpendicular direction to the incoming wave. However, no signature of a multiple-scattering regime has been observed from this model, while it has been clearly observable for the large compact cluster model. Furthermore, we pointed out the importance of the geometrical shape of the monolithic model on the interaction of $f$-mode waves with a sunspot in a high frequency range ($\nu =$ 5 mHz). These results are a contribution to the observational effort to distinguish seismically between different configurations of magnetic flux tubes within sunspots and plage.