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

TL;DR

This study uses numerical simulations to analyze how $f$-mode waves interact with different sunspot models, revealing effects of cluster size and shape on wave scattering and multiple-scattering regimes.

Contribution

It provides new insights into the scattering behavior of $f$-mode waves with compact and large sunspot models, emphasizing the role of geometrical shape and cluster size.

Findings

Small clusters cause slight wave distortion without multiple scattering.

Large clusters exhibit clear multiple-scattering effects.

Shape of the sunspot influences high-frequency wave interactions.

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.