Simulation of f-Mode Propagation Through a Cluster of Small Identical Magnetic Flux Tubes

Abstract

Motivated by the question of how to distinguish seismically between monolithic and cluster models of sunspots, we have simulated the propagation of an $f$-mode wave packet through two identical small magnetic flux tubes (R=200 km), embedded in a stratified atmosphere. We want to study the effect of separation $d$ and incidence angle $\chi$ on the scattered wave. We have demonstrated that the horizontal compact pair of tubes ($d/R=2$, $\chi=0$) oscillate as a single tube when the incident wave is propagating, which gives a scattered wave amplitude of about twice that from a single tube. The scattered amplitude decreases with increasing $d$ when $d$ is about $\lambda/2\pi$ where $\lambda$ is the wavelength of the incident wave packet. In this case the individual tubes start to oscillate separately in the manner of near-field scattering. When $d$ is about twice of $\lambda/2\pi$, scattering from individual tubes reaches the far-field regime, giving rise to coherent scattering with an amplitude similar to the case of the compact pair of tubes. For perpendicular incidence ($\chi=\pi/2$), the tubes oscillate simultaneously with the incident wave packet. Moreover, simulations show that a compact cluster oscillates almost as a single individual small tube and acts more like a scattering object, while a loose cluster shows multiple-scattering in the near-field and the absorption is largest when $d$ within the cluster is about $\lambda/2\pi$. This is the first step to understand the seismic response of a bundle of magnetic flux tubes in the context of sunspot and plage helioseismology.