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.

16 pages, 11 figures, accepted for publication in Solar Physics

References in corpus (3)

• SLiM: a code for the simulation of wave propagation through an inhomogeneous, magnetised solar atmosphere
• {\it f}-mode interactions with thin flux tubes: the scattering matrix
• 3D Numerical Simulations of f-Mode Propagation Through Magnetic Flux Tubes

Cited by in corpus (4)

• Numerical simulations of multiple scattering of the $f-$mode by flux tubes
• Evaluation of the capability of local helioseismology to discern between monolithic and spaghetti sunspot models
• Multiple Scattering of Seismic Waves from Ensembles of Upwardly Lossy Thin Flux Tubes
• $f$-mode interaction with models of sunspot : near-field scattering and multi-frequency effects