Numerical Simulation of Excitation and Propagation of Helioseismic MHD Waves in Magnetostatic Models of Sunspots

TL;DR

This study compares numerical simulations of MHD wave propagation in two sunspot models, revealing how magnetic field strength and source position influence wave behavior, with implications for interpreting helioseismic observations.

Contribution

It introduces a detailed comparison of wave propagation in deep and shallow sunspot models, highlighting the effects of magnetic field strength and non-uniformity on wave characteristics.

Findings

Deep sunspot models distort wavefronts more than shallow models.

Surface gravity waves are more affected by sunspots than p-modes.

Wave amplitude depends on magnetic field strength and source distance.

Abstract

We present comparison of numerical simulations of propagation of MHD waves,excited by subphotospheric perturbations, in two different ("deep" and "shallow") magnetostatic models of the sunspots. The "deep" sunspot model distorts both the shape of the wavefront and its amplitude stronger than the "shallow" model. For both sunspot models, the surface gravity waves (f-mode) are affected by the sunspots stronger than the acoustic p-modes. The wave amplitude inside the sunspot depends on the photospheric strength of the magnetic field and the distance of the source from the sunspot axis. For the source located at 9 Mm from the center of the sunspot, the wave amplitude increases when the wavefront passes through the central part of the sunspot. For the source distance of 12 Mm, the wave amplitude inside the sunspot is always smaller than outside. For the same source distance from the sunspot center but for the models with different strength of the magnetic field, the wave amplitude inside the sunspot increases with the strength of the magnetic field. The simulations show that unlike the case of the uniform inclined background magnetic field, the p- and f-mode waves are not spatially separated inside the sunspot where the magnetic field is strongly non-uniform. These properties have to be taken into account for interpretation of observations of MHD waves traveling through sunspot regions.