Helioseismology of Sunspots: Confronting Observations with Three-Dimensional MHD Simulations of Wave Propagation

TL;DR

This study combines observations and 3D MHD simulations to analyze wave propagation through sunspots, demonstrating that accurate modeling requires accounting for magnetic effects and can match observed data.

Contribution

It introduces a method to compare observed helioseismic data with detailed 3D MHD simulations, advancing understanding of sunspot magnetic structures.

Findings

Simulation matches observations for a 3 kG sunspot model

Magnetic field significantly influences wave propagation

Full-waveform modeling of sunspots is achievable

Abstract

The propagation of solar waves through the sunspot of AR 9787 is observed using temporal cross-correlations of SOHO/MDI Dopplergrams. We then use three-dimensional MHD numerical simulations to compute the propagation of wave packets through self-similar magneto-hydrostatic sunspot models. The simulations are set up in such a way as to allow a comparison with observed cross-covariances (except in the immediate vicinity of the sunspot). We find that the simulation and the f-mode observations are in good agreement when the model sunspot has a peak field strength of 3 kG at the photosphere, less so for lower field strengths. Constraining the sunspot model with helioseismology is only possible because the direct effect of the magnetic field on the waves has been fully taken into account. Our work shows that the full-waveform modeling of sunspots is feasible.