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

Abstract

The propagation of solar waves through the sunspot of AR 9787 is observed by using temporal cross-correlations of SOHO/MDI Dopplergrams. We then use threedimensional MHD numerical simulations to compute the propagation of wave packets through self-similar magnetohydrostatic 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 and 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.

Inversion of Full Acoustic Wavefield in Local Helioseismology: A Study With Synthetic Data

“…This means that during inversion we are attempting to retrieve only the acoustic wavefield structure, and for the purpose of demonstrating waveform inversion in this study we have assumed that acoustic source function remains constant. Although stochastic sources have been simulated in previous helioseismic studies (Hanasoge et al 2006;Cameron et al 2008), our adoption of a constant acoustic source function is consistent with the approach used in current studies for constructing helioseismic forward models (e.g., Werne et al 2004;Hanasoge et al 2007). However, in principle it is possible to invert for the source function and wavefield structure simultaneously.…”

Surface-Focused Seismic Holography of Sunspots: II. Expectations from Numerical Simulations Using Sound-Speed Perturbations

“…In this work, we employ the two separate numerical simulations codes: i) the code introduced by Hanasoge, Duvall, and Couvidat (2007) (hereafter referred to as H07) and ii) the SLiM code (Cameron, Gizon, and Daiffallah, 2007;Cameron, Gizon, and Duvall, 2008).…”

“…In the SLiM code, wave damping is explicitly modeled; the details are described by Cameron, Gizon, and Duvall (2008). The simulations described in this paper are two dimensional with 200 grid points in the horizontal direction and 558 grid points in the vertical direction.…”

3D Numerical Simulations of f-Mode Propagation Through Magnetic Flux Tubes

“…The approach is already yielding interesting results in the context of sunspots, see e.g. Cameron, Gizon, and Daiffallah (2007), Hanasoge (2008), Khomenko, Collados, and Fellipe (2008), Cameron, Gizon, and Duvall (2008), Khomenko et al (2009).…”