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While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this article, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out a helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by Gizon et al. (2009aGizon et al. ( , 2009b. We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.

We report the discovery of one of the most powerful sunquakes detected to date, produced by an X1.2‐class solar flare in active region AR10720 on 2005 January 15. We used helioseismic holography to image the source of seismic waves emitted into the solar interior from the site of the flare. Acoustic egression power maps at 3 and 6 mHz with a 2‐mHz bandpass reveal a compact acoustic source strongly correlated with impulsive hard X‐ray and visible‐continuum emission along the penumbral neutral line separating the two major opposing umbrae in the δ‐configuration sunspot that predominates AR10720. At 6 mHz the seismic source has two components, an intense, compact kernel located on the penumbral neutral line of the δ‐configuration sunspot that predominates AR10720, and a significantly more diffuse signature distributed along the neutral line up to ∼15 Mm east and ∼30 Mm west of the kernel. The acoustic emission signatures were directly aligned with both hard X‐ray and visible continuum emission that emanated during the flare. The visible continuum emission is estimated at 2.0 × 1023 J, approximately 500 times the seismic emission of ∼4 × 1020 J. The flare of 2005 January 15 exhibits the same close spatial alignment between the sources of the seismic emission and impulsive visible continuum emission as previous flares, reinforcing the hypothesis that the acoustic emission may be driven by heating of the low photosphere. However, it is a major exception in that there was no signature to indicate the inclusion of protons in the particle beams thought to supply the energy radiated by the flare. The continued strong coincidence between the sources of seismic emission and impulsive visible continuum emission in the case of a proton‐deficient white‐lightflare lends substantial support to the ‘back‐warming’ hypothesis, that the low photosphere is significantly heated by intense Balmer and Paschen continuum‐edge radiation from the overlying chromosphere in white‐light flares.

We investigate the direct contribution of strong, sunspot-like magnetic fields to helioseismic wave travel-time shifts via two numerical forward models, a 3D ideal MHD solver and MHD ray theory. The simulated data cubes are analyzed using the traditional time-distance center-to-annulus measurement technique. We also isolate and analyze the direct contribution from purely thermal perturbations to the observed travel-time shifts, confirming some existing ideas and bring forth new ones: (i) that the observed travel-time shifts in the vicinity of sunspots are largely governed by MHD physics, (ii) the travel-time shifts are sensitively dependent on frequency and phase-speed filter parameters and the background power below the p 1 ridge, and finally, (iii) despite its seeming limitations, ray theory succeeds in capturing the essence of the travel-time variations as derived from the MHD simulations.

The well-observed acoustic halo is an enhancement in time-averaged Doppler velocity and intensity power with respect to quiet-sun values which is prominent for weak and highly inclined field around the penumbra of sunspots and active regions. We perform 3D linear wave modelling with realistic distributed acoustic sources in a MHS sunspot atmosphere and compare the resultant simulation enhancements with multi-height SDO observations of the phenomenon. We find that simulated halos are in good qualitative agreement with observations. We also provide further proof that the underlying process responsible for the halo is the refraction and return of fast magnetic waves which have undergone mode conversion at the critical a = c atmospheric layer. In addition, we also find strong evidence that fast-Alfvén mode conversion plays a significant role in the structure of the halo, taking energy away from photospheric and chromospheric heights in the form of field-aligned Alfvén waves. This conversion process may explain the observed "dual-ring" halo structure at higher (> 8 mHz) frequencies.