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

Abstract

Helioseismic observations of sunspots show that wave travel times, at fixed horizontal phase speed, depend on the temporal frequency of the waves employed in the data analysis. This frequency variation has been suggested to be consistent with near-surface (vertical length scales of order one Mm or smaller) changes in wave propagation properties relative to the quiet Sun. We investigate this suggestion by employing numerical simulations of acoustic-wave propagation through models with horizontally and vertically inhomogeneous structure. Standard methods of surface-focused helioseismic holography are applied to the resulting simulated wave fields. We find that the travel-time shifts measured using holography from the simulations with deep sound-speed perturbations (relative to a planeparallel quiet-Sun model) do not show a systematic frequency dependence at phase speeds above about 20 km s −1 . However, shallow sound-speed perturbations, similar to those proposed to model the acoustic scattering properties of sunspots observed with Hankel analysis, produce systematic frequency dependence at these phase speeds. In both cases, positive travel-time shifts can be caused by positive sound-speed perturbations. The details of the travel-time shifts are, however, model dependent.

The Need for Physics-based Inversions of Sunspot Structure and Flows

“…. This behavior has also been qualitatively (and in some cases remarkably quantitatively) reproduced with artificial data -derived from hydrostatic models [7], magnetostatic models [8], and MHD models [9] -in which no slower layer is present. In contrast to measurements made using phase-speed filters, travel-time perturbations derived using ridge filters are exclusively negative (implying faster wave speeds) in sunspots [4].…”

Helioseismic Holography of Simulated Sunspots: Magnetic and Thermal Contributions to Travel Times

“…This technique has been used in several prior studies (i.e. Hanasoge et al 2007;Birch et al 2009;Dombroski et al 2013). …”

Towards physics-based helioseismic inversions of subsurface sunspot structure

“…However, recently observed variations of travel-time perturbations with frequency (at fixed phase-speed) have been suggested as evidence of strong near-surface perturbations (Couvidat & Rajaguru 2007;Braun & Birch 2006;2008). In addition, the nature and interpretation of the positive (slower) travel-time perturbations and the sensitivity of the travel-time perturbations to the analysis methodology have been questioned (Braun & Birch 2008;Birch et al 2009;Gizon et al 2009;Moradi et al 2010). Positive travel-time shifts (slower waves) have also been measured 380 Braun et at. in artificial datasets where the wave-speed perturbations are positive (Birch et al 2009;Moradi et al 2009).…”

“…In addition, the nature and interpretation of the positive (slower) travel-time perturbations and the sensitivity of the travel-time perturbations to the analysis methodology have been questioned (Braun & Birch 2008;Birch et al 2009;Gizon et al 2009;Moradi et al 2010). Positive travel-time shifts (slower waves) have also been measured 380 Braun et at. in artificial datasets where the wave-speed perturbations are positive (Birch et al 2009;Moradi et al 2009). …”