Wave propagation in the magnetic sun

The evolution of the solar interior is actively studied theoretically, numerically, and observationally. Many recent advancements in our understanding of the structure and dynamics of the sun have been made by studying solar oscillation. This is the science of helioseismology. Through groundand satellite-based telescopes, oscillations on the solar surface are being observed and, through appropriate techniques, are used to infer information about the sun’s internal structure and composition. One interesting technique provides so-called far-side images of the sun (Lindsey & Braun 2000), where maps of active regions on the far side (the side of the sun facing away from earth) are inferred from the oscillations observed on the front side (the one facing earth). For a review of other helioseismic methods, as well as general properties of the observed solar oscillations, see Christensen-Dalsgaard (2002). In general, these inferences are based on simplified models of wave propagation, and researchers in the field (e.g., Werne, Birch & Julien 2004) have expressed their need for wave propagation simulations to test and calibrate these methods. Of course, wave propagation can be studied by simulating the full compressible equations; for instance, simulations of the shallow upper layer of the solar convection zone by Stein & Nordlund (2000) demonstrate excellent agreement with existing analytical theories and observations. But due to the enormous computational requirements, these types of simulations are able to simulate only a very small part of the sun. For global simulations such an approach is not expected to be feasible in the immediate future. Except for the very near surface region, though, flow velocities in the sun are much smaller than the speed of sound and a perturbation approach is applicable. Thus, acoustic waves can be treated here as small perturbations traveling through a base flow. This is the foundational idea of the this project. The base flow itself can be either artificially prescribed or it can be provided by other simulations such as three-dimensional global simulations of solar convection in the anelastic approximation (Miesch 1998; Brun & Toomre 2002; Brun, Miesch & Toomre 2004). Our work extends that of Hartlep & Mansour (2005) by including the effects of a prescribed magnetic field on the propagation of waves, which is especially of interest for testing the far-side imaging technique previously mentioned. We present here the perturbation equations we derived and our numerical method, and comment on the current status of this project.