Three-dimensional numerical simulations of the acoustic wave field in the upper convection zone of the Sun

Results of numerical three-dimensional (3D) simulations of propagation of acoustic waves inside the Sun are presented. A linear 3D code which utilizes the realistic OPAL equation of state was developed. A modified convectively stable standard solar model with a smoothly joined chromosphere was used as a background model. A high-order dispersion relation-preserving numerical scheme was used. The top nonreflecting boundary condition established in the chromosphere absorbs waves with frequencies greater than the acoustic cutoff frequency which pass through the chromosphere, simulating a realistic situation. We simulate acousto-gravity wave fields on the Sun, generated by localized randomly distributed sources in a subphotospheric layer. Three applications for solar wave physics are presented: changes in oscillation properties due to the mechanism of wave damping, effects of nonuniform distribution of sources, and effects of nonuniform localized perturbations on wave properties. In particular, we studied two models of wave damping with leakage and with an explicit friction-type damping term in the photospheric layers and chromosphere. In both cases we were able to reproduce observed characteristics of the acoustic spectrum (line widths and amplitude distribution). We found that the suppression of acoustic sources, e.g., in sunspots, may significantly contribute to the observed power deficit. The lower sound speed in sunspot areas may cause an increase of the wave amplitude, but this effect is less important for the acoustic power distribution than the suppression of the acoustic sources.