Understanding the travel-time asymmetry of acoustic waves in sunspots with time─distance helioseismology

Abstract

Mapping the subsurface structure and flow field of sunspots has been a challenging task for helioseismology. In this work, we investigate the propagation of acoustic waves in a sunspot in NOAA active region 11312 using time─distance helioseismology. Travel-times of waves traveling into and out of the sunspot are measured as functions of travel distance and azimuthal angle relative to the local radial direction. The same time─distance analysis is also applied to simulated data based on a magnetohydrostatic (MHS) model of the sunspot, and forward modeling of travel-times is performed using ray tracing based on both the MHS sunspot model and a magnetohydrodynamic (MHD) simulation. We find that both ingoing (traveling from the quiet area into the sunspot) and outgoing waves (traveling from the sunspot into the quiet area) have shorter travel-times than in the quiet Sun, with travel-time reductions of up to ∼40 s. The magnitude of the mean time shift is largest for waves traveling along the radial direction at small travel distances. A clear asymmetry is detected between ingoing and outgoing waves: outgoing waves generally exhibit shorter travel-times. This asymmetry is strongest for the radial direction and small travel distances, with differences exceeding 1 minute for 3.5 and 4.5 mHz waves. From the results of both observations and models, our analysis indicates that the overall reduction in travel-time could be primarily caused by the combined effects of Wilson depression, magnetic field, and wave-speed perturbations, while the ingoing─outgoing asymmetry could be partly attributable to subsurface flows. Although the forward-modeling results reproduce several qualitative features of the observations, quantitative discrepancies remain, highlighting limitations of current sunspot models and ray-theoretical approximations.