Time-Distance Modelling In A Simulated Sunspot Atmosphere
  One of the main uncertainties associated with time-distance measurements is how to interpret observations made in regions of strong magnetic field as isolating the effects of the magnetic field from thermal or sound-speed perturbations has proved to be quite complex. One possible way to decouple these effects is by using a 3D sunspot model, with a surrounding stratified, quiet-Sun atmosphere to model the magneto-acoustic ray propagation, and analyze the resulting ray travel-time perturbations that will directly account for the magnetic field. These artificial travel-time perturbation profiles have provided us with several related but distinct observations: i) that strong surface magnetic fields have a dual effect on helioseismic rays -- increasing their skip distance while at the same time speeding them up considerably compared to their quiet-Sun counterparts, ii) there is a clear and significant frequency dependence of both skip-distance and travel-time perturbations across the simulated sunspot radius, iii) the negative sign and magnitude of these perturbations appears to be directly related to the sunspot magnetic-field strength and inclination, iv) by ``switching off'' the magnetic field inside the sunspot, we are able to completely isolate the thermal component of the travel-time perturbations observed, which is seen to be both opposite in sign and much smaller in magnitude than those measured when the magnetic field is present. These results tend to suggest that purely thermal perturbations are unlikely to be the main effect seen in travel times through sunspots and that strong, near-surface magnetic fields may be directly and significantly altering the magnitude and lateral extent of sound-speed inversions of sunspots made by time-distance helioseismology. 
H. Moradi, P.S. Cally