Time-Dependence of Subsurface Solar Convection Using the Time-Distance Deep-Focus Method

Abstract

We re-examine the deep-focus methodology of time-distance helioseismology previously used to estimate the power spectrum of the solar convection at a depth of about 30 Mm, which was found to be significantly weaker than predicted by theory and simulations. The Global Acoustic, Linearized Euler (GALE) and Eulerian Lagrangian (EULAG) codes are used to generate ground-truth simulations to evaluate the accuracy of the inferred convective power spectrum. This validation process shows that the power spectrum derived using the time-distance methodology diverges significantly from ground truth beyond spatial scales corresponding to the spherical harmonic degree $\ell=15$--$30$ because of the limited resolution of helioseismic measurements at that depth. However, the power estimated at larger spatial scales ($\ell<15$) is sufficiently accurate. We then apply the methodology to solar data selected from throughout Solar Cycle 24 and find some evidence that the magnitude of the convective power changes throughout the Cycle. An average of the convective power across the Solar Cycle reveals a spectrum that is qualitatively similar to previous estimates, though about half an order of magnitude greater. The disagreement between observations of solar convection and the magnitudes predicted by simulations persists.