Inference of Solar Rotation from Perturbations of Acoustic Mode Eigenfunctions

Abstract

Abstract Today’s picture of the internal solar rotation rate profile results essentially from helioseismic analyses of frequency splittings of resonant acoustic waves. Here we present another, complementary estimation of the internal solar rotation rate using the perturbation of the shape of the acoustic waves. For this purpose, we extend a global helioseismic approach developed previously for the investigation of the meridional flow to work on the components of the differential rotation. We discuss the effect of rotation on mode eigenfunctions and the observables based thereon. Based on a numerical study using a simulated rotation rate profile, we tailor an inversion approach and also consider the case of the presence of an additional meridional flow. This inversion approach is then applied to data from the Michelson Doppler Imager (MDI) on board the Solar Heliospheric Observatory and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory. In the end, rotation rate profiles estimated from eigenfunction perturbation and frequency splittings are compared. The rotation rate profiles from the two different approaches are qualitatively in good agreement, especially for the MDI data. Significant differences are obtained at high latitudes >50° and near the subsurface. The result from HMI data shows larger discrepancies between the different methods. We find that the two global helioseismic approaches provide complementary methods for measuring the solar rotation. Comparing the results from different methods may help to reveal systematic influences that affect analyses based on eigenfunction perturbations, like meridional flow measurements.