Improved Helioseismic Analysis of Medium-$\ell$ Data from the Michelson Doppler Imager

Abstract

We present a comprehensive study of one method for measuring various parameters of global modes of oscillation of the Sun. Using velocity data taken by the Michelson Doppler Imager (MDI), we analyze spherical harmonic degrees l <= 300. Both current and historical methodologies are explained, and the various differences between the two are investigated to determine their effects on global-mode parameters and systematic errors in the analysis. These differences include a number of geometric corrections made during spherical harmonic decomposition; updated routines for generating window functions, detrending timeseries, and filling gaps; and consideration of physical effects such as mode profile asymmetry, horizontal displacement at the solar surface, and distortion of eigenfunctions by differential rotation. We apply these changes one by one to three years of data, and then reanalyze the entire MDI mission applying all of them, using both the original 72-day long timeseries and 360-day long timeseries. We find significant changes in mode parameters, both as a result of the various changes to the processing, as well as between the 72-day and 360-day analyses. We find reduced residuals of inversions for internal rotation, but seeming artifacts remain, such as the peak in the rotation rate near the surface at high latitudes. An annual periodicity in the f-mode frequencies is also investigated.