The Solar Rotation and Its Evolution during Cycle 23

We present the most exhaustive and accurate inferences of the internal solar rotation rate and its evolution during solar cycle 23. A full solar cycle of Michelson Doppler Imager (MDI) observations has been analyzed using our state of the art fitting methodology. Time series of various lengths have been fitted, from a single 4608-day long epoch (64 x 72 day or 12.6 year) down to 64 separate segments for the traditional 72-day long epochs. We used time series of spherical harmonic coefficients computed by the MDI group but using an improved spatial decomposition. This decomposition now includes our best estimate of the image plate scale and of the MDI instrumental image distortion. The leakage matrix used or the fitting includes the effect of the distortion of the eigenfunctions by the solar differential rotation, and the undistorted leakage matrix was itself carefully reviewed and independently recomputed. Rotation inversions were carried out for all the available mode sets for that epoch and all available segments, including the MDI and Global Oscillation Network Group (GONG) pipeline sets. The improved inversion method we used is an iterative methodology based on a regularized least-squares. It implements a model grid optimization derived from the actual information in the input set. This optimized model grid is itself irregular, namely with a variable number of latitudes at different depths. We present the most accurate mean rotation rate, to date. We also focus on the change of the rotation rate with activity levels and how well these changes are assessed at high latitudes and below the surface, clown to the base of the convection zone.