Analysis of the Sensitivity of Solar Rotation to Helioseismic Data from GONG, GOLF, and MDI Observations

Accurate determination of the rotation rate in the radiative zone of the Sun from helioseismic observations requires rotational frequency splittings of exceptional quality as well as reliable inversion techniques. Here we present inferences based on mode parameters calculated from 2088 day MDI, GONG, and GOLF time series that were fitted to estimate very low frequency rotational splittings ([image] mHz). These low-frequency modes provide data of exceptional quality, since the width of the mode peaks is much smaller than the rotational splitting, and hence it is much easier to separate the rotational splittings from the effects caused by the finite lifetime and the stochastic excitation of the modes. We have also implemented a new inversion methodology that allows us to infer the rotation rate of the radiative interior from mode sets that span [image] to 25. Our results are compatible with the Sun rotating like a rigid solid in most of the radiative zone, and slowing down in the core. A resolution analysis of the inversion was carried out for the solar rotation inverse problem. This analysis effectively establishes a direct relationship between the mode set included in the inversion and the sensitivity and information content of the resulting inferences. We show that such an approach allows us to determine the effect of adding low-frequency and low-degree p-modes, high-frequency and low- degree p-modes, and some g-modes on the derived rotation rate in the solar radiative zone, and in particular the solar core. We conclude that the level of uncertainty that is needed to infer the dynamical conditions in the core when only p-modes are included is unlikely to be reached in the near future, and hence sustained efforts are needed toward the detection and characterization of g-modes.