Inversion of the Internal Solar Rotation Rate

Abstract

Accurate determination of the rotation rate in the inner radiative zone (0.2 < r/R☉ < 0.5) of the Sun from helioseismic observations requires rotational frequency splittings of exceptional quality. Indeed, only the very low degree modes are sensitive to the dynamics of the deep interior. Low- and intermediate-degree splittings have been estimated from a variety of instruments and different data analysis procedures. Therefore, it is not surprising that these determinations present significant differences. We have attempted to build consistent data sets to constrain the dynamics of the solar core, excluding features in the data that are not common to all sets as well as excluding modes for frequencies for which such measurements are not reliable. Our inferences of the solar internal rotation profile were obtained from a full two-dimensional numerical inversion based on the optimal mesh distribution methodology, a variant of the regularized least-squares technique. Our results show that the radiative zone rotates at a rate of approximately 435 nHz, slowing down slightly in the core (r/R☉ < 0.35). We also did not find any significant angular differential rotation below the base of the convective zone (r/R☉ ≈ 0.7). We can rule out any departure of the rotation rate in the solar deep interior, 0.2 < r/R☉ < 0.4, by more than 20% of the surface rotation rate at midlatitude. This result is in clear disagreement with the theoretical hydrodynamical models that expect a much faster rotation rate in the solar core, some 10-50 times faster than the surface rate.