Stellar Mixing IV. The angular momentum problem

We present a formalism that provides the Reynolds stresses needed to solve the angular momentum equation. The traditional Reynolds stress model assumes that the only contribution comes from shear (a down-gradient flux), but this leads to an extraction of angular momentum from the interior that is far too small compared to what is required to explain the helio seismological data. An illustrative solution of the new Reynolds stress equations shows that the presence of vorticity in a stably stratified regime, such as the one in the radiative zone, contributes a new term to the angular momentum equation that has an up-gradient flux like the one provided by the IGW model (internal gravity waves). The time scale entailed by such a term may be of the same order of 10(7) yrs produced by the IGW model. It would be instructive to solve the new angular momentum equation together with the formalism developed in Paper III to study not only the solar angular momentum distribution vs. helio data, but also the evolution of elements such as (7)Li and (4)He. These results would allow a more quantitative assessment of the overall model. The complete model yields Reynolds stresses that include differential rotation, unstable/stable stratification, double diffusion, radiative losses (arbitrary Peclet number), and meridional currents.