On mixing by the Eddington–Sweet circulation

Abstract

The unimpeded Eddington-Sweet [ohm]-currents' in a rapidly rotating, evolving Cowling model star could keep the mean molecular weight, , nearly uniform over the bulk of the star; however, the analogous -currents' due to the resulting non-spherical -distribution tend to choke the E-S circulation near the convective core. The formulation given earlier of the equations governing possible states of steady mixing is rediscussed in order to bring out explicitly the dependence on the two relevant parameters - the centrifugal ratio{varepsilon} and the ratio [IMG]f1.gif" ALT="Formula" BORDER="0"> of the Kelvin-Helmholtz time to the nuclear evolution time. For steady mixing to be possible, a necessary condition is that the compound parameter [IMG]f2.gif" ALT="Formula" BORDER="0"> be sufficiently small. The present paper confirms the earlier conclusion that even when all but the P2 contribution to the -field are ignored, the consequent lower limit on{varepsilon} in a uniform rotator is unrealistically large, and that only by appeal to an implausible non-uniform rotation field could one reconcile steady mixing of even part of the star by the E-S circulation with the limitations set by hydrostatic equilibrium near the surface. To ensure that the curves of constant are topologically acceptable, a representation of the -field in a state of steady mixing must in fact include many terms beyond P2; their effect is to increase the -choke and so to make mixing still less likely to occur.