Meridional circulation in rotating stars. VII - The effects of chemical inhomogeneities

Abstract

In this paper we discuss the effects of a gradient of mean molecular weight ..mu.. on the rotationally driven currents that pervade the radiative zone of a single, nonmagnetic, main-sequence star. Detailed numerical calculations are made for the hydrogen-burning core of a solar-type star, assuming that departures from spherical symmetry are not too large. It is found that meridional streaming virtually dies out from the center outward as the ..mu..-gradient grows in a leisurely fashion. This prevents a substantial mixing of matter between the inner (inhomogeneous) and outer (homogeneous) regions in the radiative zone, although the inner region may be penetrated to some degree. To first order in the ratio of the centrifugal force to gravity at the equator, this pattern of circulation is independent of the mean angular velocity. To this order, then, there is no critical rotation rate above which unimpeded mixing may take place. These quantitative results are compared with diverse statements that can be found in the phenomenological literature on rotational mixing.