Some Comments on the Problem of Rotation and Mixing in Stars

Abstract

In the 1950’s, Sweet (1950) and Öpik (1951) rediscussed the resolution of the von Zeipel paradox in a uniformly rotating stellar radiative zone, showing that the time-scale of the Eddington (1929)-Vogt (1925) thermally-driven circulation would be of the order of the Kelvin-Helmholtz time τK H, divided by an appropriate value for the ratio q of centrifugal to gravitational acceleration. In a Cowling-type star, the streamlines emerge near the poles of the convective core, traverse the radiative envelope, and return to the core at the equator. In a rapid rotator, the time τc of circulation is still short compared with the time-scale τn for transmutation in the core of H into He, and it seemed that the mean molecular weight μ would remain nearly uniform, with the star evolving up and slightly to the left of the Main Sequence in the H-R Diagram; while in a moderate rotator, there could still be enough mixing to affect noticeably the expected evolution towards the Giant Domain. Prima facie, significant mixing would occur provided the value q(rc) of q at the convective core surface exceeded τK H/τn ≈ 10−3.