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Semiconvection is known to be important in the evolution of massive ($M>10M_{\sun}$) main sequence stars and in horizontal branch stars. The physical nature of the semiconvective instability, as described by stellar evolutionists, often differs from the description given by fluid dynamicists. The ``canonical semiconvection prescription'' used in stellar evolution defines a semiconvective region as a zone of partial mixing and neutral stability outside the convective core as defined by the Schwarzschild criterion. To a fluid dynamicist, semiconvection is a vibrational instability in a fluid that is thermally driven, but stabilized by a composition gradient. In this case, the semiconvection zone lies inside, not outside, the Schwarzschild boundary. The mixing time associated with this instability is much longer than the convective time scale, so that the approximation of instantaneous mixing used in the convective core is not appropriate for the semiconvective zone. Here, we investigate the physics of the latter approach.
We show that the complex criteria defining the conditions for semiconvection simplify to the familiar ``text book'' criteria for reasonable stellar parameters. The turbulent velocity of a semiconvective zone may be $\sim 10^9$ times smaller than the convective zone, so that the composition gradient of the semiconvective zone can act as an effective barrier to rapid mixing. Turbulent transport of heat is so inefficient that the temperature gradient is nearly radiative and quite superadiabatic. We compute the semiconvective mixing rate and the self-consistent temperature gradient from the equations describing double-diffusive transport, and ranch stars with compositions and masses typical for globular clusters has been studied. The implications for the derived ages of globular clusters are discussed briefly.
