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A Semitheory for Semiconvection

Published online by Cambridge University Press:  25 April 2016

D. J. Stevenson
D. J. Stevenson*
Affiliation:
Research School of Earth Sciences, Australian National University
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Extract

Semiconvection is the name given to a situation that arises in the evolution of large-mass main-sequence stars and lower-mass horizontal-branch stars, in which a layer forms where almost all of the heat flux is transported by radiation, but where slow convection is required to redistribute a stably stratified solute (e.g. helium). For a general discussion on semiconvection, see Spiegel (1969). The main problem is to determine the correct relationship between the solute distribution and the temperature gradient in the inhomogeneous layer. Ledoux (1947) and Schwarzschild and Harm (1958) have proposed two very different prescriptions. Since theory and experiment indicate that the Schwarzschild-Harm (SH) prescription is correct for the onset of convection (in the form of overstability), Spiegel (1969) has proposed that SH are correct. However, neither observation (oceanographic or laboratory) nor theory precludes a substantial deviation from the SH prescription as applied to finite amplitude semiconvection. The observational evidence is only readily applicable to stars if Pr≳, 1, where Pr is the Prandtl number of the fluid. In fact, Pr≪ 1 in stars. It is shown below that if one could have stars in which Pr ≳ 1, then the SH prescription would probably be wrong, and the Ledoux criterion might then be nearer to being correct. In the real situation (Pr≪ 1), observations or experiments are lacking and theory alone does not provide an unequivocal answer to the problem. This paper does not attempt a complete discussion of the problem, and a more detailed report will be submitted elsewhere. Some aspects of the problem have already been discussed in the context of the giant planets (Stevenson and Salpeter 1977).

Type
Contributions
Information
Publications of the Astronomical Society of Australia , Volume 3 , Issue 2 , September 1977 , pp. 165 - 167
Copyright
Copyright © Astronomical Society of Australia 1977

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