On the inversion of the density gradient at the fringe of the convection zone

Abstract

Introduction. It is well known that the total pressure and the temperature increase as one goes inward from the surface to the center of a star. That the density, on the other hand, does not necessarily increase with depth below the surface was pointed out by Hoyle and Schwarzschild (1955) and was borne out quite clearly by the numerical integrations of the solar surface layers by Faulkner, Griffiths, and Hoyle (1963). The question was raised by Tayler and Gough (1963) as to whether the density gradient inversion was real or whether it was due to the particular model of convection adopted by Faulkner et al. It is the purpose of this note to show that the inversion is indeed genuine and results from the steep temperature gradient that exists in the outermost layers of the convection zone where convection is not fully efficient and carries only a fraction (<1/2) of the total energy flux. Also, the electron pressure-temperature plane can be divided into regions where dp/dT is negative and positive. The dividing line depends, in an insensitive manner, on the assumed model and efficiency of convection. In the case of the sun it is the hydrogen ionization at about 10^4 °K that causes the opacity to go up sharply and as a result the temperature gradient steepens there by inverting the density gradient. The inversion necessarily results in a Rayleigh-Taylor instability.

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