Abstract
Collecting the basic differential equations for a spherically symmetric star derived in Chap. I, we are then led by (1.6), (2.16), (4.27, 28), (7.32), and (8.4) to:
In (9.5) we have a set of I equations (one of which may be replaced by the normal-ization ∑ i X i =1) for the change of the mass fractions X i of the relevant nuclei i=1,…, I having masses m i . An additional formula (8.26) regulates the mixing of the composition in convective regions. In (9.3), \( \delta \equiv - {(\partial \ln \varrho /\partial \ln T)_P} \), and in (9.4), \( \nabla \equiv d\ln T/d\ln P \). If the energy transport is due to radiation (and conduction), then \( \nabla \) has to be replaced by \( {\nabla_{{rad}}} \), which is given by (5.28):
If the enerty is carried by convection, then \( \nabla \) in (9.4) has to be replaced by a value obtained from a proper theory of convection; this may be \( {\nabla_{{rad}}} \) in the deep interir, or obtained from a solution of the cubic equation (4.26) for superadiabatic convection in the outer layers.
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© 1990 Springer-Verlag Berlin Heidelberg
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Kippenhahn, R., Weigert, A. (1990). The Differential Equations of Stellar Evolution. In: Stellar Structure and Evolution. Astronomy and Astrophysics Library. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61523-8_9
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DOI: https://doi.org/10.1007/978-3-642-61523-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58013-3
Online ISBN: 978-3-642-61523-8
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