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EQUATIONS OF STELLAR STRUCTURE General Equations

EQUATIONS OF STELLAR STRUCTUREG eneral EquationsWe shall consider a spherically symmetric, self-gravitating star. All the physical quantities willdepend on two independent variables:radiusandtime, (r, t). First, we shall derive all the equationsof STELLAR STRUCTURE in a General , non spherical case, but very quickly we shall restrict ourselves tothe spherically symmetric microscopic properties of matter at any given point may be described with density , tem-peratureT, and chemical composition, the abundances of various elementsXi, withi= 1,2, as many values as there are elements. All thermodynamic properties and transport coeffi-cients are functions of ( , T, Xi). In particular we have: pressureP( , T, Xi), internal energy perunit volumeU( , T, Xi), entropy per unit massS( , T, Xi), coefficient of thermal conductivity perunit volume ( , T, Xi), and heat source or heat sink per unit mass ( , T, Xi).

structure equations are incomplete. They have to be supplemented with a set of equations describing the nuclear reaction network, i.e. providing ∂Xi/∂t as a function of ρ,T,Xj. This will introduce a new time dependence, with its accompanying nuclear time scale. There is another problem with our equations.

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