Stability of stellar structure in non-equilibrium thermodynamics II. C-N-O cycle

A star is an open system which exchanges energy and matter with its surroundings and is also a thermodynamic system far from the equilibrium state. Using Prigogine's stability criterion of excess entropy production in non-linear and non-equilibrium thermodynamics for such a system, we study the stability of stars located at the upper part of the main sequence, for which the CNO cycle is the main energy source. We assume that the star is in hydrostatic equilibrium, the temperature in the region of nuclear reaction is constant, and convection and diffusion are unimportant. We have obtained five conditions for stability, that is, the formulae (14). The first three conditions are satisfied for a star. But the last two conditions, that is, the formulae (15) and (16), contradict each other. Therefore, the thermodynamic system is unstable. We discuss the reasons for the contradiction, and show that convection, diffusion, temperature variation and the cycle reactions other than the CNO cycle must be considered.