Abstract
In a previous paper we have shown that the function \Gamma(M, EOS)=\alpha\beta_{GR}/\Lambda^{0.9}(R) is constant (~ 0.4) for pre main-sequence stars (PMS), white dwarfs (WD) and for some neutron star (NS) models, where \alpha_{GR} and \beta_{GR} are the form-factors of the gravitational potential energy and of the moment of inertia. To investigate the structural evolution of another type of celestial bodies, we use the MESA code to extend these calculations to gaseous planets. We show that this function is conserved for all models during the whole planetary evolution and is independent of the planet mass. We also analyse the cases for which this function is not conserved during some stellar evolutionary phases. For the PMS to the WD cooling sequences, we have found a connection between the strong variations of \Gamma(M, EOS) during the intermediary evolutionary phases and the specific nuclear power. A threshold for the specific nuclear power was determined. Below this limit this function is invariant (~ 0.4) for these models, i.e., at the initial and final stages (PMS and WD). Concerning NS, we study the influence of the equation of state (EOS) on this function and refine the exponent of the auxiliary function \Lambda(R) to be ~ 0.8. It is shown that the function \Gamma(M, EOS) is also invariant (~ 0.4) and is independent of the EOS and of the stellar mass. Therefore, we confirm that regardless of the final products of the stellar evolution, NS or WD, they recover the initial value of \Gamma(M, EOS) ~ 0.4 acquired at the PMS. Finally, we have introduced a macroscopic stability "criterion" for neutron star models based on the properties of the relativistic product \alpha\beta_{GR}.
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