Simulating the Classical and Relativistic Equation of State of the Stars upon Variation of the Electron to Baryon Ratio

摘要

The stability of the stars is sustained through the competition between fermionic Pauli pressure and the gravitational attraction of their own masses, as expressed by the hydrodynamic equilibrium of their constituent particles (the equation of state). As the stars getting older, the composition of the star is changed and dominated by heavy elements due to fusion reaction inside the stars. This compositional change will affect the mass and radius of the star. In this paper we discussed the equation of state of the stars classically and, relativistically upon variation of electron to baryon ratio or the Y_e (Y_e=Z/A). By solving the polytropic equation of classical and relativistic star using fourth order Runge-Kutta method, we were able to describe the mass-radius relationship of the stars from extremely low to high electron content. Including a "simplified version of neutron stars" which is assumed to have Ye=0.10. It was also found that a numerical trick is needed in order to solve the polytropic equation using a MATLAB program. Overall the results state that the decreasing value of Ye will result in the decreasing value of the mass and radius of the stars, but increasing density of the stars.