Mass-Radius diagram for compact stars

Abstract

The compact stars represent the final stage in the evolution of ordinary stars, they are formed when a star ceases its nuclear fuel, in this point the process that sustain its stability will stop. After this, the internal pressure can no longer stand the gravitational force and the star colapses [2]. In this work we investigate the structure of these stars which are described by the equations of Tolman-Openheimer-Volkof (TOV) [1]. These equations show us how the pressure varies with the mass and radius of the star. We consider the TOV equations for both relativistic and non-relativistic cases. In the case of compact stars (white dwarfs and neutron stars) the internal pressure that balances the gravitational pressure is essentialy the pressure coming from the degeneracy of fermions. To have solved the TOV equations we need a equation of state that shows how this internal pressure is related to the energy density or mass density. Instead of using politropic equations of state we have solved the equations numericaly using the exact relativistic energy equation for the model of fermion gas at zero temperature. We obtain results for the mass-radius relation for white dwarfs and we compared with the results obtained using the politropic equations of state. In addition we discussed a good fit for the mass-radius relation.