On the mass-radius relation for neutron stars

Abstract

The classical equation of state for a nonrelativistically degenerate gas containing free fermions gives an upper limit to the radius of a neutron star while the Schwarzschild radius gives the lower limit. The lower mass limit for a neutron star is given by the Oppenheimer-Volkoff solution. These three curves define a triangular region in the mass-radius plane which is available for a real neutron star. If the equation of state for interacting neutrons is represented by a polytropic relation, the region where neutron stars would be found can be delimited. Realistic values of the polytropic index give a mass between 1.8 and 2.8 M_⊙ and radius between 10 and 11 km for the neutron star.