Neutron stars,β-stable ring-diagram equation of state, and Brown-Rho scaling

Abstract

Neutron star properties, such as mass, radius, and moment of inertia, are calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations using the ring-diagram equation of state (EOS) obtained from realistic low-momentum $\mathit{NN}$ interactions ${V}_{\mathrm{low}--\mathrm{k}}$. Several $\mathit{NN}$ potentials (CDBonn, Nijmegen, Argonne V18, and BonnA) have been employed to calculate the ring-diagram EOS where the particle-particle hole-hole ring diagrams are summed to all orders. The proton fractions for different radial regions of a $\ensuremath{\beta}$-stable neutron star are determined from the chemical potential conditions ${\ensuremath{\mu}}_{n}\ensuremath{-}{\ensuremath{\mu}}_{p}={\ensuremath{\mu}}_{e}={\ensuremath{\mu}}_{\ensuremath{\mu}}$. The neutron star masses, radii, and moments of inertia given by the aforementioned potentials all tend to be too small compared with the accepted values. Our results are largely improved with the inclusion of a Skyrme-type three-body force based on Brown-Rho scalings where the in-medium meson masses, particularly those of $\ensuremath{\omega}$, $\ensuremath{\rho}$, and $\ensuremath{\sigma}$, are slightly decreased compared with their in-vacuum values. Representative results using such medium-corrected interactions are maximum neutron-star mass $M~1.8{M}_{\ensuremath{\bigodot}}$ with radius $R~9$ km and moment of inertia $~60{M}_{\ensuremath{\bigodot}} {\mathrm{km}}^{2}$, values given by the four $\mathit{NN}$ potentials being nearly the same. The effects of nuclei-crust EOSs on the properties of neutron stars are discussed.