Neutron star and $\beta$-stable EOS with Brown-Rho scaled low-momentum NN interactions

Neutron star properties, such as its mass, radius, and moment of inertia, are calculated by solving the Tolman-Oppenheimer-Volkov equations using the ring-diagram equation of state (EOS) obtained from realistic low-momentum NN interactions $V_{low-k}$. Several NN potential models (CDBonn, Argonne, Nijmegen) have been employed to calculate the ring-diagram EOS where pphh ring diagrams are summed to all orders. The proton fraction for a $\beta$-stable neutron star is determined from the chemical potential condition $\mu_n-\mu_p=\mu_e$. The neutron star masses and radii given by the above potentials alone both tend to be about $30\%$ too small compared with accepted values. Our results are largely improved with the inclusion of medium corrections based on Brown-Rho scaling where the in-medium meson masses, particulaly those of $\omega$, $\rho$ and $\sigma$, are slightly decreased compared with their in-vacumn values. Initial results using such medium corrected $V_{low-k}$ are neutron star mass $M\sim 1.6 M_{sun}$ and radius $R\sim 8$ km. Effects from superconducting neutron EOS are discussed.