Neutron star, $\beta$-stable ring-diagram equation of state and Brown-Rho scaling

TL;DR

This paper calculates neutron star properties using a ring-diagram EOS derived from realistic NN interactions, and improves results by incorporating Brown-Rho scaling to account for medium effects on meson masses.

Contribution

It introduces medium corrections based on Brown-Rho scaling into the ring-diagram EOS, enhancing the accuracy of neutron star property predictions.

Findings

Initial models underestimate neutron star masses and radii.

Medium corrections increase predicted neutron star mass to about 1.8 solar masses.

Mass-radius trajectories from different potentials largely overlap.

Abstract

Neutron star properties, such as its 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 NN interactions $V_{low-k}$. Several 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 $\beta$-stable neutron star are determined from the chemical potential conditions $\mu_n-\mu_p = \mu_e = \mu_\mu$. The neutron star masses, radii and moments of inertia given by the above potentials all tend to be too small compared with the accepted values. Our results are largely improved with the inclusion of medium corrections based on Brown-Rho scaling where the in-medium meson masses, particularly those of $\omega$, $\rho$ and $\sigma$, are slightly decreased compared with their in-vacuum values. Representative results using such medium corrected interactions are neutron star mass $M\sim 1.8 M_{\odot}$, radius $R\sim 9$ km and moment of inertia $\sim 60 M_{\odot}km^2$. The mass-radius trajectories given by the above four realistic NN potentials are by and large overlapping.