The equation of state for nucleon matter and neutron star structure

TL;DR

The paper reconstructs the neutron-star EOS by combining state-of-the-art nuclear forces (Argonne $v_{18}$ NN interaction and Urbana IX three-nucleon force) with variational chain summation, explicitly incorporating relativistic boost corrections and exploring quark-matter admixtures via the bag model. It finds that boost corrections raise the NS mass limit from $\sim 1.67\,M_\odot$ to $\sim 1.80\,M_\odot$ without TNI and to $\sim 2.20\,M_\odot$ with UIX, while the presence of quark admixtures can reduce the maximum mass to about $2.02\,M_\odot$ (for $B=200$ MeV fm$^{-3}$) or $1.91\,M_\odot$ (for $B=122$ MeV fm$^{-3}$). The work also identifies a phase transition to a neutral pion condensed high-density phase and examines the impact of mixed phases on composition and the adiabatic index $\Gamma$, as well as the potential implications for neutron-star cooling and stability. Overall, the results constrain the high-density EOS and connect microscopic nuclear interactions to macroscopic NS properties, including the possibility of quark admixtures and the limits imposed by causality and incompressibility.

Abstract

Properties of dense nucleon matter and the structure of neutron stars are studied using variational chain summation methods and the new Argonne v18 two-nucleon interaction. The neutron star gravitational mass limit obtained with this interaction is 1.67 M_{solar}. Boost corrections to the two-nucleon interaction, which give the leading relativistic effect of order (v/c)^2, as well as three-nucleon interactions, are also included in the nuclear Hamiltonian. Their successive addition increases the mass limit to 1.80 and 2.20 M_{solar}. Hamiltonians including a three-nucleon interaction predict a transition in neutron star matter to a phase with neutral pion condensation at a baryon number density of 0.2 fm^{-3}. We also investigate the possibility of dense nucleon matter having an admixture of quark matter, described using the bag model equation of state. Neutron stars of 1.4 M_{solar} do not appear to have quark matter admixtures in their cores. However, the heaviest stars are predicted to have cores consisting of a quark and nucleon matter mixture. These admixtures reduce the maximum mass of neutron stars from 2.20 to 2.02 (1.91) M_{solar} for bag constant B = 200 (122) MeV/fm^3. Stars with pure quark matter in their cores are found to be unstable. We also consider the possibility that matter is maximally incompressible above an assumed density, and show that realistic models of nuclear forces limit the maximum mass of neutron stars to be below 2.5 M_{solar}. The effects of the phase transitions on the composition of neutron star matter and its adiabatic index are discussed.

Figures (21)

• Figure 1: Central and tensor healing distances ($d_c$ and $d_t$), for SNM and PNM, with A18 interaction alone (upper graph), and with A18+UIX interaction (lower graph.)
• Figure 2: The energy per nucleon, $E(\rho)$, of SNM for various interaction models.
• Figure 3: The energy per nucleon, $E(\rho)$, of PNM for various interactions models.
• Figure 4: Kinetic and interaction energies in A18+$\delta v$+UIX$^*$ model of SNM.
• Figure 5: Kinetic and interaction energies in A18+$\delta v$+UIX$^*$ model of PNM.