Stability of $\beta$-equilibrated dense matter and core-crust transition in neutron stars

The stability of the $\beta$-equilibrated dense nuclear matter is analyzed with respect to the thermodynamic stability conditions. Based on the density dependent M3Y effective nucleon-nucleon interaction, the effects of the nuclear incompressibility on the proton fraction in neutron stars and the location of the inner edge of their crusts and core-crust transition density and pressure are investigated. The high-density behavior of symmetric and asymmetric nuclear matter satisfies the constraints from the observed flow data of heavy-ion collisions. The neutron star properties studied using $\beta$-equilibrated neutron star matter obtained from this effective interaction for a pure hadronic model agree with the recent observations of the massive compact stars. The density, pressure, and proton fraction at the inner edge separating the liquid core from the solid crust of neutron stars are determined to be ${\rho }_t=0.0938 {\mathrm{fm}}^{-3}$, ${\mathrm{P}}_t=0.5006 \mathrm{MeV} {\mathrm{fm}}^{-3}$, and ${\mathrm{x}}_{p\left(t\right)}=0.0308$, respectively.

Figure 1

Plots for pressure $P$ of dense nuclear matter as functions of $\rho /{\rho }_0$. The continuous line represents the pure neutron matter and the dashed line represents the $\beta$-equilibrated neutron star matter. The dotted line represents the same for A18 model using variational chain summation (VCS) of Akmal et al. [42]. The areas enclosed by the continuous and the dashed lines correspond to the pressure regions for neutron matter consistent with the experimental flow data after inclusion of the pressures from asymmetry terms with weak (soft NM) and strong (stiff NM) density dependences, respectively [43].

Figure 2

The $\beta$-equilibrium proton fractions obtained from the nuclear symmetry energy (approx.) and from exact calculations using the DDM3Y interaction are plotted as functions of $\rho /{\rho }_0$.