Effect of the equation of state for dilute neutron matter on the composition of the inner crust of neutron stars

The composition of the inner crust of neutron stars is usually studied using phenomenological interactions such as Skyrme energy-density functionals. But most of these functionals do not agree well with ab initio calculations of very dilute neutron matter. In this work, we study the inner crust of neutron stars in the model of phase coexistence of dense neutron-rich nuclear clusters and dilute neutron gas, and we investigate how employing a realistic microscopic equation of state for the neutron gas alters the composition. Our results indicate that, with a functional that reproduces the correct equation of state of neutron matter at moderate densities, one can obtain a good description of the crust even if the functional does not have the correct behavior at extremely low density.

Figure 1

Comparison of low-density neutron-matter EoS obtained from phenomenological Skyrme EDF (SLy4 (orange dashes) [7] and BSk22 (green dash-dot) [8, 9]) with various EoS obtained from realistic $nn$ interactions: third-order BMBPT (blue solid line) [18], MBPT (red stars) [17], and various QMC calculations [14] (green squares), [16] (purple triangle), and [15] (black circles). The vertical axis represents the ground-state energy in units of the energy of the free Fermi gas ($E_{\text{FG}}$), as a function of Fermi momentum ($k_{\text{F}}$).

Figure 2

(a) Comparison of different neutron and proton densities in the liquid and in the gas as functions of the total baryon density, obtained after taking the Skyrme interaction (SLy4) for both the clusters and the gas phase (orange lines), and taking the Skyrme interaction (SLy4) for the clusters and realistic $nn$ interaction (BMBPT3) for the gas phase (blue lines). (b) Corresponding volume fractions of nuclear clusters as functions of total baryon density, (c) proton fraction, and (d) corresponding pressures, including the pressures of nucleons and electrons.

Figure 3

Same as Fig. 2 but for BSk22 interaction instead of SLy4.