Neutron stars: From the inner crust to the core with the (extended) Nambu–Jona-Lasinio model

Nucleonic matter is described within an SU(2) extended Nambu–Jona-Lasinio (NJL) model. Several parametrizations with different nuclear matter saturation properties are proposed. At subsaturation, nuclear pasta phases are calculated within two methods: the coexistence-phases approximation and the compressible liquid drop model, with the surface tension coefficient determined using a geometrical approach at zero temperature. A unified equation of state of stellar matter for the inner crust, with the nuclear pasta phases, and the core is calculated. The mass and radius of neutron stars within this framework are obtained for several families of hadronic and hybrid stars. The quark phase of hybrid stars is described within the SU(3) NJL model including a vector term. Stellar macroscopic properties are in accordance with some of the recent results in the literature.

Figure 1

Energy per baryon (a) and energy density (b) versus density, where the two coexistence points are shown, for homogeneous (hm) and nonhomogeneous (nhm) matter.

Figure 2

Symmetric nuclear matter properties as a function of the density for all the models considered in this study.

Figure 3

Symmetry energy, $E_{\mathrm{sym}}$, (a) and (c), and its slope, $L$, (b) and (d), for the models considered in this study.

Figure 4

Pressure as a function of the density for symmetric nuclear matter and for all the models considered in this study. The red region represents the experimental results from Danielewicz et al. [50] and the green region from the KaoS experiment. In the right panel, (b), a Maxwell construction for the eNJL1 and eNJL2 models is also shown.

Figure 5

Pressure as a function of the density for neutron matter for the eNJLx, $\mathrm{eNJLx}\omega \rho \mathrm{y}$, and eNJLx(m)$\sigma \rho \mathrm{y}$ interactions considered in this study. The colored bands are the results from [48] (green) and [49] (gold).

Figure 6

Energy per baryon, and pressure, as a function of the density for the eNJL1 interaction, for $\beta$-equilibrium matter, (c) and (f), $y_p=0.3$, (b) and (e), and $y_p=0.5$, (a) and (d), proton fractions. Results with pasta [within the CP (black dots) and CLD (pink dots) approaches] and for homogeneous matter (red solid line) are shown.

Figure 7

Pasta phases for the eNJL1 (1), $\mathrm{eNJL}1\omega \rho 1$ (2), eNJL3 (3), and $\mathrm{eNJL}3\sigma \rho 1$ (4) interactions within the CP (a) and CLD (b) calculations for $\beta$-equilibrium, $y_p=0.3$, and $y_p=0.5$ matter. The temperature is fixed to 0 MeV.

Figure 8

Mass-radius relation (a) and mass as a function of the central density (b) for the family of hadronic stars that passed the imposed constraints. We have considered pasta in the EOS. The outer crust is given by the BPS EOS. The black dots correspond to the maximum-mass star.

Figure 9

Mass-radius relation for the $\mathrm{eNJL}3\sigma \rho 1$ model, with pasta from a CP (green) and a CLD (blue) calculations in the EOS, and without it (red). The outer crust is given by the BPS EOS. The black dots correspond to the maximum mass star.

Figure 10

Mass-radius relation (a) and mass as a function of the central density (b) for the hybrid stars families. Pasta is included in the hadronic EOS. The black dots correspond to the maximum-mass star, and the dashed lines in the left panel correspond to the mixed hadron-quark phase in the stars.