Equation of state and thickness of the inner crust of neutron stars

The cell structure of $\beta$-stable clusters in the inner crust of cold and warm neutron stars is studied within the Thomas–Fermi approach by using relativistic mean-field nuclear models. The relative size of the inner crust and the pasta phase of neutron stars is calculated, and the effect of the symmetry energy slope parameter $L$ on the profile of the neutron star crust is discussed. It is shown that, while the size of the total crust is mainly determined by the incompressibility modulus, the relative size of the inner crust depends on $L$. It is found that the inner crust represents a larger fraction of the total crust for smaller values of $L$. Finally, it is shown that, at finite temperature the pasta phase in $\beta$-equilibrium matter essentially melts above $5\text{to}6$ MeV, and that the onset density of the rod-like and slab-like structures does not depend on the temperature.

Figure 1

(top panel) Crust (full symbols) and inner-crust (empty symbols) thickness. (bottom panel) Thickness of the nondroplet pasta (ndpasta; full symbols) and the slab (empty symbols) phases. The symbol shape identifies the star mass: $1M_{\odot }$ (upward triangles), $1.44M_{\odot }$ (circles), $1.6M_{\odot }$ (downward triangles), and maximum mass (squares).

Figure 2

(top panel) Fraction of the crust occupied by the the inner crust. (middle panel) Fraction of the inner crust occupied by the nondroplet pasta (ndpasta) phase. (bottom panel) Fraction of the nondroplet pasta phase occupied by the slab phase. The symbol shapes have the same meaning as in Fig. 1.

Figure 3

Correlation between the inner crust thickness and the ratio $E_{\mathrm{sym}}/K_0$ for star with $M=1M_{\odot },1.44M_{\odot },1.6M_{\odot }$. The slope of the three straight lines is similar $\sim -7.6\pm 1.95$ km.

Figure 4

Profiles of neutron stars with a mass equal to $1M_{\odot },1.44M_{\odot },1.6M_{\odot }$ and the maximum mass, for different nuclear models. The symbols stay at the the BPS-droplet, droplet-rod, rod-slab, slab-homogeneous transition for $1M_{\odot }$ (triangles), $1.44M_{\odot }$ (circles), $1.6M_{\odot }$ (squares), and maximum mass (diamonds). Panels (a) and (b) show the complete profile for NL3 and FSU, respectively. All other panels [(c)–(i)] focus on the crust profile.

Figure 5

(top panel) Density range of the crust as a function of temperature for all models considered in the present study. (middle and bottom panels) Size of the pasta phases versus $T$ for DDME2 and IU-FSU. In these two panels, the dotted (dashed) line represents the transition droplet rod (rod slab).

Figure 6

(top panel) Density range of the crust as a function of temperature for some of the relativistic mean-field models considered in the present study, obtained by using a TF calculation (thin lines) and a DS calculation (thick lines).

Figure 7

Radius of the cells as a function of the temperature at the densities reported at the top of the panels.

Figure 8

Radius of the cells as a function of matter density for the TM1 model within the DS calculation (thick lines) and TF calculation (thin lines).