Constraints on the inner edge of neutron star crusts from relativistic nuclear energy density functionals

The transition density $n_t$ and pressure $P_t$ at the inner edge between the liquid core and the solid crust of a neutron star are analyzed using the thermodynamical method and the framework of relativistic nuclear energy density functionals. Starting from a functional that has been carefully adjusted to experimental binding energies of finite nuclei, and varying the density dependence of the corresponding symmetry energy within the limits determined by isovector properties of finite nuclei, we estimate the constraints on the core-crust transition density and pressure of neutron stars: $0.086\hspace{0.5em}{\mathrm{fm}}^{-3}⩽n_t<0.090\hspace{0.5em}{\mathrm{fm}}^{-3}$ and $0.3\hspace{0.5em}\mathrm{MeV}\hspace{0.5em}{\mathrm{fm}}^{-3}<P_t⩽0.76\hspace{0.5em}\mathrm{MeV}\hspace{0.5em}{\mathrm{fm}}^{-3}$.

Figure 1

The symmetry energy $E_{\mathrm{sym}}$ as a function of the nucleon density $n$ for various values of the parameter $\langle S_2\rangle$. The symmetry energy at saturation is $a_4=33$ MeV.

Figure 2

The transition density $n_t$ (a) and the transition pressure $P_t$ (b), as functions of $\langle S_2\rangle ,$ for three values of the nuclear matter volume energy coefficient $a_v$.

Figure 3

The transition pressure $P_t$ as a function of the transition density $n_t$. For a fixed value of the symmetry energy at saturation $a_4=33$ MeV and three values of the nuclear matter volume energy coefficient $a_v$, the parameter $\langle S_2\rangle$ is varied in the interval between 27.6 and 28.6 MeV. The resulting constraints of $P_t$ and $n_t$ are plotted in comparison with results obtained using different models (for details see Ref. [43]). The lines $P_t=0.2$ MeV fm${}^{-3}$ and $P_t=0.65$ MeV fm${}^{-3}$ correspond to the measure of the current uncertainty in the density dependence of the symmetry energy [6].

Figure 4

RHB predictions for the differences between neutron and proton rms radii of (a) Sn and (b) Pb isotopes, in comparison with available data [46, 47, 48], for different choices of the symmetry energy at saturation density $a_4$ (in MeV).

Figure 5

The symmetry energy $E_{\mathrm{sym}}$ as a function of the nucleon density $n$ for various values of the symmetry energy at saturation $a_4$. The parameter $\langle S_2\rangle$ (see text) is kept constant at 27.8 MeV.

Figure 6

The transition density $n_t$ (a) and the transition pressure $P_t$ (b), as functions of the symmetry energy at saturation density $a_4$, for three values of the nuclear matter volume energy coefficient $a_v$.

Figure 7

Same as described in the caption to Fig. 3 but for fixed $\langle S_2\rangle =27.8$ MeV and the symmetry energy at saturation in the interval 30 MeV $⩽a_4⩽$ 35 MeV.

Figure 8

The transition density $n_t$ (a) and the transition pressure $P_t$ (b) as functions of the slope parameter $L$.

Figure 9

The transition density $n_t$ as a function of the neutron-skin thickness $R_n-R_p$ of ${}^{208}\mathrm{Pb}$. The values of $n_t$ calculated using the thermodynamical model in the present work (solid line) are compared with those of Ref. [19] dashed line (see text for description).