Crust-core transition of a neutron star: Effects of the symmetry energy and temperature under strong magnetic fields

We study the simultaneous effects of the symmetry energy and temperature on the crust-core transition of a magnetar. The dynamical and the thermodynamical spinodals are used to calculate the transition region within a relativistic mean-field approach for the equation of state. Quantizing magnetic fields with intensities in the range of $2\times {10}^{15}<B<5\times {10}^{16}\mathrm{G}$ are considered. Under these strong magnetic fields, the crust extension is very sensitive to the density dependence of the symmetry energy, and the properties that depend on the crust thickness could set a constraint on the equation of state. It is shown that the effect on the extension of the crust-core transition is washed out for temperatures above ${10}^9$ K. However, for temperatures below that value, a noticeable effect exists that grows as the temperature decreases and which should be taken into account when the evolution of magnetars is studied.

Figure 1

Transition densities, ${\rho }_1$ and ${\rho }_2$ (a) the crust thickness, $\mathrm{\Delta }R$ and $\mathrm{\Delta }{R}^{*}=R\left(\mathrm{tot}\right)-R\left({\rho }_1\right)$ (b) the crust fractional momentum of inertia, calculated with $({\rho }_1,P_1)$ and with $({\rho }_2,P_2)$ (c) versus the symmetry energy slope $L$, obtained at $T=0$ with $B^{*}={10}^3$ (red) and $B=0$ (black solid), within the dynamical spinodal formalism including the AMM. For $L=55$ MeV also $B^{*}={10}^2$ is shown (blue stars). $B=0$ results from the thermodynamical spinodal calculation are also included (black dashed).

Figure 2

The transition densities, ${\rho }_1$ (empty) and ${\rho }_2$ (full) obtained with the $L=55$ MeV model, at $T=0$, for several values of $B^{*}$, and using the thermodynamical spinodal formalism with (squares) and without AMM (circles), and the dynamical spinodal with AMM (triangles).

Figure 3

Details of the crossing of the thermodynamical spinodal with the EoS (black solid line) for $\mathrm{NL}3\omega \rho$ with $B^{*}={10}^3$, considering different temperatures, and taking $\mathrm{AMM}=0$.

Figure 4

The transition densities, ${\rho }_1$ (empty) and ${\rho }_2$ (full), (a), the crust thickness (b), and the momentum of inertial crustal fraction (c) for $\mathrm{NL}3\omega \rho$, with $L=55$ MeV, for several values of $B^{*}$ and $T$.