Transition density and pressure in hot neutron stars

Using the momentum-dependent effective interaction (MDI) for nucleons, we have studied the transition density and pressure at the boundary between the inner crust and the liquid core of hot neutron stars. We find that their values are larger in neutrino-trapped neutron stars than in neutrino-free neutron stars. Furthermore, both are found to decrease with increasing temperature of a neutron star as well as increasing slope parameter of the nuclear symmetry energy, except that the transition pressure in neutrino-trapped neutron stars for the case of small symmetry energy slope parameter first increases and then decreases with increasing temperature. We have also studied the effect of the nuclear symmetry energy on the critical temperature above which the inner crust in a hot neutron star disappears and found that with increasing value of the symmetry energy slope parameter, the critical temperature decreases slightly in neutrino-trapped neutron stars but first decreases and then increases in neutrino-free neutron stars.

Figure 1

(a) Density dependence of symmetry energies, (b) single-particle potentials in symmetric nuclear matter, and (c) symmetry potentials in cold nuclear matter at ${\rho }_0/2$ for the MDI.

Figure 2

The proton fraction $x_p$ as a function of baryon density $\rho$ from the MDI for both neutrino-trapped matter (a) and neutrino-free matter (b) with different $x$ parameters and at different temperatures. Note that different scales for $x_p$ are used for the neutrino-free and the neutrino-trapped matter.

Figure 3

The instability region and the relative neutron-proton abundance of hot neutron-star matter for different temperatures and nuclear symmetry energy parameters. Regions where they cross each other are shown in the insets at enlarged scales.

Figure 4

Transition densities ${\rho }_t$ (a, c) and pressure $P_t$ (b, d) as functions of the slope parameter $L$ of the symmetry energy at different temperatures for both the neutrino-trapped matter (a, b) and the neutrino-free matter (c, d).

Figure 5

Transition densities ${\rho }_t$ (a, c) and pressure $P_t$ (b, d) as functions of temperature $T$ with $x=0$ and $x=-1$ for both the neutrino-trapped matter (a, b) and the neutrino-free matter (c, d). Note that different scales for temperatures are used for the neutrino-trapped matter and the neutrino-free matter.

Figure 6

Critical temperature $T_c$ as a function of the slope parameters $L$ of the symmetry energy for both the neutrino-trapped matter and the neutrino-free matter.