Critical properties of calibrated relativistic mean-field models for the transition to warm, nonhomogeneous nuclear and stellar matter

The critical properties for the transition to warm, asymmetric, nonhomogeneous nuclear matter are analyzed within a thermodynamical spinodal approach for a set of well-calibrated equations of state. It is shown that even though different equations of state are constrained by the same experimental, theoretical, and observational data, and the properties of symmetric nuclear matter are similar within the models, the properties of very asymmetric nuclear matter, such as the one found inside of neutron stars, differ a lot for various models. Some models predict larger transition densities to homogeneous matter for $\beta$-equilibrated matter than for symmetric nuclear matter. Since one expects that such properties have a noticeable impact on the the evolution of either a supernova or neutron star merger, this different behavior should be understood in more detail.

Figure 1

The symmetry energy (top), the symmetry energy slope (middle), and the neutron matter pressure (bottom) as a function of the density for the models under consideration. The gray band in the bottom panel represents the $1\sigma$ constraint from chiral effective field theoretical calculations [48].

Figure 2

The spinodal regions on the $({\rho }_n,{\rho }_p)$ plane for the SFHo model at $T=0,6,10,12$, and 14 MeV. Also shown are the $\beta$-equilibrium EoS at $T=0$ (green solid) and 10 MeV (green dashed), the critical points line (black dashed), and the symmetric matter line (blue solid).

Figure 3

The spinodal sections on the $({\rho }_n,{\rho }_p)$ plane for SFHx (top left), SFHo (top right), FSU2H (bottom left), and FSU2R (bottom right) at $T=0,6,10,12$, and 14 MeV. The SFHx model is the only one that presents an unstable region at $T=15\mathrm{MeV}$. The critical points line is given by the black dashed line.

Figure 4

The spinodal sections on the $({\rho }_n,{\rho }_p)$ plane for TM1 (top) and TM1e (bottom), at $T=0,6,10,12$, and 14 MeV.

Figure 5

The spinodal sections on the $({\rho }_n,{\rho }_p)$ plane for DD2 (top left), DDME2 (top right), D1 (bottom left), and D2 (bottom right) at $T=0,6,10$, and 12 MeV. The smallest unstable regions shown are for $T=13\mathrm{MeV}$ (DD2 and DDME2), 12.2 MeV (D1), and 14 MeV (D2).

Figure 6

The critical density (top) and the critical proton fraction (bottom), as defined in Eq. (29), as a function of the temperature $T$ for some of the models considered in this work.

Figure 7

The transition density, ${\rho }_t$, as a function of the temperature for $\beta$-equilibrium (top) and fixed proton fraction (bottom) matter for some of the models considered in this work.

Figure 8

The different pasta structures from a Thomas-Fermi calculation for cold $\beta$-equilibrium matter for some of the models under consideration. The points represent the transition densities from a thermodynamical spinodal calculation given in Table 2.

Figure 9

The fluctuations $\delta {\rho }_p^{-}/\delta {\rho }_n^{-}$ at $T=0,6$, and 12 MeV as function of the density, with $y_p=0.3$ (thick lines) and 0.05 (thin lines), corresponding to ${\rho }_p/{\rho }_n=0.43$ and 0.05, for DD2 and DDME2.

Figure 10

The fluctuations $\delta {\rho }_p^{-}/\delta {\rho }_n^{-}$ at $T=0$ (left panels) and 12 MeV (right panels) as a function of the density, with $y_p=0.3$ (top panels) and 0.05 (bottom panels), corresponding to ${\rho }_p/{\rho }_n=0.43$ and 0.05, for FSU2R and FSU2H, SFHo and SFHx, DD2 and DDME2, TM1 and TM1e.