Light clusters, pasta phases, and phase transitions in core-collapse supernova matter

The pasta phase in core-collapse supernova matter (finite temperatures and fixed proton fractions) is studied within relativistic mean-field models. Three different calculations are used for comparison: the Thomas–Fermi, the coexisting phases, and the compressible liquid drop approximations. The effects of including light clusters in nuclear matter and the densities at which the transitions between pasta configurations and to uniform matter occur are also investigated. The free energy, pressure, entropy, and chemical potentials in the range of particle number densities and temperatures expected to cover the pasta region are calculated. Finally, a comparison with a finite-temperature Skyrme–Hartree–Fock calculation is drawn.

Figure 1

Free energy per baryon as a function of the density for the FSU interaction, $y_p=0.3$, for (a) $T=4$ MeV and (b) 8 MeV. Results are shown with pasta (within CP, CLD, and TF approaches) and for homogeneous matter, and including (for homogeneous matter and pasta within CP) or not clusters. The effect of these aggregates are only seen for very small densities (insets).

Figure 2

Total pressure as a function of the baryonic chemical potential for the FSU interaction, $y_p=0.3$, for (a) $T=4$ MeV and (b) 8 MeV. Results with pasta are shown (within CP, CLD and TF approaches) and for homogeneous matter, and including (for homogeneous matter and pasta within CP) or not clusters.

Figure 3

Total pressure as a function of the density for the FSU interaction, $y_p=0.3$, for (a) $T=4$ and (b) 8 MeV. Results are shown with and without pasta, and including or not clusters. The effect of these aggregates are only seen for very small densities (insets).

Figure 4

(a) Fractions of the nucleons and clusters and (b) chemical potentials of the nucleons as a function of the density for the FSU interaction, $y_p=0.3$, and $T=4$ MeV, for homogeneous matter with and without clusters (HMwC and HM).

Figure 5

Pressure as a function of the density for the FSU interaction, $y_p=0.3$, and (a) $T=4$ MeV and (b) 8 MeV. Homogeneous matter (HM; solid), CP (dashed line), CLD (dash-dot), and TF (open circles) results are shown for the baryonic (red) and electronic (blue) components.

Figure 6

Neutron chemical potential as a function of the density for the FSU interaction, $y_p=0.3$, and (a) $T=4$ MeV and (b) 8 MeV. Results with and without pasta, and including or not clusters, are shown. The effect of these aggregates are only seen below $0.01 {\mathrm{fm}}^{-3}$.

Figure 7

Proton chemical potential as a function of the density for the FSU interaction, $y_p=0.3$, and (a) $T=4$ MeV and (b) 8 MeV. Results are shown with and without pasta, and including or not clusters. The effect of these aggregates are only seen below $0.01 {\mathrm{fm}}^{-3}$.

Figure 8

The ${\mu }_p+{\mu }_e$ chemical potential as a function of the density for the FSU interaction, $y_p=0.3$, and (a) $T=4$ MeV and (b) 8 MeV. Results are shown with and without pasta, and including or not clusters. The effect of these aggregates are only seen for very small densities.

Figure 9

Baryonic chemical potential as a function of the density for the FSU interaction, $y_p=0.3$, and (a) $T=4$ MeV and (b) 8 MeV. Results are shown with and without pasta, and including or not clusters. The effect of these aggregates are only seen for very small densities.

Figure 10

Total entropy per baryon as a function of the density for the FSU interaction, $y_p=0.3$, and (a) $T=4$ MeV and (b) 8 MeV. Results are shown with and without pasta, and including or not clusters. The effect of these aggregates are only seen for very small densities.

Figure 11

Crust-core transition densities, normalized to the nuclear saturation density ${\rho }_0$, as a function of the temperature, for the 3D-HFEOS (upward triangles) calculation and the ${\mathrm{SkM}}^{*}$ (green), SLy4 (pink), SQMC700 (blue), NRAPR (yellow) models, and the Thomas–Fermi (diamonds) calculation for the FSU (red) and TW (gray) models, and the CP (circles), and CLD (squares) results for the FSU (red) model. The proton fraction is fixed to 0.3.

Figure 12

Pasta phases for the FSU interaction within the (a) TF, (b) CP, and (c) CLD calculations for several temperatures. The proton fraction is fixed at 0.3.

Figure 13

Pasta phases for the TW interaction within the TF calculation for several temperatures. The proton fraction is fixed at 0.3 (data taken from [26]).