Beyond nuclear “pasta” : Phase transitions and neutrino opacity of new “pasta” phases

In this work, we focus on different length scales within the dynamics of nucleons in conditions according to the neutron star crust, with a semiclassical molecular dynamics model, studying isospin symmetric matter at subsaturation densities. While varying the temperature, we find that a solid-liquid phase transition exists, which can be also characterized with a morphology transition. For higher temperatures, above this phase transition, we study the neutrino opacity, and find that in the liquid phase, the scattering of low momenta neutrinos remain high, even though the morphology of the structures differ significatively from those of the traditional nuclear pasta.

Figure 1

Energy as a function of temperature for different densities. We see that there is a discontinuity in the range of $T_l=0.35$ to $T_h=0.65\text{MeV}$, depending on the density, a signal of a first-order phase transition. In the figure, densities range from $\rho =0.03$ and $\rho =0.13{\text{fm}}^{-3}$, increasing $\Delta \rho =0.01{\text{fm}}^{-3}$ upwards.

Figure 2

Lindemann coefficient and energy as a function of temperature for a chosen density $\rho =0.05{\text{fm}}^{-3}$. The sudden change in their value is a signal of a solid–liquid phase transition. We can see that both discontinuities are at the same temperature.

Figure 3

Radial distribution function for different densities, both below and above the transition temperature, and snapshots of the system in the liquid phase. Although the first peaks of the distribution are in the same position for both temperatures, the following peaks, which exhibit a long-range order typical of solids, are only present below the transition temperature.

Figure 4

Euler number and mean breadth for $\rho =0.05{\text{fm}}^{-3}$. We observe a sharp transition for both Minkowski functionals.

Figure 5

Critical temperature as a function of density. We see the overlap between the Minkowski and the Lindeman critical temperatures.

Figure 6

Spatial distribution for $\rho =0.05{\text{fm}}^{-3}$, both above and below the transition temperature. The structures are similar, but much more disordered above the transition.

Figure 7

Peak of $S\left(k\right)$ for low momenta as a function of the temperature, for $\rho =0.05{\text{fm}}^{-3}$. We see two behaviors, for $T<0.5\text{MeV}$ and $T>0.5\text{MeV}$.

Figure 8

Peak of $S\left(k\right)$ for low momenta: zoom into the temperature region between $T=0.5$ and $T=0.7\text{MeV}$. The labels of the different curves correspond to those of the Fig. 9, where we can see that the structures obtained for these runs are different among each other and they yield different absorption peaks for low momenta.

Figure 9

Spatial distribution for $\rho =0.05{\text{fm}}^{-3}$ for different initial conditions at temperature $T=0.6\text{MeV}$. We see that we obtain the usual lasagna, but also intertwined lasagnas and other structures that are not of the usual past type. Despite being different from the usual pasta phases, these shapes have a peak for low momentum in the structure factor. In Fig. 8 we see the corresponding absorption peaks for each structure. The unusual pasta phases show a larger absorption than the usual lasagna in the range of temperatures shown in the figure mentioned above.

Figure 10

Energy distribution for a canonical ensemble. It can be seen that, for $T=0.8\text{MeV}$, all three distributions overlap completely. However, in $T=0.6\text{MeV}$, the histograms, albeit split, still overlap significatively.