Formation of Nuclear “Pasta” in Supernovae

In supernova cores, nuclear “pasta” phases such as a triangular lattice of rodlike nuclei and layered structure of slablike nuclei are considered to exist. However, it is still unclear whether or not they are actually formed in collapsing supernova cores. Using ab initio simulations called quantum molecular dynamics, here we solve this problem by demonstrating that a lattice of rodlike nuclei is formed from a bcc lattice by compression. We also find that, in the transition process, the system undergoes a zigzag configuration of elongated nuclei, which are formed by a fusion of two original spherical nuclei.

Figure 1

Snapshots (two-dimensional projection) of the transition process from the bcc lattice of spherical nuclei to the pasta phase with rodlike nuclei. The red particles show protons and the green ones neutrons. In panels (a)–(g) and (h-1), nucleons in a limited region relevant for the two rodlike nuclei in the final state (h) [surrounded by the dotted lines in panel (h-2)] corresponding to eight nuclei in the initial condition (a) are shown for visibility. The vertices of the dashed lines in panels (a) and (d) show the equilibrium positions of nuclei in the bcc lattice and their positions in the direction of the line of sight are indicated by the size of the circles: vertices with a large circle, with a small circle, and those without a circle are in the first, second, and third lattice plane, respectively. The dotted circle in panel (c) show the first pair of nuclei start to touch. The solid lines in panel (d) represent the direction of the two elongated nuclei: they take zigzag configuration. In the final state [(h-1) and (h-2)], almost perfect triangular lattice of rodlike nuclei is obtained. The box sizes are rescaled to be equal in the figures.

Figure 2

Distance $r_{\mathrm{nn}}$ between centers of mass of nearest-neighbor nuclei in the compression process. The blue line shows the mean value $⟨r_{\mathrm{nn}}⟩$ and the blue filled region shows the standard deviation $\Delta r_{\mathrm{nn}}$ of $r_{\mathrm{nn}}$ normalized by $r_{\mathrm{nn}}^{(0)}$ (a value of $r_{\mathrm{nn}}$ for a perfect bcc lattice without displacement of nuclei). Panel (a) is for the isothermal compression at $T=0\mathrm{MeV}$ and panel (b) is for the adiabatic compression starting from $T=0.25\mathrm{MeV}$. The first pair of nuclei touch at a density in the red filled region (corresponding to $r_{\mathrm{nn}}^{(0)}\simeq 18.9\mathrm{fm}$ for both cases) whose width shows its uncertainty.

Figure 3

Snapshots of the transition process in the simulation of isothermal compression at $T<0.01\mathrm{MeV}$ using the simplified model. Starting from the bcc lattice of nuclei (a), the first pairing (b), zigzag pairing around the first pair (c), and finally a zigzag structure (d) are observed. The red particles show the centers of mass of nuclei and the nuclei within the distance less than $0.89r_{\mathrm{nn}}^{(0)}$ are connected by a blue line. Nuclei and connections within only two lattice planes normal to the line of sight are shown.