Topological characterization of neutron star crusts

Neutron star crusts are studied using a classical molecular dynamics model developed for heavy-ion reactions. After the model is shown to produce a plethora of the so-called pasta shapes, a series of techniques borrowed from nuclear physics, condensed matter physics, and topology is used to craft a method that can be used to characterize the shape of the pasta structures in an unequivocal way.

Figure 1

Smörgåsboard of pasta shapes corresponding to the densities shown and to $x=0.5$ and $T=0.1\text{MeV}$.

Figure 2

Temperature evolution of the fragment size distribution obtained from 200 configurations with $x=0.3$ and $\rho \approx {\rho }_0/10$.

Figure 3

Relative abundance of large clusters as a function of density for $x=0.3$ and $0.5$ at $T=0.1\text{MeV}$.

Figure 4

Root-mean-square displacement of the nucleons from their original position as a function of the simulation time steps for systems with $\rho =0.015{\text{fm}}^{-3}$ and $x=0.3$ at the listed temperatures.

Figure 5

Time evolution of the persistency for the listed temperatures as a function of the simulation time steps for $x=0.3$ and $\rho =0.015{\text{fm}}^{-3}$.

Figure 6

Example of the $x$ value ($x=p/A$) of the clusters vs their size, corresponding to systems with $\rho =0.015{\text{fm}}^{-3}$ and $x=0.5$ (top two plots) and $x=0.3$ (bottom four plots) at the temperatures listed.

Figure 7

Examples of the radial correlation function for $x=0.5$, $T=0.1\text{MeV,}$ and various densities. Also shown is the case when nearest neighbors are as probable as second nearest neighbors indicating a lasagna-type structure; $r$ is in femtometers.

Figure 8

Sample transformation of a nuclear structure to a corresponding polyhedron. The structure corresponds to a case with $x=0.5$, $\rho =0.33{\text{fm}}^{-3}$, and $T=0.1\text{MeV}$.

Figure 9

Spatial configurations formed under $T=0.4$ MeV and $\rho =0.045{\text{fm}}^{-3}$ (left) and $T=1.0$ MeV and $\rho =0.072{\text{fm}}^{-3}$ (right), both for $x=0.3$.

Figure 10

Multiplicites corresponding to Fig. 9; although not identical they are very similar.

Figure 11

Euler and curvature of the structures shown in Fig. 9; the difference between the two cases is easy to spot.

Figure 12

Typical artificial “pastas” used to test the classification powers of the Euler-curvature combination. Respectively, they are the “jungle gym” (top left), “lasagnas” (top right), “straight spaghettis” (bottom left), and a “curled spaghetti.”

Figure 13

Systematic classification of the artificial structures in terms of the curvature and Euler number.

Figure 14

Curvature-Euler coordinates of the structures listed in Table . Labels “A,” “a,” “L,” and “t” correspond, respectively, to the initial and final points in the table.