Effect of topological defects on “nuclear pasta” observables

Background: The “pasta” phase of nuclear matter may play an important role in the structure and evolution of neutron stars. Recent works suggest nuclear pasta has a high resistivity which could be explained by the presence of long-lived topological defects. The defects act as impurities that decrease thermal and electrical conductivity of the pasta.

Purpose: To quantify how topological defects affect transport properties of nuclear pasta and estimate this effect using an impurity parameter $Q_{\text{imp}}$.

Methods: Contrast molecular dynamics simulations of up to 409 600 nucleons arranged in parallel nuclear pasta slabs (perfect pasta) with simulations of pasta slabs connected by topological defects (impure pasta). From these simulations we compare the viscosity and heat conductivity of perfect and impure pasta to obtain an effective impurity parameter $Q_{\text{imp}}$ due to the presence of defects.

Results: Both the viscosity and thermal conductivity calculated for both perfect and impure pasta are anisotropic, peaking along directions perpendicular to the slabs and reaching a minimum close to zero parallel to them. In our 409 600 nucleon simulation topological defects connecting slabs of pasta reduce both the thermal conductivity and viscosity on average by about 37%. We estimate an effective impurity parameter due to the defects of order $Q_{\text{imp}}\sim 30$.

Conclusions: Topological defects in the pasta phase of nuclear matter have an effect similar to impurities in a crystal lattice. The irregularities introduced by the defects reduce the thermal and electrical conductivities and the viscosity of the system. This effect can be parametrized by a large impurity parameter $Q_{\text{imp}}\sim 30$.

Figure 1

Charge density isosurfaces of runs with 51 200, 76 800, 102 400, and 204 800 nucleons for systems with mean density $n=0.05{\mathrm{fm}}^{-3}$, temperature $kT=1.0\mathrm{MeV}$, and proton fraction $Y_p=0.40$. The system with 409 600 nucleons produced defects very similar to the 204 800 nucleon simulation and is not shown. The first three columns show the same impure pasta configuration seen from three different angles that facilitate the view of the defects. The last column shows the final configuration of the perfect pasta simulation. Golden surfaces represent isosurfaces of charge density $n_{\mathrm{ch}}=0.03{\mathrm{fm}}^{-3}$, while the cream color shows regions such that $n_{\mathrm{ch}}>0.03{\mathrm{fm}}^{-3}$. The figures were generated with ParaView software [32].

Figure 2

(a) Average mean curvature $B/A$ and (b) average Gaussian curvature $\chi /A$ as a function of time for impure pasta simulations. The curvatures for perfect pasta quickly reach values close to zero and, thus, are not shown.

Figure 3

Comparison of structure factor $S\left(\mathit{q}\right)$ for (a) neutrons and (b) protons for $\theta$ in three ranges: $0^{\circ }\le \theta \le 4^{\circ }$ (solid black lines), ${43}^{\circ }\le \theta \le {47}^{\circ }$ (red short dashed lines), and ${86}^{\circ }\le \theta \le {90}^{\circ }$ (blue long dashed lines). Thin lines are for simulation of perfect plates while thick lines are for simulations of impure pasta.

Figure 4

Heat map of proton structure factor $S_p\left(\mathit{q}\right)$ as a function of momentum transfer $q=\left|\mathit{q}\right|$ and angle $\theta$ given by Eq. (9) for pasta configurations (a) with defects and (b) without defects. Values of ${log}_{10}{S}_p\left(\mathit{q}\right)$ were limited to the range $-1$ to 1 because very few points lie outside this range.

Figure 5

Comparison of (a) heat conductivity $\kappa$ and (b) viscosity $\eta$ for the 409 600-nucleon simulations for the pasta phases with defects (perfect pasta, dashed blue lines) and without defects (impure pasta, solid black lines) averaged over directions that form an angle $\theta$ with the vector ${\mathit{q}}^{\prime }$ perpendicular to the pasta slabs.