Thermal fluctuations in nuclear pasta

Despite their astrophysical relevance, nuclear pasta phases are relatively unstudied at high temperatures. We present molecular dynamics simulations of symmetric nuclear matter with several topologies of “lasagna” at a range of temperatures to study the pasta-uniform transition. Using the Minkowski functionals, we quantify trends in the occupied volume, surface area, mean breadth, and Euler characteristic. The amplitude of surface displacements of the pasta increase with temperature which produce short-lived topological defects such as holes and filaments near melting, resulting in power laws for increasing surface curvature with temperature. We calculate the static structure factor and report the shear viscosity and thermal conductivity of pasta, finding that the shear viscosity is minimized at the melting temperature. These results may have implications for the thermoelastic properties of nuclear pasta and finite-temperature corrections to the equation of state at pasta densities.

Figure 1

Faces of our pasta configurations at the lowest temperature studied in this work, $T/T_m=0.70$, effectively our initial conditions. The golden surfaces are isosurfaces of charge density of $n_{\mathrm{ch}}=0.03{\mathrm{fm}}^{-3}$ (i.e., surfaces bounding the region where the protons are most abundant) while the cream fill shows where charge density of $n_{\mathrm{ch}}>0.03{\mathrm{fm}}^{-3}$ within the pasta structure, visible due to the intersection of the pasta structure with the periodic box boundary. Panels (a)–(c) show three orthogonal faces of the simulation with “defects.” The defects consist of a wall of helicoids, seen in (a), connecting the plates; in (b) one can see the axis of the helicoids on the left, highlighted by the arrows. In (c), one can see how the following the helicoids cause the plates to bend up at the periodic boundary on the right, connecting the seemingly distinct plates. These can be compared with the related configuration without defects, which we call “nonparallel,” shown in (d)–(f). In (g) and (h) we show two views of the configuration which is “parallel” with the box, and in (i) we show a configuration above the melting temperature.

Figure 2

Faces of our pasta configurations at a range of temperatures. Top three rows show our “defects,” “nonparallel,” and “parallel” configurations at three temperatures (columns). The bottom row shows simulations above the melting temperature. See the SM for animations.

Figure 3

The four normalized Minkowski functionals for our simulations. Clockwise from top right: The occupied volume fraction, surface area density, Euler characteristic, and mean breadth. Note the sign on the units of the Euler characteristic.

Figure 4

Radial distribution functions $g\left(r\right)$ as function of temperature for (top) neutron-proton correlations, (center) neutron-neutron correlations, and (bottom) proton-proton correlations. We normalize to 1 at the position of the first peak which occurs at 1.9 fm for $g_{np}\left(r\right)$ and at 2.5 fm for both $g_{nn}\left(r\right)$ and $g_{pp}\left(r\right)$. The inset in $g_{np}\left(r\right)$ shows the approximate 0.1 fm broadening of the first peak, discussed in text. Below $T_m$ we use configurations from our “parallel” simulations. Note the similarity between $g_{nn}\left(r\right)$ and $g_{pp}\left(r\right)$ which may be due to the equal numbers of protons and neutrons in these simulations (compare to Fig. 2 in Ref. [19]).

Figure 5

Angle-averaged proton structure factor $S_p\left(q\right)={\langle S_p\left(\mathit{q}\right)\rangle }_q$ for the range of temperatures studied, smoothed with Bragg peaks removed; (top) configurations with defects, (middle) nonparallel plates, and (bottom) parallel plates. Lines $T/T_m>1$ are the same in all three plots. Neutron structure factors $S_n\left(q\right)$ are nearly identical, following from similarities in $g_{nn}\left(r\right)$ and $g_{pp}\left(r\right)$ in Fig. 4.

Figure 6

Top: Angle-averaged proton static structure factor $S_p\left(q\right)={\langle S_p\left(\mathbf{q}\right)\rangle }_q$ (solid black) bounded by the maximum and minimum in $S_p\left(q\right)$ for each $q=\left|\mathbf{q}\right|$ for our simulations with (left) defects, (center) nonparallel plates, and (right) parallel plates. Bottom: Heat map of proton structure factor $S_p\left(q\right)$ as a function of momentum transfer $q=\left|\mathbf{q}\right|$ and angle $\theta$.

Figure 7

Top: Angle-averaged proton static structure as in Fig. 6 for our disordered configurations above the melting temperature and (bottom) heat map of proton structure factor $S_p\left(q\right)$ as a function of momentum transfer $q=\left|\mathbf{q}\right|$ and angle $\theta$.

Figure 8

Averaged shear viscosity (top) and averaged thermal conductivity (bottom).