Fluctuations in the nuclear pasta phase

Baryonic matter close to the saturation density is very likely to present complex inhomogeneous structures collectively known under the name of nuclear pasta phase. At finite temperature, the different geometric structures are expected to coexist with potential consequences on the neutron star crust conductivity and neutrino transport in supernova matter. In the framework of a statistical multicomponent approach, we calculate the composition of matter in the pasta phase considering density, proton fraction, and geometry fluctuations. Using a realistic energy functional from relativistic mean-field theory and a temperature- and isospin-dependent surface tension fitted from Thomas-Fermi calculations, we show that different geometries can coexist in a large fraction of the pasta phase, down to temperatures of the order of the crystallization temperature of the neutron star crust. Quantitative estimates of the charge fluctuations are given.

Figure 1

Probability for the pasta structures at proton fractions $Y_p=0.1$ (left) and 0.3 (right) and temperatures $T=5$, 3, 1 MeV plotted with solid, dash-double-dotted, and dashed lines, respectively. Geometries are plotted with different colors: droplets are in magenta, rods in yellow, and slabs in blue. The vertical lines show the transition densities between geometries in the SNA for $T=1$ MeV.

Figure 2

Average linear radius (dashed-dotted) and equilibrium linear radius (colored dashed), as given by Eqs. (29) and (8), for proton fractions $Y_p=0.1$, 0.3, and $T=3$ MeV. The values in the SNA are colored according to the geometry, as described in Fig. 1.

Figure 3

Total (solid line) and orientation-dependent (dashed) average proton number in the cluster for $T=1$ MeV, $Y_p=0.1$ and 0.3. The $x$, $y$, and $z$ axis denote the direction of motion of the probe, and are represented by the colors red, green, and blue, respectively. We assume local domains of different geometries aligned along a common symmetry axis $x$.

Figure 4

Same as Fig. 3 for the proton number variances.