Hyperons in the nuclear pasta phase

We have investigated under which conditions hyperons (particularly $\mathrm{\Lambda }\mathrm{s}$ and ${\mathrm{\Sigma }}^{-}\mathrm{s}$) can be found in the nuclear pasta phase. As the density and temperature are larger and the electron fraction is smaller, the probability is greater that these particles appear, but always in very small amounts. $\mathrm{\Lambda }$ hyperons only occur in gas and in smaller amounts than would occur if matter were homogeneous, never with abundancies above ${10}^{-5}$. The amount of ${\mathrm{\Sigma }}^{-}$ in the gas is at least two orders of magnitude smaller and can be disregarded in practical calculations.

Figure 1

Free energy vs baryon density for homogeneous matter (dotted line) and for the pasta phase (solid line) for $T=10$ MeV and $Y_e=0.3$.

Figure 2

$\mathrm{\Lambda }$ fractions obtained with with $\rho =0.05{\mathrm{fm}}^{-3}$ as function of (a) the charge fraction at $T=10$ MeV and (b) the temperature with $Y_e=0.3$.

Figure 3

$\mathrm{\Lambda }$ fraction as a function of (a) temperature in the clustered (red) and gas (black) phases; (b) electron fraction; (c) density under the conditions that predict fractions above ${10}^{-7}$. In panel (a), to improve the visibility, the temperature of the clusters was shifted to the right by $\mathrm{\Delta }T=0.1$ MeV. In panels (b) and (c), only the $\mathrm{\Lambda }$ fractions in the clustered phase are shown, and temperature (in MeV) is indicated by a color index.

Figure 4

$\mathrm{\Lambda }$ fraction as a function of the number of nucleons in the heavy clusters under the conditions that predict fractions above ${10}^{-7}$. The temperature (in MeV) is indicated by a color index.

Figure 5

Hyperon fractions obtained with $\rho =0.05{\mathrm{fm}}^{-3}$ as function of (a) the charge fraction at $T=10$ MeV and (b) $Y_{\mathrm{\Sigma }}$ obtained as a function of the temperature with $Y_e=0.3$. In panel (c) the fractions of $\mathrm{\Lambda }\mathrm{s}$ and ${\mathrm{\Sigma }}^{-}\mathrm{s}$ are given as a function of temperature for a range of densities between 0.015 and 0.035 ${\mathrm{fm}}^{-3}$ and electron fraction $Y_e$ between 0.15 and 0.5. Blue lines refer to $\mathrm{\Sigma }\mathrm{s}$ and red lines to $\mathrm{\Lambda }\mathrm{s}$.