Hyperon-Induced Inhomogeneous Pion Condensation and Moat Regimes in Neutron Star Cores

Abstract

We perform a stability analysis of the homogeneous ground state of nuclear matter against inhomogeneous perturbations of the pion condensate. In $β$-equilibrium, restricting the baryon species to nucleons only, we observe no instability; however, at high densities, the pseudoscalar density-density correlations assume a moat regime, i.e. a damped oscillatory patterned spatial correlation, which in momentum space appears as a non-zero global minimum for some finite three-momentum. When hyperons are permitted to appear, this minimum can cross down to negative values, which configures an instability towards an inhomogeneous pion condensate which ultimately will affect the equation of state.

Figures (4)

• Figure 1: Densities of each fermion species shown in proportion to the total baryon number. Both plots taken with $m_\sigma = 600$ MeV. On the left we see the result including the full baryon octet and, on the right, we show the species fraction for nucleons only (plus electrons and muons).
• Figure 2: Inverse pion two-point functions for different densities without hyperons. The dotted line shows the first line with a negative inclination at the origin, i.e., the first density to manifest a moat regime $n_B\approx$0.5 fm$^{-3}$.
• Figure 3: Same as Fig. \ref{['fig:pions0']}, now including the full baryon octet. Up till a density of $n_B\approx$0.5 fm$^{-3}$, which is where the moat sets in, matter consists of nucleons only. After that there are deviations from Fig. \ref{['fig:pions0']} and eventually, at a density of $n_B\approx$0.65 fm$^{-3}$, shown in the dashed line, the minima begin to cross zero.
• Figure 4: Isoscalar SDF, including the full baryon octet, in $\beta$-equilibrium.