Nuclear Pasta and Crustal Quasi-Periodic Oscillations in Neutron Star

Abstract

We investigate the impact of nuclear pasta on crustal structure and torsional oscillations using a Bayesian ensemble of unified neutron-star equations of state based on relativistic mean-field models constrained by nuclear experiments, empirical saturation properties, chiral effective field theory, and multimessenger observations. For each posterior sample, we compute the pasta sequence within a compressible liquid-drop model and quantify the onset density, thickness, and mass fraction of the pasta layers. We show that the appearance and extent of nuclear pasta are primarily controlled by the symmetry-energy slope parameter $L$. While spherical and rod-like pasta configurations are present for all equations of state, only a small fraction of the posterior supports slab, tube, or bubble geometries. The transition from spherical nuclei to rods is tightly constrained to occur at a density of $ρ_{\rm sr} = 0.0588^{+0.0045}_{-0.0065}\,\mathrm{fm^{-3}}$. We further predict that the nuclear pasta layer occupies a relative radial thickness of $ΔR_{\rm pasta}/ΔR_{\rm c} = 0.140^{+0.025}_{-0.036}$ and contributes a relative mass fraction of $ΔM_{\rm pasta}/ΔM_{\rm c} = 0.475^{+0.071}_{-0.113}$. Using the resulting crust models, we present the first quasi-periodic oscillations (QPOs) analysis based on a Bayesian posterior ensemble of neutron-star equations of state and systematically assess their compatibility with observed low-frequency quasi-periodic oscillations. We find that the predicted QPO frequencies are strongly correlated with the curvature of the symmetry energy evaluated at sub-saturation density, $K_{\rm sym}(ρ_0/2)$, and that uncertainties in the equation of state translate into a range of angular indices $\ell$ consistent with the observed frequencies.

Figures (9)

• Figure 1: Posterior distributions of the transition densities between different nuclear pasta geometries obtained within the CLDM framework using RMF parameter sets drawn from the Bayesian posterior. The violin plots summarize the probability distributions of the transition densities between successive geometries, with the width indicating the relative posterior weight.
• Figure 2: Correlation between the appearance of nuclear pasta geometries and the symmetry-energy parameters evaluated at half the saturation density, $L(\rho_0/2)$, $K_{\mathrm{sym}}(\rho_0/2)$, and $J(\rho_0/2)$. The equations of state are classified into three categories, guided by Fig. \ref{['fig:pasta_posterior']}: models exhibiting only spherical nuclei and cylindrical rods; models that additionally favor the slab geometry; and models that predict further pasta geometries beyond slabs, including tubes and bubbles.
• Figure 3: Corner plot showing the joint posterior distributions of the crust--core transition pressure and chemical potential, $P_t$ and $\mu_t$, the relative pasta thickness and mass fractions, $\Delta R_{\rm pasta}/\Delta R_c$ and $\Delta M_{\rm pasta}/\Delta M_c$, and the symmetry-energy slope and curvature evaluated at sub-saturation density, $L(\rho_0/2)$ and $K_{\rm sym}(\rho_0/2)$.
• Figure 4: Posterior distributions of the shear modulus $\mu$ and the corresponding shear-wave speed $v_s$ throughout the neutron-star crust. For each equation of state drawn from the Bayesian posterior, the shear modulus is computed using Eq. (\ref{['eq:shearmodulus']}) for the spherical nuclear lattice and is subsequently modified according to Eq. (\ref{['eq:mubar']}) to account for the progressive reduction of rigidity in the pasta phases. The color coding indicates the value of the symmetry-energy slope parameter $L$ evaluated at half the saturation density, $L(\rho_0/2)$.
• Figure 5: Left panel: Fundamental crustal torsional oscillation frequencies ($n=0$, $\ell=2$) as a function of neutron-star mass, shown for models with and without nuclear pasta. Right panel: Posterior probability distributions of the fundamental crustal frequency for different neutron-star masses, comparing cases with nuclear pasta included and neglected. The black dotted line indicates the lowest-frequency QPO observed in SGR 1806$-$20. The blue and red lines represent the average QPO frequencies for the cases without pasta and with pasta, respectively.