SU(3) parity doubling in cold neutron star matter

We present a phenomenological model to investigate the chiral phase transition characterized by parity doubling in dense, beta equilibrated, cold matter. Our model incorporates effective interactions constrained by SU(3) relations and considers baryonic degrees of freedom. By constraining the model with astrophysical data and nuclear matter properties, we find a first-order phase transition within realistic values of the slope parameter L. The inclusion of the baryon octet and negative parity partners, along with a chiral-invariant mass $m_0$, allows for a chiral symmetric phase with massive hadrons. Through exploration of parameter space, we identify parameter sets satisfying mass and radius constraints without requiring a partonic phase. The appearance of the parity partner of the nucleon, the N(1535) resonance, suppresses strangeness, pushing hyperonization to higher densities. We observe a mild first-order phase transition to the chirally restored phase, governed by $m_0$. Our calculations of surface tension highlight its strong dependence on $m_0$. The existence of mixed phases is ruled out since they become energetically too costly. We compare stars with metastable and stable cores using both branches of the equation of state. Despite limited lifespans due to low surface tension values, phase conversion and star contraction could impact neutron stars with masses around 1.3 solar masses or more. We discuss some applications of this model in its nonzero temperatures generalization and scenarios beyond beta equilibrium that can provide insights into core-collapse supernovae, protoneutron star evolution, and neutron star mergers. Core-collapse supernovae dynamics, influenced by chiral symmetry restoration and exotic hadronic states, affect explosion mechanisms and nucleosynthesis.

Figure 1

From left to right the parameter space for $L=65$, 70 and 80 MeV. In all panels the blue region corresponds to parameters that satisfy the astrophysical constraints, the red region corresponds to parameters that lead to crossovers. The gray region leads to a unstable vacuum potential with $a_4<0$. The asterisks mark the sample sets of parameters of Table 1.

Figure 2

Scalar condensate as a function of baryon chemical potential for the four parameter choices of Table 1. Solid (Dashed) lines correspond to stable (metastable) solutions in each case.

Figure 3

The surface tension as a function of $m_0$ in the domain wall setup for both lepton chemical potentials at the phase transition. The region shaded in yellow corresponds to the values of the invariant mass that satisfy astrophysical constraints. On the other hand, the region shaded in blue indicates values of $m_0$ for which nuclear matter exists solely as a metastable solution and the chirally broken phase used in the surface tension calculation is the vacuum phase.

Figure 4

Surface tension of bubbles in the spinodal region for $m_0=250$, 350, 450 MeV. Red squares mark the corresponding domain wall solution at the phase transition.

Figure 5

Free energy densities of mixed phases (purple curve) and homogeneous phases (red curve) relative to the Gibbs constructed solutions (black horizontal line) for $\mathrm{\Sigma }=0.32\mathrm{MeV}/{\mathrm{fm}}^2$. The dotted line marks the critical baryon chemical potential.

Figure 6

Particle fractions for $M_0/M_N=0.65$ and $m_0=460\mathrm{MeV}$. On the left panel, parity partners are decoupled and matter consists solely of the baryon octet and leptons. On the right panel all parity partners are included. The blue band represents the discontinuity associated with the phase transition, while the red vertical lines indicate the maximum density reached within the interiors of the most massive stable stars built using the respective equations of state.

Figure 7

Comparing parity doubling and hyperonization effects on the EoS. Left panel: EoS for nucleons and N(1535) states, revealing pressure reduction with parity doubling onset due to increased degrees of freedom post-transition. Parity doubling maintains consistent EoS slope through identical vector meson coupling. Right panel: Hyperonization-induced softening, stronger with rising strange baryon presence. Both positive and negative parity baryons were included. Weak hyperon-vector coupling eases repulsion, lowering pressure and speed of sound. All EoS were computed for the same parameters and couplings.

Figure 8

Mass-radius diagrams from EoS in Fig. 7. Gray ellipses: one-sigma confidence NICER radii measurements. Black bars: radii at 1.4 and 2.0 solar masses. Left: softening due to parity doubling, affecting larger stars; minimal impact on 1.4 solar mass stars. All curves stay NICER data compatible. Right: hyperonization across baryon octet, both parities. Hyperons at high densities impact $>2.0$ solar mass stars, suggesting small hyperonization core region.

Figure 9

Y-axis: $g_{i,\omega }\omega +g_{i,\rho }\rho +g_{i,\varphi }+{\mu }_{i,\text{charge}}$, with $i=n,p,\mathrm{\Sigma }$. A vertical red line indicates the maximum density achieved in the most massive stable star. Additionally, a vertical dotted line represents the onset of the ${\mathrm{\Sigma }}^{-}$ baryon, the sole strange baryon onset in our model. The plotted quantity serves to quantify the increased repulsion within the system as the number of the $i$th species is elevated for a given density.

Figure 10

Left panel: mass-radius relations for the stable and metastable branches, distinguished by the orange and blue curves, respectively. The shaded orange band represents the mass range within which both configurations coexist. The gray ellipses correspond to constraints from NICER with black bars marking radii of 1.4 and 2.0 solar mass stars. Right panel: baryon density vs. star radius for stars with an identical baryonic mass of 1.3 solar masses. These stars are built using solutions from both branches of the equation of state, resulting in distinct density-radius profiles at the core.

Figure 11

Gravitation mass (left panel) and radius (right panel) for star configurations with the same baryonic mass. Both branches correspond to the metastable and stable EoS obtained for parameters $M_0/M_N=0.65$ and $m_0=460\mathrm{MeV}$.