Probing the impact of Delta-Baryons on Nuclear Matter and Non-Radial Oscillations in Neutron Stars

TL;DR

This work investigates how heavy baryons, especially $\Delta$-baryons and hyperons, modify neutron-star properties by employing a density-dependent relativistic mean-field framework with the DD-MEX parameterization. It analyzes $\Delta$-admixed matter in both hypernuclear and hyperon-free compositions, computing the equation of state, mass–radius relations, and the non-radial $f$-mode frequencies, and it evaluates the dimensionless tidal deformability $\Lambda$ via $\Lambda = \frac{2}{3} k_2 C^{-5}$ with $C$ as the compactness. Key findings show that $\Delta$-baryons can increase the $f$-mode frequency and decrease $\Lambda$, with the effects strongly controlled by the $\sigma$-$\Delta$, $\omega$-$\Delta$, and $\rho$-$\Delta$ couplings; notably, stronger $\sigma$-$\Delta$ attraction softens the EoS at intermediate densities while $\omega$-$\Delta$ and $\rho$-$\Delta$ repulsion can offset this to maintain compatibility with observations such as NICER and GW constraints. The results illuminate how internal composition and density-dependent couplings shape observable neutron-star signals and offer a route to reconcile hyperon-rich cores with massive NS observations. The study also highlights that $\Delta^-$ is often the most favored nucleation channel under charge neutrality and that a phase-transition scenario to exotic matter may occur if $m_N^\ast$ tends toward zero at high densities.

Abstract

The presence of heavy baryons, such as $Δ$-baryons and hyperons can significantly impact various properties of Neutron Stars (NSs), like oscillation frequencies, dimensionless tidal deformability, mass, and radii. We explored these effects within the Density-Dependent Relativistic Mean Field formalism. Our analysis considered $Δ$-admixed NS matter in both hypernuclear and hyperon-free scenarios, providing insights into particle compositions and their effects on NS properties. Our study of non-radial $f$-mode oscillations revealed a distinct increase in frequency due to the additional baryons. The degree of increase was significantly influenced by the meson-baryon coupling strengths. Notably, the coupling between $Δ$-resonances and $σ$-mesons played a highly influential role. In some cases, it led to an approximately 20\% increase in the $f$-mode oscillation frequency of canonical NSs. These couplings also affect other bulk properties of NSs, including mass, radii, and dimensionless tidal deformability ($Λ$). Comparing our results with available observational data from pulsars (NICER) and gravitational waves (LIGO-VIRGO collaboration), we found strong agreement, particularly concerning $Λ$.

Figures (6)

• Figure 1: Normalized nucleon effective mass as a function of density for hyperon-free $\Delta$-admixed NS matter (upper half) and $\Delta$-admixed hypernuclear matter (lower half). The sub-figures on the left correspond to the combination of $x_{\omega\Delta}=1.0$ and $x_{\rho\Delta} = 0.5$, while the ones on the right correspond to $x_{\omega\Delta}=1.1$ and $x_{\rho\Delta} = 1.5$, respectively. The $\sigma-\Delta$ coupling strength is varied in the range $x_{\sigma\Delta}\in [0.8, 1.2]$ in all the sub-figures (corresponding colour given in the colour-bar on the right). The solid black line in the sub-figures is the $m_N^*/m_N$ of NS matter composed of only nucleons and leptons, whereas the dashed black line is for NS matter containing nucleons, leptons and hyperons.
• Figure 2: Histograms depicting the distribution of the threshold densities of the $\Delta$-baryons in the NS matter. The sub-figures correspond to the different possible combinations of $x_{\omega\Delta}$ and $x_{\rho\Delta}$. The different baryons are represented using the colors in the legend provided in the first sub-figure.
• Figure 3: Similar to figure \ref{['fig:population_ND']} but for $\Delta$-admixed hypernuclear matter.
• Figure 4: Mass-radius curves showing the effect of varying $x_{\sigma\Delta}$ with different combinations of $x_{\omega\Delta}$ and $x_{\rho\Delta}$ for hyperon-free $\Delta$-admixed NS matter (upper half) and $\Delta$-admixed hypernuclear matter (lower half). The solid and dashed black lines represent compositions of NS matter corresponding to nucleons and leptons, and nucleons, leptons and hyperons respectively. The value of $x_{\sigma\Delta}$ taken for each curve is represented by the corresponding colour given in the color-bar on the right. The horizontal green band at the top is the mass constraint obtained from the gravitational wave event GW190814 abbott_gw190814_2020, while the green region with shading located at the bottom left is the constraint obtained from GW170817 abbott_gw170817_2017. The constraints on mass and radius obtained from pulsars is given by the pink region for PSR J0030+0451 from the 2019 NICER data riley_nicer_2019miller_psr_2019, and by the blue region for PSR J0740+6620 from the 2021 NICER data riley_nicer_2021fonseca_refined_2021.
• Figure 5: Dimensionless tidal deformability ($\Lambda$) against NS mass for $\Delta$-admixed NS matter (upper half) and $\Delta$-admixed hypernuclear matter (lower half), showing the effect of varying $x_{\sigma\Delta}$ with different combinations of $x_{\omega\Delta}$ and $x_{\rho\Delta}$. To represent the different $x_{\sigma\Delta}$ values, we use the corresponding color given in the adjoining color-bar. A solid black line is used to represent NS matter containing nucleons and leptons only, whereas the dashed black line is for NS matter containing nucleons, hyperons and leptons only. Observational constraints are represented by the green error-bar and grey shaded patch for GW170817 abbott_gw170817_2017, and the blue error-bar for GW190814 abbott_gw190814_2020.