$f$-mode oscillations in hot Neutron Stars: Effect of hyperons and neutrino trapping

TL;DR

This study develops a finite-temperature equation of state in a non-linear relativistic mean field framework that consistently includes hyperons and neutrino trapping, enabling systematic variation of nuclear and hypernuclear parameters under multi-disciplinary constraints. Using a Bayesian approach, it generates a large ensemble of hot NS EOSs constrained by $\\chi$EFT, Astrophysical observations, and Heavy Ion Collision data, and computes $f$-mode frequencies in the Cowling approximation to explore how thermal effects and composition affect macroscopic observables. The results show that in hyperonic, neutrino-trapped stars, the saturation density $n_{sat}$ exhibits strong correlations with intermediate-mass NS radii and tidal/shear properties, while the nucleon effective mass $m^*/m$ remains a key driver in some cases but its influence weakens with HIC constraints. The study provides modified $f$-mode and $C$–Love universal relations for neutrino-trapped hyperonic matter and publishes finite-temperature EOS tables for use in simulations, highlighting the inadequacy of simple $\,\Gamma$-law thermal treatments in hot, dense matter and the importance of hyperon physics for accurate NS modeling.$

Abstract

In this work, we present an equation of state formalism for hot Neutron Stars (NSs) which consistently includes the effects of finite temperature, hyperons as well as neutrino trapping, relevant for the study of proto-neutron stars, binary neutron star mergers and supernova explosions. Within a non-linear relativistic mean field description, the framework allows for a systematic variation of nuclear parameters within the range allowed by uncertainties in nuclear experimental data, ensuring compatibility with nuclear theory, astrophysical and heavy-ion data. We then investigate the role of nuclear and hypernuclear parameters as well as thermal effects on NS macroscopic properties and $f$-mode oscillations in hot neutron stars within Cowling approximation. Our results reveal that in hyperonic neutron stars with trapped neutrinos, the saturation nuclear density shows moderate to strong correlation with NS astrophysical observables. We also investigate whether thermal effects break universal relations and provide fit relations for hot NS configurations in the neutrino-trapped regime.

Figures (16)

• Figure 1: Posteriors of isoscalar nuclear parameters with different constraints for NY-matter. (a) $n_{sat}$ posteriors, (b) $K_{sat}$ posteriors, (c) $m^*/m$ posteriors
• Figure 2: Thermal contributions to energy density and pressure. Nuclear and hypernuclear properties are set to fixed values mentioned in Table \ref{['tab:prior']} (a) $\epsilon_{th}$ vs $n_B$, (b) $p_{th}$ vs $n_B$ [Hyperon thresholds are shown with vertical lines: dashed(solid) lines correspond to appearance in case of hot(cold) matter]
• Figure 3: $\Gamma$-law and particle fractions. Nuclear and hypernuclear properties are set to fixed values mentioned in Table \ref{['tab:prior']} (a) $\Gamma_{th}$ vs $n_B$, (b) particle fractions vs $n_B$ [Solid (dashed) curves are for $T=0~(T=20~\rm{MeV})$, $Y_Q=0.2$ case(s)]
• Figure 4: Comparison between $\nu$-free and $\nu$-trapped cases for nucleonic (N-) matter. Solid (dashed) curves indicate $\nu$-free ($\nu$-trapped) cases. The nuclear properties are set to the fixed values mentioned in Table \ref{['tab:prior']}. (a) Temperature profiles, (b) Mass-Radius relations
• Figure 5: Comparison between $\nu$-free and $\nu$-trapped cases for hyperonic (NY-) matter. Solid (dashed) curves indicate $\nu$-free ($\nu$-trapped) cases. The nuclear and hypernuclear properties are set to the fixed values mentioned in Table \ref{['tab:prior']}. (a) Temperature profiles, (b) Mass-Radius relations