A Study on the Triggering of Nucleonic Direct Urca Processes in Neutron Stars of Specific Masses and Their Hyperon Dependence

This work aims to analyze how hyperons affect neutrino radiation properties in nucleonic direct URCA processes, expecting to provide useful references for finding evidence of the existence of hyperons in astronomical observations. This analysis is carried out using the GM1 and NL3 parameter sets under the SU(6) and SU(3) flavor symmetries in the relativistic mean field theory framework. Combined with the inferred mass and radius values of PSRs J1231-1411, J0030+0451, and J0740+6620, our results show that nucleonic direct Urca processes are absent in PSR J1231-1411 due to momentum conservation violation. In hyperon-containing PSR J0030+0451 (NL3 parameter set), the nucleonic direct Urca processes involving $e^{-}$/ $μ^{-}$ would occur. A large inferred mass span induces hyperon fraction variations, affecting neutrino emissivity. If the inferred mass of PSR J0030+0451 exceeds approximately 1.8 $M_{\odot}$, the neutrino luminosity of the nucleonic direct Urca processes under the SU(3) flavor symmetry remains nearly the same as that in npe$μ$ matter, without depending on hyperons. However, it exhibits an obvious hyperon dependence under the SU(6) spin-flavor symmetry. For hyperon-containing J0740+6620, the nucleonic direct Urca processes under the SU(3) flavor symmetry in GM1 parameter set predicts faster neutrino luminosity decline with hyperonic fraction than npe$μ$ matter, and under the SU(6) spin-flavor symmetry in NL3 parameter set it shows monotonic decreasing trend. The research shows that hyperonic fraction significantly affect the neutrino radiation properties of the nucleonic direct URCA processes in neutron stars. Different-mass pulsars (e.g., PSRs J1231-1411, J0030+0451, J0740+6620) exhibit the distinct nucleonic direct URCA processes behaviors, dependent on inferred masses/radii, parameter sets, and theoretical models.

💡 Research Summary

This paper investigates how the presence of hyperons influences the nucleonic direct Urca (DU) processes and the resulting neutrino emission in neutron stars of different masses. Using relativistic mean‑field (RMF) theory, the authors adopt two widely used equation‑of‑state (EOS) parameter sets—GM1 and NL3—and implement two symmetry schemes for the baryon‑meson couplings: the SU(3) flavor symmetry and the SU(6) spin‑flavor symmetry. The meson sector includes σ, ω, ρ, σ* and φ, while Σ hyperons are omitted because of their uncertain appearance at saturation density. For each combination (GM1‑SU(3), GM1‑SU(6), GM1‑SU(6‑no σ* φ, NL3‑SU(3), NL3‑SU(6), NL3‑SU(6‑no σ* φ) the authors solve the charge‑neutral, β‑equilibrated RMF equations, obtain the particle fractions, and then integrate the Tolman‑Oppenheimer‑Volkoff (TOV) equations to generate mass‑radius (M‑R) curves.

The study focuses on three pulsars whose masses and radii have been inferred from NICER observations: PSR J1231‑1411 (M≈1.04 M⊙, R≈12.6 km), PSR J0030+0451 (M≈1.70 M⊙, R≈14.4 km) and PSR J0740+6620 (M≈2.07 M⊙, R≈12.5 km). By locating the observed (M,R) points on the theoretical M‑R curves, the authors assign each pulsar to a specific EOS‑symmetry case: J1231‑1411 matches the low‑mass branch of GM1 (no hyperons), J0030+0451 aligns with the intermediate‑mass branch of NL3 (hyperon‑rich under SU(6) or SU(3)), and J0740+6620 corresponds to the high‑mass branch of GM1 (hyperon‑rich under SU(3)) or NL3 (hyperon‑rich under SU(6)).

The nucleonic direct Urca reactions are
n → p + ℓ + ν̄ℓ and p + ℓ → n + νℓ (ℓ = e⁻, μ⁻).
They are allowed only when the momentum‑conservation condition Θ(p_Fℓ + p_Fp − p_Fn) ≥ 0 is satisfied, where p_Fi are the Fermi momenta of the participating particles. The authors compute the neutrino emissivity Q using the relativistic Fermi‑golden‑rule expression (Eq. 1) and integrate it over the stellar volume to obtain the total neutrino luminosity L_ν.

Key findings:

1. PSR J1231‑1411 (low mass) – For all EOS‑symmetry combinations, the proton fraction is too low to satisfy the DU threshold; Θ = 0 everywhere, so nucleonic direct Urca is completely suppressed. Consequently, cooling must proceed via modified Urca, bremsstrahlung, or other slower channels.

2. PSR J0030+0451 (intermediate mass) – In the NL3‑SU(6) case the star’s mass and radius are reproduced and hyperons (Λ first, then Ξ⁻ at higher density) appear. Both electron‑ and muon‑Urca channels become operative because the proton fraction exceeds the critical value. When the stellar mass exceeds ≈1.8 M⊙, the SU(3) symmetry predicts that the neutrino luminosity remains essentially identical to that of a pure npeμ composition, i.e., hyperons do not further enhance cooling. By contrast, under SU(6) the growing hyperon fraction reduces the electron and muon chemical potentials, leading to a noticeable decline in L_ν with increasing hyperon content.

3. PSR J0740+6620 (high mass) – For GM1‑SU(3) the core contains Λ, Ξ⁻ and Ξ⁰. Direct Urca is allowed throughout most of the core, but the hyperon fraction strongly modifies the Fermi momenta of nucleons and leptons. As hyperons become more abundant, the DU emissivity drops sharply, producing a faster decline of L_ν compared with a hyperon‑free npeμ star. In the NL3‑SU(6) scenario, the hyperon fraction also grows with mass, but the momentum‑threshold factor Θ remains roughly constant; thus L_ν decreases monotonically but more gently with hyperon content.

The authors also examine the Keplerian (mass‑shedding) frequency as a function of mass, showing that sub‑millisecond rotation (≈1000 Hz) would be possible for stars with M ≈ 1.9–2.7 M⊙, depending on the EOS.

Overall, the paper demonstrates that hyperons have a dual role: they soften the EOS, lowering the DU threshold mass, yet their presence can either enhance or suppress the neutrino luminosity depending on the symmetry‑driven coupling constants. Low‑mass stars remain DU‑inactive regardless of hyperons, while intermediate‑ and high‑mass stars exhibit a rich variety of cooling behaviours that are sensitive to the chosen RMF parameter set and the flavor symmetry. These results provide a theoretical framework for interpreting future thermal‑evolution observations and for using neutron‑star cooling as a probe of hyperonic matter in dense QCD.