$\Lambda$ hyperons in core-collapse supernovae: Equilibration and neutrino opacities

Technical Summary: $\Lambda$ Hyperons in Core-Collapse Supernovae: Equilibration and Neutrino Opacities

Problem Statement
In the dense, hot, and isospin-asymmetric matter of proto-neutron stars (PNS) formed during core-collapse supernovae (CCSN), strange hadrons such as $\Lambda$ hyperons are expected to appear. Standard equation-of-state (EOS) models typically assume these particles are in local chemical equilibrium ($\mu_\Lambda = \mu_n$). However, the timescales required to establish this equilibrium via weak interactions in CCSN conditions have not been systematically assessed. Furthermore, the presence of hyperons introduces new weak-interaction channels that could modify neutrino opacities and transport, potentially influencing the "muonization" of supernova matter and the overall PNS evolution. A critical gap exists in understanding whether local chemical equilibrium is a valid approximation given the macroscopic hydrodynamical and neutrino-transport timescales of the PNS.

Methodology
The authors compute $\Lambda$-hyperon production rates under representative post-bounce PNS thermodynamic conditions ($T \approx 38.3$ MeV, $\rho \approx 10^{14}$ g cm$^{-3}$), derived from a 20 $M_\odot$ progenitor simulation using the LS220 EOS. The study distinguishes between two classes of weak processes:

1. Nonleptonic Reactions: Strangeness-changing processes ($\Delta S = 1$) including baryon-baryon scattering ($NN \leftrightarrow N\Lambda$) and pion-baryon coalescence/decay ($\pi B \leftrightarrow \Lambda$).
2. Semileptonic Reactions: Charged-current processes involving leptons and neutrinos ($\ell B \leftrightarrow \nu \Lambda$, $\bar{\nu} B \leftrightarrow \ell \Lambda$, and three-body coalescence).

For nonleptonic rates, the authors employ an Effective Field Theory (EFT) framework tailored to weak $\Lambda + N \to N + N$ transitions, constrained by hypernuclear non-mesonic weak-decay data. This framework includes:

• Long-range contributions from one-meson exchange (pions and kaons).
• Short-range contributions from four-baryon contact interactions, parameterized by low-energy constants (LECs) fitted to hypernuclear data.
  The authors calculate thermal absorption rates and collision operators to determine the local chemical equilibration timescale ($\tau_\Lambda$) for each channel.

For semileptonic rates, the authors utilize a weak effective Lagrangian with standard $SU(3)$-flavor relations for form factors. They compute scattering and coalescence rates to assess their contribution to equilibration and, crucially, to calculate the resulting neutrino and antineutrino opacities. These opacities are compared against standard nucleonic contributions.

Key Contributions and Results

• Equilibration Timescales: The study finds that local $\Lambda$ chemical equilibration is driven overwhelmingly by nonleptonic reactions, specifically the scattering channels $n + n \to n + \Lambda$ and $p + n \to p + \Lambda$.

  • The characteristic equilibration timescales are of order $10^{-11}$ to $10^{-10}$ s ($0.01$–$0.1$ ns).
  • These timescales are many orders of magnitude shorter than macroscopic PNS evolution timescales (hydrodynamical $\sim 10^{-3}$ s, convective $\sim 10^{-2}$–$10^{-1}$ s, and deleptonization/cooling $\sim 1$–$60$ s).
  • Consequently, the assumption of local chemical equilibrium for $\Lambda$ hyperons is robust under the studied conditions.

• Dominance of Contact Interactions: In the EFT calculation, short-range contact interactions dominate the nonleptonic scattering rates. This contrasts with earlier estimates at lower temperatures where one-pion exchange (OPE) was dominant. The contact terms, fitted to hypernuclear decay data, yield collision operators roughly an order of magnitude larger than those predicted by models relying solely on $W$-boson exchange or pure OPE.

• Role of Semileptonic Channels: Semileptonic reactions are found to be too slow to set the equilibrium $\Lambda$ abundance, with timescales roughly four orders of magnitude longer than nonleptonic processes ($\sim 10^{-6}$ s). However, they are significant for neutrino transport.

  • Neutrino Opacities: $\Lambda$-induced semileptonic processes open new absorption channels for low-energy muon neutrinos and antineutrinos (e.g., $\nu_\mu + \Lambda \to \mu^- + p$ and $p + \mu^- + \bar{\nu}_\mu \to \Lambda$).
  • Flavor Dependence: In the energy windows $E_{\nu_\mu} \lesssim 50$ MeV and $E_{\bar{\nu}_\mu} \lesssim 80$ MeV, the $\Lambda$-induced opacities for muon (anti)neutrinos exceed the corresponding nucleonic contributions. This is due to kinematic thresholds that suppress muon production on nucleons but are accessible via hyperons.
  • Electronic Sector: The impact on electron neutrino and antineutrino opacities is negligible, as low-energy absorption on nucleons is not kinematically suppressed.

Significance and Claims
The paper claims to provide the first systematic assessment of $\Lambda$ hyperon equilibration timescales in CCSN conditions. The primary conclusion is that local chemical equilibrium for $\Lambda$ hyperons is effectively instantaneous on macroscopic timescales, validating its use in EOS constructions and simulations.

The study highlights that while hyperons do not alter the bulk equilibration dynamics, their presence introduces flavor-dependent microphysics. Specifically, the new low-energy absorption channels for muon (anti)neutrinos could influence the evolution of the muon lepton number during PNS deleptonization ("muonization"). The authors note that these results provide new weak-interaction inputs for flavor-dependent neutrino transport and suggest that fully self-consistent CCSN simulations incorporating these hyperonic opacities are necessary to quantitatively assess their impact on explosion dynamics and PNS cooling. The work also underscores the importance of short-range weak physics in hot, dense matter, with implications for hyperonic bulk-viscosity studies in neutron star mergers.