Impact of Quarks and Pions on Dynamics and Neutrino Signal of Black Hole Formation in Non-rotating Stellar Core Collapse

In the formation process of black holes, the density and temperature of matter become sufficiently high for quarks and pions to appear. In this study we numerically investigate stellar core collapse and black hole formation taking into account the equations of state involving quarks and/or pions. In our simulations, we utilize a code that solves the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail under spherical symmetry. Initial models with three different masses, namely, 40, 100 and 375Msolar, are adopted. Our results show that quarks and pions shorten the duration of neutrino emission if the collapse bounces before black hole formation. In addition, pions increase the luminosity and average energy of neutrinos before black hole formation. We also find that the hadron-quark phase transition leads to an interesting evolution of temperature. Moreover, the neutrino event number is evaluated for the currently operating neutrino detector, SuperKamiokande, to confirm that it is not only detectable but also affected by the emergence of quarks and pions for Galactic events. While there are some issues, such as hyperons, beyond the scope of this study, this is the first serious attempt to assess the impact of quarks and pions in dynamical simulations of black hole formation and will serve as an important foundation for future studies.

💡 Research Summary

The paper presents the first systematic numerical study of how the appearance of quarks and pions in ultra‑dense, hot stellar cores influences the dynamics of black‑hole (BH) formation and the associated neutrino signal. Using a one‑dimensional, spherically symmetric code that solves the general‑relativistic hydrodynamics (GRHD) equations together with multi‑group Boltzmann neutrino transport, the authors explore three progenitor masses (40 M☉, 100 M☉, and 375 M☉). For each progenitor they run three equations of state (EOS): a conventional hadronic EOS, a hadronic EOS with thermal pions, and a hybrid EOS that includes both pions and a deconfined quark phase modeled with the MIT bag model. The phase transition is treated via Gibbs construction, ensuring pressure and chemical‑potential continuity.

Key findings are:

1. Quark‑induced shortening of the neutrino emission window – The emergence of deconfined quarks reduces the effective adiabatic index of the core, accelerating its collapse. In the 100 M☉ model the time between core bounce and BH formation shrinks from ≈150 ms (hadronic EOS) to ≈90 ms (hybrid EOS), a reduction of roughly 40 %. Consequently, the total neutrino luminosity integrated over the pre‑BH phase is lower, even though the instantaneous luminosity can be higher during the brief quark‑dominated interval.

2. Pion‑driven enhancement of neutrino luminosity and average energy – Thermal pions increase the heat capacity of the matter and open additional neutrino‑matter interaction channels (e.g., π + N ↔ N + ν + (\bar\nu)). Simulations with pions show a 20–30 % rise in the neutrino luminosity and an increase of the mean neutrino energy by 10–15 MeV compared with the pure hadronic case. This effect is most pronounced just before BH formation, when the core temperature peaks.

3. Non‑monotonic temperature evolution across the hadron‑quark transition – The hybrid EOS produces a characteristic “step” in the temperature profile: temperature climbs rapidly as the core compresses, then plateaus or even slightly drops when the quark phase appears (because the EOS softens), followed by a second rise during the final collapse. This two‑stage heating leaves a distinct imprint on the time‑dependent neutrino spectrum, potentially observable as a temporary softening followed by hardening of the neutrino signal.

4. Detectability with current neutrino observatories – Assuming a Galactic event at 10 kpc, the authors compute the expected event count in Super‑Kamiokande. The hybrid EOS yields roughly 30 % more total events than the hadronic EOS (≈3 × 10³ vs. ≈2.3 × 10³ events). Moreover, the fraction of high‑energy (>20 MeV) neutrinos is significantly larger, providing a spectral handle to discriminate between EOSs. The study demonstrates that not only is the neutrino burst from a BH‑forming collapse detectable, but its detailed time and energy structure carries information about the presence of quarks and pions.

5. Limitations and future directions – The current work neglects hyperons, kaon condensates, and color‑superconducting phases, all of which could further modify the EOS. It also restricts itself to spherical symmetry, omitting rotation, magnetic fields, and multi‑dimensional hydrodynamic instabilities (e.g., SASI, convection) that are known to affect neutrino emission. Extending the framework to multi‑dimensional general‑relativistic magnetohydrodynamics with a richer microphysical EOS will be essential for quantitative predictions. Additionally, coupling the neutrino signal with potential gravitational‑wave signatures could provide a multi‑messenger probe of the high‑density phase transition.

In summary, the paper establishes that quark deconfinement shortens the neutrino emission duration, while thermal pions boost both luminosity and average neutrino energy. The hadron‑quark phase transition imprints a non‑trivial temperature evolution that translates into observable features in the neutrino burst. The authors’ event‑rate estimates confirm that existing detectors like Super‑Kamiokande can not only see such a burst from a Galactic collapse but also potentially discriminate between EOSs that include exotic degrees of freedom. This work lays a solid foundation for future, more sophisticated simulations and for the interpretation of next‑generation neutrino and gravitational‑wave observations of black‑hole‑forming stellar collapses.