Fully General Relativistic Simulations of Core-Collapse Supernovae with An Approximate Neutrino Transport

We present results from the first generation of multi-dimensional hydrodynamic core-collapse simulations in full general relativity (GR) that include an approximate treatment of neutrino transport. Using a M1 closure scheme with an analytic variable Eddington factor, we solve the energy-independent set of radiation energy and momentum based on the Thorne’s momentum formalism. To simplify the source terms of the transport equations, a methodology of multiflavour neutrino leakage scheme is partly employed. Our newly developed code is designed to evolve the Einstein field equation together with the GR radiation hydrodynamic equations. We follow the dynamics starting from the onset of gravitational core-collapse of a 15 $M_{\odot}$ star, through bounce, up to about 100 ms postbounce in this study to study how the spacial multi-dimensionality and GR would affect the dynamics in the early postbounce phase. Our 3D results support the anticipation in previous 1D results that the neutrino luminosity and average neutrino energy of any neutrino flavor in the postbounce phase increase when switching from SR to GR hydrodynamics. This is because the deeper gravitational well of GR produces more compact core structures, and thus hotter neutrino spheres at smaller radii. By analyzing the residency timescale to the neutrino-heating timescale in the gain region, we show that the criterion to initiate neutrino-driven explosions can be most easily satisfied in 3D models, irrespective of SR or GR hydrodynamics. Our results suggest that the combination of GR and 3D hydrodynamics provides the most favorable condition to drive a robust neutrino-driven explosion.

💡 Research Summary

This paper presents the first generation of multi‑dimensional core‑collapse supernova (CCSN) simulations that solve the full Einstein field equations together with general‑relativistic (GR) radiation‑hydrodynamics, while employing an approximate neutrino transport scheme. The authors adopt an energy‑independent M1 closure method with an analytic variable Eddington factor, based on Thorne’s momentum formalism, to evolve the radiation energy and momentum densities. To keep the source terms tractable, a multiflavour neutrino leakage scheme is incorporated, providing a pragmatic compromise between fidelity and computational cost. The newly developed code therefore couples GR gravity, fluid dynamics, and neutrino radiation in a self‑consistent framework.

The study follows the collapse of a 15 M⊙ progenitor from the onset of infall, through core bounce, and up to roughly 100 ms after bounce. Simulations are performed in one, two, and three dimensions, with both special‑relativistic (SR) and full GR hydrodynamics, allowing a systematic comparison of the impact of dimensionality and relativistic gravity on the early post‑bounce evolution.

Key findings include: (1) GR models produce a deeper gravitational well, leading to a more compact proto‑neutron star (PNS). Consequently, the neutrinospheres of all flavors reside at smaller radii and at higher temperatures, which raises both the neutrino luminosities and the mean neutrino energies by about 10–20 % relative to SR counterparts. (2) The three‑dimensional (3D) simulations develop vigorous non‑axisymmetric convection and standing‑accretion‑shock‑instability (SASI) motions that increase the dwell time of matter in the gain region. By comparing the residency timescale (τ_res) to the neutrino‑heating timescale (τ_heat), the authors demonstrate that the condition τ_res > τ_heat—often used as an explosion criterion—is most readily satisfied in 3D, irrespective of whether SR or GR hydrodynamics is used. However, the combination of GR gravity and 3D fluid dynamics yields the largest τ_res/τ_heat ratios, indicating the most favorable environment for a neutrino‑driven explosion.

The paper also discusses limitations. The energy‑independent treatment neglects spectral information, and the leakage approximation cannot capture detailed angle‑dependent neutrino transport. The simulations stop at 100 ms post‑bounce, so long‑term explosion dynamics and fallback are not addressed. Future work is suggested to incorporate full energy‑dependent M1 or Boltzmann transport, higher spatial resolution, magnetic fields, and longer evolution times to verify whether the early advantages observed here indeed translate into robust explosions.

In summary, this work provides compelling evidence that fully general‑relativistic gravity combined with three‑dimensional hydrodynamics creates the most conducive conditions for neutrino‑driven supernova explosions. It bridges a critical gap between earlier 1D/2D SR studies and realistic 3D GR models, highlighting the importance of both relativistic compactness and multi‑dimensional fluid motions in shaping the fate of massive stars.