The Effect of the Fast-Flavor Instability on Core-Collapse Supernova Models: II. Quasi-Equipartition and the Impact of Various Angular Reconstruction Methods

TL;DR

This paper evaluates fast flavor conversion (FFC) in 1D and 2D core-collapse supernova simulations using a 4-species transport scheme with Box3D-BGK in the Fornax code, comparing it against the traditional 3-species approach and several angular closures. It demonstrates that FFC effects on hydrodynamics are minor and largely insensitive to angular reconstruction, while significantly altering neutrino signals by transferring roughly 20% of $ u_e$ and $ar{ u}_e$ luminosities to heavy-lepton flavors at large radii; spectra also shift toward softer $ u_x$ and harder $ u_e$. A key contribution is the quasi-equipartition post-processing method, which, under conservation laws and the assumption $\ oot 2\{N^{\\mathrm{FFC}}_{\nu_e}N^{\\mathrm{FFC}}_{\bar{\nu}_e}}=\\root 2\{N^{\\mathrm{FFC}}_{\nu_x}N^{\\mathrm{FFC}}_{\bar{\nu}_x}}$, reproduces FFC-modified neutrino properties with relative errors $<2\%$ in 1D and $<10\%$ in 2D when applied to no-oscillation simulations. This provides a practical path to incorporate FFC effects into CCSN predictions without expensive re-simulations or full quantum kinetic treatments. The findings imply that FFC can be approximated post hoc for neutrino signals while leaving the hydrodynamics largely intact, though 3D effects and heavier leptons warrant future investigation.

Abstract

In this work, we explore in a consistent fashion the effects of fast flavor conversion (FFC) in 1D and 2D core-collapse supernova (CCSN) simulations. In addition, we investigate the impact of various angular reconstruction methods and compare the ``3-species'' and ``4-species'' neutrino transport schemes. We find that the FFC effects are insensitive to the different methods tested and that the FFC alters supernova hydrodynamics is only minor ways. We also present a ``quasi-equipartition'' approximation which can be used to estimate the FFC-altered neutrino properties by post-processing the neutrino signals extracted from no-oscillation CCSN simulations. The relative errors in neutrino number and energy luminosities of this phenomenological method are less than 2\% for 1D models, and less than 10\% for 2D models. This method provides a simple way to include the effects of FFC on neutrino signals without implementing a complex and expensive FFC scheme or redoing simulations.

Figures (13)

• Figure 1: Reconstructed neutrino angular distributions of the Minerbo, MEFD, and Nagakura closures. With a flux factor ($f$) of 0.2, the differences between closure choices are almost negligible. At higher flux factors, the differences become more significant. One issue of the Minerbo and Nagakura closures is that they don't explicitly introduce the Pauli's exclusion principle, and as a result, their reconstructed angular distributions are more forwardly peaked than the MEFD results and the distribution function can even exceed one when the flux factor $f$ is close to $1-e$, where $e$ is the state occupation fraction. However, this issue leads only to very minor effects on the hydrodynamics of our models because neutrinos with high flux factors have already decoupled from matter.
• Figure 2: Left: Net neutrino heating rate (in unit of $10^{51}$ erg $s^{-1}$) in the gain region behind the shock for the 1D models. Right: the maximum shock radius as a function of time. The 9 M$_\odot$ model is shown by solid lines, while the 18 M$_\odot$ model is marked by dashed lines. Different colors indicate the different treatments of neutrino fast flavor conversion. Models using the 4-species scheme and various angular reconstruction methods ("Minerbo", "MEFD", and "Nagakura") all behave very similar to the 3-species scheme model ("3-species"). Compared to the no oscillation models ("No osc"), models with FFC show slightly higher heating rates at early time in the 9 M$_\odot$ model, while in general the effects of FFC on heating rates and shock evolution are weak. This confirms the findings in wang2025.
• Figure 3: Neutrino luminosities (in unit of $10^{51}$ erg s$^{-1}$) as a function of time for the 1D models. Different line styles indicate different neutrino types. For the "3-species" and "No osc" models, for which the 3-species scheme is used, $\nu_x$ and $\bar{\nu}_x$ have exactly the same luminosities and are thus overlapping. After a slight delay, fast-flavor conversion boosts the $\nu_{x}$ and $\bar{\nu}_{x}$ luminosities by $\sim$20%. Differences between various angular reconstruction methods and FFC schemes are relatively minor. Without the FFC, the $\nu_e$ and $\bar{\nu}_e$ have similar energy luminosities which are significantly higher than those of $\nu_x$ and $\bar{\nu}_x$ neutrinos. This trend is completely changed by flavor conversion: for models with FFC, the relative differences between energy luminosities of various neutrino are less than about 10% after $\sim200$ ms post-bounce, and the luminosity order at that time is $L_{\nu_e}>L_{\bar{\nu}_x}>L_{\nu_x}>L_{\bar{\nu}_e}$.
• Figure 4: The evolution of the average energies of the different neutrino types. Different line styles indicate different neutrino types. When the FFC is operative, the $\nu_{x}$ and $\bar{\nu}_{x}$ neutrino spectra are softened, while both the $\nu_e$ and $\bar{\nu}_e$ neutrino spectra harden slightly. The differences between various angular reconstruction methods are minor. With FFC, the average energies of the four neutrino types show smaller, but non-vanishing, differences. Neutrinos ($\nu_e$ and $\nu_x$) have similar average energies, while anti-neutrinos ($\bar{\nu}_e$ and $\bar{\nu}_x$) have similar average energies, but at higher values.
• Figure 5: The neutrino number density fraction profiles for the 1D models at 50 and 300 ms post-bounce. The vertical dashed line marks the location of the shock wave, while the horizontal dashed line at $1/6\approx0.167$ marks the equipartition fraction. At early times (50 ms post-bounce), the FFC happens mostly in the FFI region interior to the shock. At relatively later times ($\sim$300 ms post-bounce), the post-shock FFI region disappears and all flavor conversion happens exterior to the shock. The final flavor state is gradually approached at thousands of kilometers.