Dynamic Competition of Fast and Collisional Neutrino Flavor Instabilities with Collisional Damping in Spatially Inhomogeneous Systems

Abstract: Neutrino flavor evolution in dense astrophysical environments such as core-collapse supernova (CCSN) is influenced by collective effects. While the Fast Flavor Instability (FFI) and the Collisional Flavor Instability (CFI) are recognized as key drivers of rapid flavor conversion, their non-linear competition with collisional damping in spatially varying environments remains poorly understood. Motivated by recent findings that FFI and resonance-like CFI co-occur in the post-bounce phase in CCSN, we scrutinize their dynamic competitions and asymptotic states. To this end, we perform numerical simulations of the quantum kinetic neutrino transport, incorporating both spatial advection and the collision terms. We demonstrate that the interplay between these coexisting neutrino flavor instabilities and collisions leads to rich dynamics. Rather than merely inducing simple decoherence, collisional damping can substantially alter the overall dynamics of collective flavor oscillations, driving the system through complex evolutionary pathways. In all cases where flavor instability develops, we find that the system converges to the same flavor-equilibrated asymptotic state, despite the diversity of intermediate dynamics. Our results suggest that this dynamic competition could alter the widely accepted picture of collisionless FFI, highlighting the need to incorporate realistic collisional effects into studies of flavor conversions in CCSN models.

• The paper solves spatially advective quantum kinetic equations to show that unstable systems converge to flavor equilibrium, while symmetric collisions can suppress shallow crossings before conversion begins.
• Collisions actively reshape angular distributions and FFI eigenmodes, producing delayed mixing, resonance-like collisional flavor swaps, and multi-stage transitions rather than merely damping coherence.
• The results show that FFI and CFI can alternate when their growth timescales are comparable, offering a timescale-based framework for subgrid models despite simplified geometry and microphysics.

Motivation and context

Collective neutrino flavor conversion is a central uncertainty in the physics of core-collapse supernovae (CCSNe) and binary neutron star mergers. Two instabilities dominate the current discussion: the fast flavor instability (FFI), triggered by zero-crossings in the angular distribution of the electron lepton number minus heavy-lepton number (ELN–XLN), and the collisional flavor instability (CFI), driven by flavor-asymmetric emission and absorption rates. Multi-dimensional Boltzmann simulations of CCSNe have shown that these two instabilities are not spatially segregated: regions hosting resonance-like CFI generically overlap with FFI-active regions in the post-bounce core (2605.10435). The paper under review addresses the resulting question—how do FFI, CFI, and collisional damping compete when they coexist, and what asymptotic state does that competition produce? To answer it, the authors solve the quantum kinetic equations (QKEs) including spatial advection and collision terms simultaneously, rather than treating each instability in isolation.

Numerical framework

The simulations are one-dimensional, single-energy ($\varepsilon_\nu = 20$ MeV), two-flavor ($\nu_e$, $\nu_x$) QKE calculations formulated in polarization-vector space, with the Hamiltonian consisting solely of the neutrino self-interaction term; vacuum and matter potentials are neglected. Collisions model charged-current emission and absorption of electron-type neutrinos only ($\Gamma_x = 0$), so $\Gamma = \Gamma_e/2$. The background equilibrium is a Fermi–Dirac distribution at $T = 6.4$ MeV with chemical potentials chosen to trigger resonance-like CFI, yielding $n^{\rm eq}_{\nu_x}/n^{\rm eq}_{\nu_e} = 0.74$. Initial conditions impose anisotropy via $g(v_z;\beta) = (1+\beta v_z)/2$: $\nu_e$ starts isotropic while the other species carry a forward-peaked distribution, mimicking flavor-dependent decoupling radii in CCSNe and setting the depth of the initial ELN–XLN crossing through $\beta \in \{1.0,\, 0.1,\, 0.01\}$.

The computational domain spans $\nu_e$0 with $\nu_e$1 cells (periodic boundaries), 128-point Gauss–Legendre angular quadrature, fifth-order WENO advection, SSP-RK(5,4) time integration at CFL 0.4, using the GPU code GANTS-QK. Collision rates are scanned over $\nu_e$2 for symmetric ($\nu_e$3) and asymmetric ($\nu_e$4) cases. The authors classify outcomes by the hierarchy among three timescales: FFI growth ($\nu_e$5, estimated from the Nagakura–Morinaga prescription), CFI growth ($\nu_e$6, from the approximate dispersion relation of Liu et al.), and collisional thermalization ($\nu_e$7). Regimes labeled "deep," "intermediate," and "shallow" refer to this hierarchy—not to geometric crossing depth alone—so the same $\nu_e$8 can fall into different regimes depending on $\nu_e$9.

Universal asymptotic state

The strongest claim of the paper is its universality result: in every case where flavor instability develops, the system converges to the same flavor-equilibrated state, with $\nu_x$0 and $\nu_x$1, regardless of the intermediate dynamics. The sole exception is the shallow-crossing case with symmetric collision rates, where collisions erase the ELN–XLN crossing before any instability can grow and no flavor conversion occurs. The universality follows because both thermalization and decoherence operate on timescales of order $\nu_x$2, much longer than the flavor-conversion timescales; any system that undergoes mixing on the faster timescale settles into essentially the same equilibrium. This convergence holds despite intermediate dynamics that differ radically across models, which supports the use of flavor-equilibrium prescriptions in subgrid models even when FFI and CFI coexist.

Diverse intermediate pathways

The path to equilibrium is strongly parameter-dependent. In the symmetric baseline (CFI prohibited), deep crossings produce near-complete equipartition followed by a persistent coherent state analogous to the "edge of instability" evolution reported elsewhere; notably, the paper demonstrates that such quasi-steady conversion survives even when both emission and absorption are included, extending earlier homogeneous results. Intermediate crossings leave incomplete mixing, later reinvigorated by collision-induced effects described below. Shallow crossings are fully stabilized.

With asymmetric rates ($\nu_x$3, as expected in neutron-rich CCSN environments), CFI becomes active and qualitatively changes the picture. Deep crossings yield incomplete equipartition because asymmetric collisions lift the ELN distribution toward isotropy faster than the FFI can equilibrate flavors. The most striking contrast occurs at shallow crossings: whereas the symmetric case is completely stable, the asymmetric case triggers a resonance-like CFI (with $\nu_x$4, $\nu_x$5) that drives an extreme nonlinear flavor swap around $\nu_x$6 for $\nu_x$7 and $\nu_x$8 for $\nu_x$9, subsequently damped to an incomplete swap before converging to equilibrium. This demonstrates that collisional flavor swap, previously identified in homogeneous QKE calculations, is robust in spatially inhomogeneous settings—an important extension of its applicability.

Collision-induced FFI eigenmode transition

A key mechanistic finding is that collisions do not merely damp flavor coherence; they actively reshape the angular distributions and thereby change the FFI eigenmode structure. The paper identifies a four-stage sequence: (1) FFI drives incomplete equipartition, leaving a residual crossing; (2) angle-dependent collisional relaxation isotropizes the forward and backward directions fastest, producing a wavy ELN profile with multiple ELN–XLN crossings that weakens the instability; (3) continued isotropization smooths the wavy structure; (4) the system returns to a single-crossing configuration whose dominant FFI eigenmode has a larger growth rate, triggering sudden strong mixing long after the initial episode saturated. In the asymmetric case, non-conservation of $\Gamma_x = 0$0 adds further structure: $\Gamma_x = 0$1 emission at backward angles drives the late-time crossing even though $\Gamma_x = 0$2, because detailed balance leaves $\Gamma_x = 0$3 nearly equilibrated while $\Gamma_x = 0$4 still deviates. The authors also confirm quantitatively that the depth of the ELN–XLN crossing is a poor predictor of FFI impact—a small-amplitude late-time crossing produces near-equipartition at the affected angles.

Intermittent FFI–CFI competition

In the asymmetric intermediate regime ($\Gamma_x = 0$5), the system exhibits multiple discrete mixing events at $\Gamma_x = 0$6, $\Gamma_x = 0$7, and $\Gamma_x = 0$8. The first is FFI-driven and simultaneously suppresses CFI by driving $\Gamma_x = 0$9 from $\Gamma = \Gamma_e/2$0 to $\Gamma = \Gamma_e/2$1 and violating the resonance condition $\Gamma = \Gamma_e/2$2. Between events, flavor coherence grows locally at backward angles ($\Gamma = \Gamma_e/2$3) even though no global ELN–XLN crossing exists—the paper shows explicitly, via phase-space maps of polarization-vector amplitudes, that a local FFI operates there. This local FFI terminates when collisional restoration of $\Gamma = \Gamma_e/2$4 (faster than $\Gamma = \Gamma_e/2$5, since $\Gamma = \Gamma_e/2$6) eliminates the local crossing. Later, as thermalization efficiency wanes near detailed balance, a non-resonant CFI overtakes damping and produces the third event. This sequence establishes that FFI and CFI can alternate as the dominant driver within a single evolutionary history, mediated by collisional thermalization.

Limitations and open questions

The authors state several limitations plainly. The collision rates used are artificially enhanced relative to real CCSNe, though the classification relies on timescale hierarchies rather than absolute values. Periodic boundary conditions are inappropriate for realistic CCSN geometry, and global high-density QKE simulations remain computationally intractable even with attenuation prescriptions. The initial conditions violate the steady-state constraint expected in realistic environments, which only a self-consistent global transport–flavor framework could remove. Finally, the single-energy, two-flavor treatment omits energy dependence, full scattering kernels, and the muon-neutrino sector, which can introduce additional CFI channels. Open questions left by the work include whether the universal flavor-equilibrated attractor persists under realistic collision rates and boundary conditions, and how subgrid models should represent the multi-stage FFI–CFI pathways identified here.

Conclusion

This paper provides the first systematic characterization of the nonlinear competition between coexisting FFI, CFI, and collisional relaxation in spatially inhomogeneous neutrino transport. Its principal results are the universality of the flavor-equilibrated asymptotic state across all unstable cases, the demonstration that collisions can act as active drivers—through eigenmode transitions and resonance-like CFI-driven flavor swaps—rather than mere decoherence sources, and the identification of intermittent, multi-stage mixing when FFI and CFI timescales are comparable. These findings indicate that flavor conversion dynamics inferred from collisionless FFI studies alone may misrepresent the behavior of realistic CCSN cores, and they supply a physical basis—timescale-hierarchy classification plus a robust final state—for constructing subgrid treatments of collective oscillations in regimes where fast and collisional instabilities overlap (2605.10435).