[Paper Review] Collisional flavor instability in dense neutrino gases

Zewei Xiong, Lucas Johns+2 more|arXiv (Cornell University)|Dec 7, 2022

Neutrino Physics Research4 citations

TL;DR

This paper identifies two distinct types of collisional flavor instability (CFI) in dense neutrino gases—distinguished by their frequency dependence on neutrino density—showing that CFI transitions between types near zero net electron lepton number, with exponential growth at a rate proportional to $ n_{ u}^{1/2} $. The instability is most prominent in high-density environments like black hole accretion disks, suggesting potential for significant flavor conversion and implications for kilonova emission and remnant cooling.

ABSTRACT

Charged-current neutrino processes such as $ν_e + n ightleftharpoons p + e^-$ and $\barν_e + p ightleftharpoons n + e^+$ destroy the flavor coherence among the weak-interaction states of a single neutrino and thus damp its flavor oscillation. In a dense neutrino gas such as that inside a core-collapse supernova or the black hole accretion disk formed in a compact binary merger, however, these "collision" processes can trigger large flavor conversion in cooperation with the strong neutrino-neutrino refraction. We show that there exist two types of collisional flavor instability in a homogeneous and isotropic neutrino gas which are identified by the dependence of their real frequencies on the neutrino density $n_ν$. The instability transitions from one type to the other and exhibits a resonance-like behavior in the region where the net electron lepton number of the neutrino gas is negligible. In the transition region, the flavor instability grows exponentially at a rate $\propto n_ν^{1/2}$. We find that the neutrino gas in the black hole accretion disk is susceptible to the collision-induced flavor conversion where the neutrino densities are the highest. As a result, large amounts of heavy-lepton flavor neutrinos may be produced through flavor conversion, which can potentially have important ramifications in the subsequent evolution of the remnant.

Motivation & Objective

• To investigate the existence and characteristics of collisional flavor instability (CFI) in dense, homogeneous, and isotropic neutrino gases.
• To determine how CFI arises from the interplay between charged-current processes and neutrino-neutrino refraction in dense environments.
• To identify the transition between two distinct types of CFI based on their real frequency dependence on neutrino density.
• To assess the potential for CFI to drive significant flavor conversion in astrophysical environments such as black hole accretion disks and core-collapse supernovae.
• To evaluate the implications of CFI for neutrino-driven dynamics, element production, and kilonova emission in compact binary merger remnants.

Proposed method

• Modeling the neutrino gas using a mean-field density matrix formalism with flavor coherence $ S $ and occupation numbers $ f_{ u_e}, f_{ u_x} $, assuming ultra-relativistic neutrinos.
• Deriving the effective Hamiltonian that includes both neutrino-neutrino refraction and collisional processes via charged-current reactions $ \nu_e + n \rightleftharpoons p + e^- $ and $ \bar{\nu}_e + p \rightleftharpoons n + e^+ $.
• Solving the linearized equation of motion for flavor coherence $ S $ in the presence of a continuous energy spectrum, using a discrete group approximation with $ N $ energy groups.
• Computing the normal mode frequencies $ \Omega = \omega_P + i\gamma $ from the eigenvalue problem of the matrix $ \Lambda_{ij} = -[\omega_{\text{eff}}(E_i)\delta_{ij} + \mu g_j \Delta E_j] $, where $ \mu \propto n_{\nu_e} $.
• Analyzing the dispersion relation $ \Omega(\mathbf{K}) $ to identify instability growth rates $ \gamma $, particularly focusing on regions with negligible net electron lepton number.
• Validating results against numerical simulations of the BH accretion disk model M3A8m3a5 at $ t = 20 $ ms, using realistic neutrino emission and absorption rates.

Experimental results

Research questions

• RQ1 What types of collisional flavor instability (CFI) exist in a homogeneous and isotropic dense neutrino gas, and how do they differ in their frequency dependence on neutrino density?
• RQ2 How does the transition between the two types of CFI occur, and what physical conditions—particularly near zero net electron lepton number—enable a resonance-like instability?
• RQ3 What is the growth rate of the instability in the transition region, and how does it scale with neutrino density?
• RQ4 In what astrophysical environments, such as black hole accretion disks, is CFI most likely to occur and lead to significant flavor conversion?
• RQ5 Can CFI operate independently of fast flavor instabilities, and what are its implications for neutrino-driven dynamics in core-collapse supernovae and compact binary mergers?

Key findings

• Two distinct types of collisional flavor instability (CFI) exist in dense neutrino gases, differentiated by the dependence of their real frequency $ \omega_P $ on neutrino density: one with $ \omega_P/\mu \approx 0 $ (plus type), and another with $ \omega_P \propto (n_{\nu_e} - n_{\bar{\nu}_e}) $ (minus type).
• The CFI transitions from the plus type to the minus type in regions where the net electron lepton number is negligible, exhibiting a resonance-like behavior with maximum growth rate at $ \gamma \propto n_{\nu}^{1/2} $.
• The instability grows exponentially in the transition region with a growth rate proportional to $ n_{\nu}^{1/2} $, indicating a critical role of density and lepton number balance.
• In the black hole accretion disk model M3A8m3a5, the CFI of the plus type dominates in the inner torus where $ n_{\nu_e} \gg n_{\bar{\nu}_e} $, while the minus type emerges in the outer torus where $ n_{\nu_e} \approx n_{\bar{\nu}_e} $.
• The CFI is most prominent in high-density regions such as the inner torus of the accretion disk, suggesting a strong potential for large-scale flavor conversion and enhanced production of $ \nu_{\mu/\tau} $ and $ \bar{\nu}_{\mu/\tau} $.
• The CFI can operate independently of fast flavor instabilities, existing even in regions and epochs where fast flavor conversion is not yet active, thus broadening the scope of collective neutrino effects in compact object environments.