Fast flavor conversions of supernova neutrinos: Classifying instabilities via dispersion relations

Abstract

Supernova neutrinos can exhibit a rich variety of flavor conversion mechanisms. In particular, they can experience "fast" self-induced flavor conversions almost immediately above the core. Very recently, a novel method has been proposed to investigate these phenomena, in terms of the dispersion relation for the complex frequency and wave number (ω, k) of disturbances in the mean field of the νeνx flavor coherence. We discuss a systematic approach to such instabilities, originally developed in the context of plasma physics, and based of the time-asymptotic behavior of the Green's function of the system. Instabilities are typically seen to emerge for complex ω, and can be further characterized as convective (moving away faster than they spread) and absolute (growing locally), depending on k-dependent features. Stable cases emerge when k (but not ω) is complex, leading to disturbances damped in space, or when both ω and k are real, corresponding to complete stability. The analytical classification of both unstable and stable modes leads not only to qualitative insights about their features but also to quantitative predictions about the growth rates of instabilities. Representative numerical solutions are discussed in a simple two-beam model of interacting neutrinos. As an application, we argue that supernova and binary neutron star mergers exhibiting a "crossing" in the electron lepton number would lead to an absolute instability in the flavor content of the neutrino gas.

Fast neutrino flavor instability in the neutron-star convection layer of three-dimensional supernova models

“…A specific condition such as, e.g., our instability criteria of Eqs. (2), (13), and (18) or any other analytical criterion relating physical quantities that are available on a discrete numerical mesh, may fail to identify the spatial locations of instability. We speculate that also the investigations in Refs.…”

“…The physical thickness of these boundary layers of the ∆n ν < 0 volumes, i.e., the "skins" in which the flavor-instability condition is fulfilled, can be roughly estimated from Eqs. (13) or (18) by making use of the diffusion approximation to express the lepton-number flux, ∆F r ν = F r νe − F r νe through F r νi = −D νi ∂n νi /∂r, where D νi = 1 3 cλ νi is the diffusion coefficient and λ νi the (energy-averaged) mean free path. Introducing a mean free pathλ suitably averaged between ν e andν e , we can write for the effective neutrino-lepton number flux in the diffusion regime:…”

“…In this context, a peculiar type of self-induced flavor conversions, called "fast" instabilities [4,8,10,[15][16][17][18][19][20][21][22][23][24][25][26][27][28], is expected to lead to flavor conversions developing on very short distances, r O(1) m. Fast flavor conversions have been associated with "crossings" in the electron lepton number (ELN) angular distribution, i.e., with a change of sign in the difference between ν e andν e number densities as a function of emission angle [16,18,24]. Conditions for crossings in the ELN were expected to be possible in the neutrino decoupling region in SN cores, where the different flavors have significantly different angular distributions.…”

Fast neutrino flavor conversion modes in multidimensional core-collapse supernova models: The role of the asymmetric neutrino distributions

“…However, neutrinos could also undergo the so-called fast flavor conversions on scales as short as a few cm in the densest regions of the SN core [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Unlike the traditional collective modes which occur on scales determined by the neutrino vacuum frequency ω = ∆m 2 /2E (∼ O(1) km for a 10 MeV neutrino and atmospheric mass splitting), fast modes occur on scales ∼ G −1 F n −1 ν with n ν and G F being the neutrino number density and the Fermi coupling constant, respectively.…”

Spatiotemporal linear instability analysis for arbitrary dispersion relations on the Lefschetz thimble in multidimensional spacetime

“…Note that not all the critical points give the pinch of the integration contour. The theory has been applied to shear flows [3,4], jets [5], solitons [6] and even neutrino oscillations recently [7,8].…”