Breaking the symmetries in self-induced flavor conversions of neutrino beams from a ring

Self-induced flavor conversions of supernova (SN) neutrinos have been characterized in the spherically symmetric "bulb" model, reducing the neutrino evolution to a one dimensional problem along a radial direction. We lift this assumption, presenting a two-dimensional toy-model where neutrino beams are launched in many different directions from a ring. We find that self-interacting neutrinos spontaneously break the spatial symmetries of this model. As a result the flavor content and the lepton number of the neutrino gas would acquire seizable direction-dependent variations, breaking the coherent behavior found in the symmetric case. This finding would suggest that the previous results of the self-induced flavor evolution obtained in one-dimensional models should be critically re-examined.Comment: v2 (8 pages, 9 eps figures): Revised version. Major changes. Model improved and clarified. Calculations and figures updated. Matches the version accepted for publication on PR

Another look at synchronized neutrino oscillations

In dense neutrino backgrounds present in supernovae and in the early Universe neutrino oscillations may exhibit complex collective phenomena, such as synchronized oscillations, bipolar oscillations and spectral splits and swaps. We consider in detail possible decoherence effects on the simplest of these phenomena -- synchronized neutrino oscillations that can occur in a uniform and isotropic neutrino gas. We develop an exact formalism of spectral moments of the flavour spin vectors describing such a system and then apply it to find analytical approaches that allow one to study decoherence effects on its late-time evolution. This turns out to be possible in part due to the existence of the (previously unknown) exact conservation law satisfied by the quantities describing the considered neutrino system. Interpretation of the decoherence effects in terms of neutrino wave packet separation is also given, both in the adiabatic and non-adiabatic regimes of neutrino flavour evolution.Comment: LaTeX, 32 pages, 3 figures. V2: minor textual changes, references and an acknowledgement added, results and conclusions unchange

Temporal Instability Enables Neutrino Flavor Conversions Deep Inside Supernovae

We show that a self-interacting neutrino gas can spontaneously acquire a non-stationary pulsating component in its flavor content, with a frequency that can exactly cancel the "multi-angle" refractive effects of dense matter. This can then enable homogeneous and inhomogeneous flavor conversion instabilities to exist even at large neutrino and matter densities, where the system would have been stable if the evolution were strictly stationary. Large flavor conversions, especially close to a supernova core, are possible via this novel mechanism. This may have important consequences for the explosion dynamics, nucleosynthesis, as well as for neutrino observations of supernovae.Comment: v3: Improved Fig.1 and fixed typos. Matches version published in PR

Multi-azimuthal-angle instability for different supernova neutrino fluxes

It has been recently discovered that removing the axial symmetry in the "multi-angle effects" associated with the neutrino-neutrino interactions for supernova (SN) neutrinos, a new multi-azimuthal-angle (MAA) instability would trigger flavor conversions in addition to the ones caused by the bimodal and multi-zenith-angle (MZA) instabilities. We investigate the dependence of the MAA instability on the original SN neutrino fluxes, performing a stability analysis of the linearized neutrino equations of motion. We compare these results with the numerical evolution of the SN neutrino non-linear equations, looking at a local solution along a specific line of sight, under the assumption that the transverse variations of the global solution are small. We also assume that self-induced conversions are not suppressed by large matter effects. We show that the pattern of the spectral crossings (energies where F_{\nu_e} = F_{\nu_x}, and F_{\bar\nu_e} = F_{\bar\nu_x}) is crucial in determining the impact of MAA effects on the flavor evolution. For neutrino spectra with a strong excess of \nu_e over \bar\nu_e, presenting only a single-crossing, MAA instabilities would trigger new flavor conversions in normal mass hierarchy. In our simplified flavor evolution scheme, these would lead to spectral swaps and splits analogous to what produced in inverted hierarchy by the bimodal instability. Conversely, in the presence of spectra with a moderate flavor hierarchy, having multiple crossing energies, MZA effects would produce a sizable delay in the onset of the flavor conversions, inhibiting the growth of the MAA instability. In this case the splitting features for the oscillated spectra in both the mass hierarchies are the ones induced by the only bimodal and MZA effects.Comment: (v2: 13 pages, 9 eps figures. Revised version. Accepted for publication in PRD. Major changes: Stability analysis added. Results unchanged

Self-induced flavor instabilities of a dense neutrino stream in a two-dimensional model

We consider a simplifed model for self-induced flavor conversions of a dense neutrino gas in two dimensions, showing new solutions that spontaneously break the spatial symmetries of the initial conditions. As a result of the symmetry breaking induced by the neutrino-neutrino interactions, the coherent behavior of the neutrino gas becomes unstable. This instability produces large spatial variations in the flavor content of the ensemble. Furthermore, it also leads to the creation of domains of different net lepton number flux. The transition of the neutrino gas from a coherent to incoherent behavior shows an intriguing analogy with a streaming flow changing from laminar to turbulent regime. These finding would be relevant for the self-induced conversions of neutrinos streaming-off a supernova core.Comment: (v2: revised version: 8 pages, 7 eps figures. To appear on Physical Review D as Rapid Communication. Discussion enlarged. Two Appendices added.

Fast neutrino flavor conversions near the supernova core with realistic flavor-dependent angular distributions

It has been recently pointed out that neutrino fluxes from a supernova can show substantial flavor conversions almost immediately above the core. Using linear stability analyses and numerical solutions of the fully nonlinear equations of motion, we perform a detailed study of these fast conversions, focussing on the region just above the supernova core. We carefully specify the instabilities for evolution in space or time, andfind that neutrinos travelling towards the core make fast conversions more generic, i.e., possible for a wider range of flux ratios and angular asymmetries that produce a crossing between the zenith-angle spectra of $\nu_e$ and ${\bar\nu_e}$. Using fluxes and angular distributions predicted by supernova simulations, we find that fast conversions can occur within tens of nanoseconds, only a few meters away from the putative neutrinospheres. If these fast flavor conversions indeed take place, they would have important implications for the supernova explosion mechanism and nucleosynthesis.Comment: 18 pages, 7 figures (Improved presentation and new panel in Fig.6

Testing Lorentz invariance with neutrino bursts from supernova neutronization

Quantum-gravity (QG) effects might generate Lorentz invariance violation by the interaction of energetic particles with the foamy structure of the space-time. As a consequence, particles may not travel at the universal speed of light. We propose to constrain Lorentz invariance violation for energetic neutrinos exploiting the $\nu_e$ neutronization burst from the next galactic supernova (SN). This prompt signal is expected to produce a sharp peak in the SN $\nu_e$ light curve with a duration of $\sim 25$ ms. However presence of energy-dependent Lorentz invariance violation would significantly spread out the time structure of this signal. We find that the detection the SN $\nu_e$ burst from a typical galactic explosion at $d=10$ kpc in a Mton-class water Cerenkov detector, would be sensitive to a quantum-gravity mass scale $M_{\rm QG} \sim 10^{12}$ GeV ($2 \times10^{5}$ GeV) for the linear (quadratic) energy dependence of Lorentz invariance violation. These limits are rather independent of the neutrino mass hierarchy and whether the neutrino velocity is super or subluminal.Comment: 4 pages, 3 figures, Revised version. Minor changes. Matches published versio

Damping the neutrino flavor pendulum by breaking homogeneity

The most general case of self-induced neutrino flavor evolution is described by a set of kinetic equations for a dense neutrino gas evolving both in space and time. Solutions of these equations have been typically worked out assuming that either the time (in the core-collapse supernova environment) or space (in the early universe) homogeneity in the initial conditions is preserved through the evolution. In these cases one can gauge away the homogeneous variable and reduce the dimensionality of the problem. In this paper we investigate if small deviations from an initial postulated homogeneity can be amplified by the interacting neutrino gas, leading to a new flavor instability. To this end, we consider a simple two flavor isotropic neutrino gas evolving in time, and initially composed by only $\nu_e$ and $\bar\nu_e$ with equal densities. In the homogeneous case, this system shows a bimodal instability in the inverted mass hierarchy scheme, leading to the well studied flavor pendulum behavior. This would lead to periodic pair conversions $\nu_e \bar\nu_e \leftrightarrow \nu_x \bar\nu_x$. To break space homogeneity, we introduce small amplitude space-dependent perturbations in the matter potential. By Fourier transforming the equations of motion with respect to the space coordinate, we then numerically solve a set of coupled equations for the different Fourier modes. We find that even for arbitrarily tiny inhomogeneities, the system evolution runs away from the stable pendulum behavior: the different modes are excited and the space-averaged ensemble evolves towards flavor equilibrium. We finally comment on the role of a time decaying neutrino background density in weakening these results.Comment: (7 pages, 5 eps figures. Figure improved. Final version appeared in PRD

Self-induced temporal instability from a neutrino antenna

It has been recently shown that the flavor composition of a self-interacting neutrino gas can spontaneously acquire a time-dependent pulsating component during its flavor evolution. In this work, we perform a more detailed study of this effect in a model where neutrinos are assumed to be emitted in a two-dimensional plane from an infinite line that acts as a neutrino antenna. We consider several examples with varying matter and neutrino densities and find that temporal instabilities with various frequencies are excited in a cascade. We compare the numerical calculations of the flavor evolution with the predictions of linearized stability analysis of the equations of motion. The results obtained with these two approaches are in good agreement in the linear regime, while a dramatic speed-up of the flavor conversions occurs in the non-linear regime due to the interactions among the different pulsating modes. We show that large flavor conversions can take place if some of the temporal modes are unstable for long enough, and that this can happen even if the matter and neutrino densities are changing, as long as they vary slowly.Comment: v2: revised version, 15 pages, 6 figures. Minor changes. Typos removed, figures improved. Matches the version accepted on JCA