Self-induced Flavor Conversion Research Articles

Supernova neutrinos: Flavor conversion independent of their mass

In extremely dense neutrino environments like in supernova core, the neutrino-neutrino refraction may give rise to self-induced flavor conversion. These neutrino flavor oscillations are well understood from the idea of the exponentially growing modes of the interacting oscillators in the flavor space. Until recently, the growth rates of these modes were found to be of the order of the vacuum oscillation frequency $$\Delta m^2/2E$$ [ $$\mathcal {O}(1~\mathrm{km}^{-1})$$ ] and were considered slow growing. However, in the last couple of years it was found that if the system was allowed to have different zenith-angle distributions for the emitted $$\nu _e$$ and $$\bar{\nu }_e$$ beams then the fastest growing modes of the interacting oscillators grew at the order of $$\mu =\sqrt{2} G_\mathrm{F}n_{\nu }$$ , a typical $$\nu $$ – $$\nu $$ interaction energy [ $$\mathcal {O}(10^5~\mathrm{km}^{-1})$$ ]. Thus the growth rates are very large in comparison to the so-called ‘slow oscillations’ and can result in neutrino flavor conversion on a much faster scale. In fact, the point that the growth rates are no longer dependent on the vacuum oscillation frequency $$\Delta m^2/2E$$ , makes these ‘fast flavor conversions’ independent of $$\Delta m^2$$ (thus mass) and energy. This is a surprising result as neutrino flavor conversions are considered to be the ultimate proof of massive neutrinos. However, the importance of this effect in the realistic astrophysical scenarios still remains to be understood.

Self-induced neutrino flavor conversion without flavor mixing

Neutrino-neutrino refraction in dense media can cause self-induced flavor conversion triggered by collective run-away modes of the interacting flavor oscillators. The growth rates were usually found to be of order a typical vacuum oscillation frequency Δ m2/2E. However, even in the simple case of a νe beam interacting with an opposite-moving ν̄e beam, and allowing for spatial inhomogeneities, the growth rate of the fastest-growing Fourier mode is of order μ=√2 GF nν, a typical ν–ν interaction energy. This growth rate is much larger than the vacuum oscillation frequency and gives rise to flavor conversion on a much shorter time scale. This phenomenon of “fast flavor conversion” occurs even for vanishing Δ m2/2E and thus does not depend on energy, but only on the angle distributions. Moreover, it does not require neutrinos to mix or to have masses, except perhaps for providing seed disturbances. We also construct a simple homogeneous example consisting of intersecting beams and study a schematic supernova model proposed by Ray Sawyer, where νe and ν̄e emerge with different zenith-angle distributions, the key ingredient for fast flavor conversion. What happens in realistic astrophysical scenarios remains to be understood.

Collective neutrino flavor conversion: Recent developments

Neutrino flavor evolution in core-collapse supernovae, neutron-star mergers, or the early universe is dominated by neutrino–neutrino refraction, often spawning “self-induced flavor conversion,” i.e., shuffling of flavor among momentum modes. This effect is driven by collective run-away modes of the coupled “flavor oscillators” and can spontaneously break the initial symmetries such as axial symmetry, homogeneity, isotropy, and even stationarity. Moreover, the growth rates of unstable modes can be of the order of the neutrino–neutrino interaction energy instead of the much smaller vacuum oscillation frequency: self-induced flavor conversion does not always require neutrino masses. We illustrate these newly found phenomena in terms of simple toy models. What happens in realistic astrophysical settings is up to speculation at present.

Self-induced flavor conversion of supernova neutrinos on small scales

Self-induced flavor conversion of supernova (SN) neutrinos is a generic feature of neutrino-neutrino dispersion. The corresponding run-away modes in flavor space can spontaneously break the original symmetries of the neutrino flux and in particular can spontaneously produce small-scale features as shown in recent schematic studies. However, the unavoidable ``multi-angle matter effect'' shifts these small-scale instabilities into regions of matter and neutrino density which are not encountered on the way out from a SN. The traditional modes which are uniform on the largest scales are most prone for instabilities and thus provide the most sensitive test for the appearance of self-induced flavor conversion. As a by-product we clarify the relation between the time evolution of an expanding neutrino gas and the radial evolution of a stationary SN neutrino flux. Our results depend on several simplifying assumptions, notably stationarity of the solution, the absence of a ``backward'' neutrino flux caused by residual scattering, and global spherical symmetry of emission.

Supernova deleptonization asymmetry: Impact on self-induced flavor conversion

During the accretion phase of a core-collapse supernova (SN), the deleptonization flux has recently been found to develop a global dipole pattern (LESA---Lepton Emission Self-sustained Asymmetry). The $\nu_e$ minus $\bar\nu_e$ flux essentially vanishes in one direction, potentially facilitating self-induced flavor conversion. On the other hand, below the stalled shock wave, self-induced flavor conversion is typically suppressed by multi-angle matter effects, preventing any impact of flavor conversion on SN explosion dynamics. In a schematic model of SN neutrino fluxes, we study the impact of modified $\bar\nu_e$-$\nu_e$ flux asymmetries on collective flavor conversion. In the parameter space consisting of matter density and effective neutrino density, the region of instability with regard to self-induced flavor conversion is much larger for a vanishing lepton number flux, yet this modification does not intersect a realistic SN profile. Therefore, it appears that, even in the presence of LESA, self-induced flavor conversion remains suppressed below the shock front.

Spontaneous Symmetry Breaking in Supernova Neutrinos

Some recent developments in supernova neutrino physics are introduced where spontaneous symmetry breaking is a common theme. The physics of self-induced flavor conversion has acquired a new complication in that a new class of instabilities breaks axial symmetry of a neutrino stream, the multi-azimuth angle (MAA) instability. A completely different new phenomenon, discovered in the first realistic three-dimensional (3D) simulations, is the Lepton-Emission Self-sustained Asymmetry (LESA) during the accretion phase. Here, a neutrino-hydrodynamical instability breaks global spherical symmetry in that the lepton-number flux (νe minus ν‾e) develops a stable dipole pattern such that the lepton flux is almost exclusively emitted in one hemisphere.

Erratum: Axial Symmetry Breaking in Self-Induced Flavor Conversion of Supernova Neutrino Fluxes [Phys. Rev. Lett.111, 091101 (2013)

Erratum: Axial Symmetry Breaking in Self-Induced Flavor Conversion of Supernova Neutrino Fluxes [Phys. Rev. Lett.<b>111</b>, 091101 (2013)

Neutrino flavor pendulum in both mass hierarchies

We construct a simple example for self-induced flavor conversion in dense neutrino gases showing new solutions that violate the symmetries of initial conditions. Our system consists of two opposite momentum modes 1 and 2, each initially occupied with equal densities of nu_e and anti-nu_e. Restricting solutions to symmetry under 1 <-> 2 allows for the usual bimodal instability ("flavor pendulum") in the inverted neutrino mass hierarchy (IH) and stability (no self-induced flavor conversion) in the normal hierarchy (NH). Lifting this symmetry restriction allows for a second pendulum-like solution that occurs in NH where the modes 1 and 2 swing in opposite directions in flavor space. Any small deviation from 1-2 symmetry in the initial condition triggers the new instability in NH. This effect corresponds to the recently identified multi-azimuth angle (MAA) instability of supernova neutrino fluxes. Both cases show explicitly that solutions of the equations of collective flavor oscillations need not inherit the symmetries of initial conditions, although this has been universally assumed.

Axial Symmetry Breaking in Self-Induced Flavor Conversionof Supernova Neutrino Fluxes

Neutrino-neutrino refraction causes self-induced flavor conversion in dense neutrino fluxes. For the first time, we include the azimuth angle of neutrino propagation as an explicit variable and find a new generic multi-azimuth-angle instability which, for simple spectra, occurs in the normal neutrino mass hierarchy. Matter suppression of this instability in supernovae requires larger densities than the traditional bimodal case. The new instability shows explicitly that solutions of the equations for collective flavor oscillations need not inherit the symmetries of initial or boundary conditions. This change of paradigm requires reconsideration of numerous results in this field.

Spurious instabilities in multiangle simulations of collective flavor conversion

The dense neutrino flux streaming from a core-collapse supernova can undergo self-induced flavor conversion caused by neutrino-neutrino refraction. Numerical studies of these nonlinear effects are challenging because representing the neutrino radiation field by discrete energy and angle bins can easily lead to unphysical solutions. In particular, if the number of angle bins N_a is too small, flavor conversion begins too deep and produces completely spurious results. At the same time, N_a=1 (single-angle approximation) can be a good proxy for the N_a -> infinity limit. Based on a linearized stability analysis, we explain some of the puzzling effects of discrete angle distributions.

Supernova neutrino halo and the suppression of self-induced flavor conversion

Neutrinos streaming from a supernova (SN) core occasionally scatter in the envelope, producing a small "neutrino halo" with a much broader angle distribution than the primary flux originating directly from the core. Cherry et al. (2012) have recently pointed out that, during the accretion phase, the halo actually dominates neutrino-neutrino refraction at distances exceeding some 100 km. However, the multiangle matter effect (which increases if the angle distribution is broader) still appears to suppress self-induced flavor conversion during the accretion phase.

Suppression of Self-Induced Flavor Conversion in the Supernova Accretion Phase

Self-induced flavor conversions of supernova (SN) neutrinos can strongly modify the flavor-dependent fluxes. We perform a linearized flavor stability analysis with accretion-phase matter profiles of a 15M[symbol: see text] spherically symmetric model and corresponding neutrino fluxes. We use realistic energy and angle distributions, the latter deviating strongly from quasi-isotropic emission, thus accounting for both multiangle and multienergy effects. For our matter and neutrino density profile we always find stable conditions: flavor conversions are limited to the usual Mikheyev-Smirnov-Wolfenstein effect. In this case one may distinguish the neutrino mass hierarchy in a SN neutrino signal if the mixing angle θ13 is as large as suggested by recent experiments.