Neutrino Flavor Conversion Research Articles

Simple method of diagnosing fast flavor conversions of supernova neutrinos

Neutrinos emitted from a supernova may undergo flavor conversions almost immediately above the core, with possible consequences for supernova dynamics and nucleosynthesis. However, the precise conditions for such fast conversions can be difficult to compute and require knowledge of the full angular distribution of the flavor-dependent neutrino fluxes, that is not available in typical supernova simulations. In this paper, we show that the overall flavor evolution is qualitatively similar to the growth of a so-called `zero mode', determined by the background matter and neutrino densities, which can be reliably predicted using only the second angular moments of the electron lepton number distribution, i.e., the difference in the angular distributions of $\nu_e$ and $\bar{\nu}_e$ fluxes. We propose that this zero mode, which neither requires computing the full Green's function nor a detailed knowledge of the angular distributions, may be useful for a preliminary diagnosis of possible fast flavor conversions in supernova simulations with modestly resolved angular distributions

Fast neutrino flavor conversion: Roles of dense matter and spectrum crossing

The flavor conversion of a neutrino usually occurs at densities $\lesssim G_F^{-1} \omega$, whether in the ordinary matter or the neutrino medium, and on time/distance scales of order $\omega^{-1}$, where $G_F$ is the Fermi weak coupling constant and $\omega$ is the vacuum oscillation frequency of the neutrino. In 2005 Sawyer and more recently both he and other groups have shown that neutrino flavor conversions can occur on scales much shorter than $\omega^{-1}$ in a very dense, anisotropic neutrino gas such as that in a core-collapse supernova or a binary neutron star merger. It has also been suggested that the fast neutrino flavor conversion require a crossing in the electron lepton number (ELN) angular distribution or spectrum. We study a few simple analytical models with which we elucidate the roles of the dense matter and the ELN spectrum crossing in neutrino fast flavor conversions. We show that a large matter density can induce fast neutrino flavor conversions in certain astrophysical scenarios such as at the early epoch of a core-collapse supernova.

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.

Matter effects on the flavor conversions of solar neutrinos and high-energy astrophysical neutrinos

Can we observe the solar eclipses in the neutrino light? In principle, this is possible by identifying the lunar matter effects on the flavor conversions of solar neutrinos when they traverse the Moon before reaching the detectors at the Earth. Unfortunately, we show that the lunar matter effects on the survival probability of solar B8 neutrinos are suppressed by an additional factor of 1.2%, compared to the day-night asymmetry. However, we point out that the matter effects on the flavor conversions of high-energy astrophysical neutrinos, when they propagate through the Sun, can be significant. Though the flavor composition of high-energy neutrinos can be remarkably modified, it is quite challenging to observe such effects even in the next-generation of neutrino telescopes.

Shell-model computed cross sections for charged-current scattering of astrophysical neutrinos off Ar40

Charged-current (anti)neutrino-$^{40}\mathrm{Ar}$ cross sections for astrophysical neutrinos have been calculated. The initial and final nuclear states were calculated using the nuclear shell model. The folded solar-neutrino scattering cross section was found to be $1.78(23)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}42}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}$, which is higher than what the previous papers have reported. The contributions from the ${1}^{\ensuremath{-}}$ and ${2}^{\ensuremath{-}}$ multipoles were found to be significant at supernova-neutrino energies, confirming the random-phase approximation (RPA) result of a previous study. The effects of neutrino flavor conversions in dense stellar matter (matter oscillations) were found to enhance the neutrino-scattering cross sections significantly for both the normal and inverted mass hierarchies. For the antineutrino scattering, only a small difference between the nonoscillating and inverted-hierarchy cross sections was found, while the normal-hierarchy cross section was 2--3 times larger than that of the nonoscillating cross section, depending on the adopted parametrization of the Fermi-Dirac distribution. This property of the supernova-antineutrino signal could probably be used to distinguish between the two hierarchies in megaton LAr detectors.

Fast neutrino flavor conversion as oscillations in a quartic potential

Neutrinos in dense environments undergo collective pair conversions $\nu_e\bar{\nu}_e \leftrightarrow \nu_x\bar{\nu}_x$, where $x$ is a non-electron flavor, due to forward scattering off each other that may be a crucial ingredient for supernova explosions. Depending on the flavor-dependent local angular distributions of the neutrino fluxes, the conversion rate can be "fast", i.e., of the order $\mu=\sqrt{2}G_F n_\nu$, which can far exceed the usual neutrino oscillation frequency $\omega=\Delta m^2/(2E)$. Until now, this surprising nonlinear phenomenon has only been understood in the linear regime and explored further using numerical experiments. We present an analytical treatment of the simplest system that exhibits fast conversions, and show that the conversion can be understood as the dynamics of a particle rolling down in a quartic potential governed dominantly by $\mu$, but seeded by slower oscillations.

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

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 ($\omega$,$k$) of disturbances in the mean field of the $\nu_e\nu_x$ 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 $\omega$, 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 $\omega$) is complex, leading to disturbances damped in space, or when both $\omega$ 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 conversions: Ubiquitous in compact binary merger remnants

The massive neutron star (NS) or black hole (BH) accretion disk resulting from NS--NS or NS--BH mergers is dense in neutrinos. We present the first study on the role of angular distributions in the neutrino flavor conversion above the remnant disk. In particular, we focus on "fast" pairwise conversions whose rate depends on the local angular intensity of the electron lepton number carried by neutrinos. Because of the emission geometry and the flux density of $\bar{\nu}_e$ being larger than that of $\nu_e$, fast conversions prove to be a generic phenomenon in NS--NS and NS--BH mergers for physically motivated disturbances in the mean field of flavor coherence. Our findings suggest that, differently from the core-collapse supernova case, fast flavor conversions seem to be unavoidable in compact mergers and could have major consequences for the jet dynamics and the synthesis of elements above the remnant disk.

Helicity coherence in binary neutron star mergers and nonlinear feedback

Neutrino flavor conversion studies based on astrophysical environments usually implement neutrino mixings, neutrino interactions with matter and neutrino self-interactions. In anisotropic media, the most general mean-field treatment includes neutrino mass contributions as well, that introduce a coupling between neutrinos and antineutrinos termed helicity or spin coherence. We discuss resonance conditions for helicity coherence for Dirac and Majorana neutrinos. We explore the role of these mean-field contributions on flavor evolution in the context of a binary neutron star merger remnant. We find that resonance conditions can be satisfied in neutron star merger scenarios while adiabaticity is not sufficient for efficient flavor conversion. We analyse our numerical findings by discussing general conditions to have multiple MSW-like resonances, in presence of non-linear feedback, in astrophysical environments.

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, and find 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 νe and ν̄e. 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.

Probing neutrino mass hierarchy by comparing the charged-current and neutral-current interaction rates of supernova neutrinos

The neutrino mass hierarchy is one of the neutrino fundamental properties yet to be determined. We introduce a method to determine neutrino mass hierarchy by comparing the interaction rate of neutral current (NC) interactions, ν(ν̄) + p → ν(ν̄) + p, and inverse beta decays (IBD), ν̄e + p → n + e+, of supernova neutrinos in scintillation detectors. Neutrino flavor conversions inside the supernova are sensitive to neutrino mass hierarchy. Due to Mikheyev-Smirnov-Wolfenstein effects, the full swapping of ν̄e flux with the ν̄x (x = μ, τ) one occurs in the inverted hierarchy, while such a swapping does not occur in the normal hierarchy. As a result, more high energy IBD events occur in the detector for the inverted hierarchy than the high energy IBD events in the normal hierarchy. By comparing IBD interaction rate with the mass hierarchy independent NC interaction rate, one can determine the neutrino mass hierarchy.

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.

Neutrino astrophysics : recent advances and open issues

We highlight recent advances in neutrino astrophysics, the open issues and the interplay with neutrino properties. We emphasize the important progress in our understanding of neutrino flavor conversion in media. We discuss the case of solar neutrinos, of core-collapse supernova neutrinos and of SN1987A, and of the recently discovered ultra-high energy neutrinos whose origin is to be determined.

Turbulence patterns and neutrino flavor transitions in high-resolution supernova models

During the shock-wave propagation in a core-collapse supernova (SN), matter turbulence may affect neutrino flavor conversion probabilities. Such effects have been usually studied by adding parametrized small-scale random fluctuations (with arbitrary amplitude) on top of coarse, spherically symmetric matter density profiles. Recently, however, two-dimensional (2D) SN models have reached a space resolution high enough to directly trace anisotropic density profiles, down to scales smaller than the typical neutrino oscillation length. In this context, we analyze the statistical properties of a large set of SN matter density profiles obtained in a high-resolution 2D simulation, focusing on a post-bounce time (2 s) suited to study shock-wave effects on neutrino propagation on scales as small as O(100) km and possibly below. We clearly find the imprint of a broken (Kolmogorov-Kraichnan) power-law structure, as generically expected in 2D turbulence spectra. We then compute the flavor evolution of SN neutrinos along representative realizations of the turbulent matter density profiles, and observe no or modest damping of the neutrino crossing probabilities on their way through the shock wave. In order to check the effect of possibly unresolved fluctuations at scales below O(100) km, we also apply a randomization procedure anchored to the power spectrum calculated from the simulation, and find consistent results within ± 1σ fluctuations. These results show the importance of anchoring turbulence effects on SN neutrinos to realistic, fine-grained SN models.

Multi-azimuthal-angle effects in self-induced supernova neutrino flavor conversions without axial symmetry

The flavor evolution of neutrinos emitted by a supernova (SN) core is strongly affected by the refractive effects associated with the neutrino-neutrino interactions in the deepest stellar regions. Till now, all numerical studies have assumed the axial symmetry for the "multi-angle effects" associated with the neutrino-neutrino interactions. Recently, it has been pointed out in \cite{Raffelt:2013rqa} that removing this assumption, a new multi-azimuthal-angle (MAA) instability would emerge in the flavor evolution of the dense SN neutrino gas in addition to the one caused by multi-zenith-angle (MZA) effects. Inspired by this result, for the first time we numerically solve the non-linear neutrino propagation equations in SN, introducing the azimuthal angle as angular variable in addition to the usual zenith angle. We consider simple energy spectra with an excess of \nu_e over anti-\nu_e. In these cases, we find that even starting with a complete axial symmetric neutrino emission, the MAA effects would lead to significant flavor conversions in normal mass hierarchy, in cases otherwise stable under the only MZA effects. The final outcome of the flavor conversions, triggered by the MAA instability, depends on the initial asymmetry between \nu_e and anti-\nu_e spectra. If it is sufficiently large, final spectra would show an ordered behavior with spectral swaps and splits. Conversely, for small flavor asymmetries flavor decoherence among angular modes develops, affecting the flavor evolution also in inverted mass hierarchy.

Open issues in neutrino astrophysics

AbstractNeutrinos of astrophysical origin are messengers produced in stars, in explosive phenomena like core‐collapse supernovae, in the accretion disks around black holes, or in the Earth's atmosphere. Their fluxes and spectra encode information on the environments that produce them. Such fluxes are modified in characteristic ways when neutrinos traverse a medium. Here the current understanding of neutrino flavour conversion in media is summarized. The importance of this domain for astrophysical observations is emphasized. Examples are given of the fundamental properties that research into astrophysical neutrinos has uncovered, or might reveal in the future.

Extended evolution equations for neutrino propagation in astrophysical and cosmological environments

We derive the evolution equations for a system of neutrinos interacting among themselves and with a matter background, based upon the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. This theoretical framework gives an (unclosed) set of first-order coupled integro-differential equations governing the evolution of the reduced density matrices. By employing the hierarchy, we first rederive the mean-field evolution equations for the neutrino one-body density matrix associated with a system of neutrinos and antineutrinos interacting with matter and with an anisotropic neutrino background. Then, we derive extended evolution equations to determine neutrino flavor conversion beyond the commonly used mean-field approximation. To this aim we include neutrino-antineutrino pairing correlations to the two-body density matrix. The inclusion of these new contributions leads to an extended evolution equation for the normal neutrino density and to an equation for the abnormal one involving the pairing mean-field. We discuss the possible impact of neutrino-antineutrino correlations on neutrino flavor conversion in the astrophysical and cosmological environments, and possibly upon the supernova dynamics. Our results can be easily generalized to an arbitrary number of neutrino families.

Effect of collective neutrino oscillations on the neutrino mechanism of core-collapse supernovae

In the seconds after collapse of a massive star, the newborn proto-neutron star (PNS) radiates neutrinos of all flavors. The absorption of electron-type neutrinos below the radius of the stalled shockwave may drive explosions (the "neutrino mechanism"). Because the heating rate is proportional to the square of neutrino energy, flavor conversion of mu and tau neutrinos to electron-type neutrinos via collective neutrino oscillations (CnuO) may in principle increase the heating rate and drive explosions. In order to assess the potential importance of CnuO for the shock revival, we solve the steady-state boundary value problem of spherically-symmetric accretion between the PNS surface (r_nu) and the shock (r_S), including a scheme for flavor conversion via CnuO. For a given r_nu, PNS mass (M), accretion rate (Mdot), and assumed values of the neutrino energies from the PNS, we calculate the critical neutrino luminosity above which accretion is impossible and explosion results. We show that CnuO can decrease the critical luminosity by a factor of at most ~1.5, but only if the flavor conversion is fully completed inside r_S and if there is no matter suppression. The magnitude of the effect depends on the model parameters (M, Mdot, and r_nu) through the shock radius and the physical scale for flavor conversion. We quantify these dependencies and find that CnuO could lower the critical luminosity only for small M and Mdot, and large r_nu. However, for these parameter values CnuO are suppressed due to matter effects. By quantifying the importance of CnuO and matter suppression at the critical neutrino luminosity for explosion, we show in agreement with previous studies that CnuO are unlikely to affect the neutrino mechanism of core-collapse supernovae significantly.