Neutrino Gas Research Articles

Collective neutrino oscillations and spontaneous symmetry breaking

Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can experience collective oscillations through nonlinear refraction in the dense neutrino medium in this environment. Significant progress has been made in the last decade towards the understanding of collective neutrino oscillations in various simplified neutrino gas models with imposed symmetries and reduced dimensions. However, a series of recent studies seem to have "reset" this progress by showing that these models may not be compatible with collective neutrino oscillations because the latter can break the symmetries spontaneously if they are not imposed. We review some of the key concepts of collective neutrino oscillations by using a few simple toy models. We also elucidate the breaking of spatial and directional symmetries in these models because of collective oscillations.

Damping of self-induced neutrino flavor transitions due to inhomogeneities

Self-induced neutrino flavor dynamics has been typically characterized 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 this talk we show that 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 νe and ν‾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. To break space homogeneity, we introduce small amplitude space-dependent perturbations in the matter potential. We find that even for arbitrarily tiny inhomogeneities, the system evolution runs away from the stable pendulum behavior and the space-averaged ensemble evolves towards flavor equilibrium.

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.

Chaotic flavor evolution in an interacting neutrino gas

Neutrino-neutrino refraction can lead to non-periodic flavor oscillations in dense neutrino gases, and it has been hypothesized that some solutions are chaotic in nature. This is of particular interest in the case of neutrino emission from core-collapse supernovae where the measurement of the spectral shape for different flavors can provide crucial information about both neutrino physics and the physical conditions close to the proto-neutron star. Whether a system is chaotic or not can be assessed by the Lyapunov exponents which quantify the rate of divergence of nearby trajectories in the system. We have done a numerical case study for a simple toy model of two neutrino flavors with two momentum states traveling against each other which is known to exhibit flavor transition instabilities. We find the leading Lyapunov exponent to be positive in all cases, confirming the chaoticity of the system for both the normal and the inverted neutrino mass hierarchy. However, more Lyapunov exponents were approximately zero in the inverted hierarchy compared to the normal which has implications for the stability of the system. To investigate this, we have calculated a generalized set of normal modes, the so-called covariant Lyapunov vectors. The covariant Lyapunov vectors associated with vanishing Lyapunov exponents showed the existence of marginally stable directions in phase space for some cases. While our analysis was done for a toy model example, it should work equally well for more realistic cases of neutrinos streaming from a proto-neutron star and provide valuable insight into the nature of the flavor instability. We finally stress that our approach captures many more properties of the physical system than the linear stability analyses which have previously been performed.

Suppression of the multi-azimuthal-angle instability in dense neutrino gas during supernova accretion phase

It has been recently pointed out that by 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 arise. In particular, for a flux ordering ${F}_{{\ensuremath{\nu}}_{e}}>{F}_{{\overline{\ensuremath{\nu}}}_{e}}>{F}_{{\ensuremath{\nu}}_{x}}$, as expected during the SN accretion phase, this instability occurs in the normal neutrino mass hierarchy. However, during this phase, the ordinary matter density can be larger than the neutrino one, suppressing the self-induced conversions. In this regard, we investigate the matter suppression of the MAA effects, performing a linearized stability analysis of the neutrino equations of motion, in the presence of realistic SN density profiles. We compare these results with the numerical solution of the SN neutrino nonlinear evolution equations. Assuming axially symmetric distributions of neutrino momenta, we find that the large matter term strongly inhibits the MAA effects. In particular, the hindrance becomes stronger including realistic forward-peaked neutrino angular distributions. As a result, in our model for a $10.8\text{ }{M}_{\ensuremath{\bigodot}}$ iron-core SNe, MAA instability does not trigger any flavor conversion during the accretion phase. Instead, for a $8.8\text{ }{M}_{\ensuremath{\bigodot}}$ O-Ne-Mg core SN model, with lower matter density profile and less forward-peaked angular distributions, flavor conversions are possible also at early times.

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.

Flavor oscillation modes in dense neutrino media

We study two-flavor neutrino oscillations in homogeneous neutrino gases in which neutrinos and anti-neutrinos are in nearly pure weak interaction states initially. We find that the monopole and dipole oscillation modes can trigger flavor instabilities in the opposite neutrino mass hierarchies in a nearly isotropic neutrino gas. For a class of simple neutrino systems we are able to identify the normal modes of neutrino oscillations in the linear regime. Our results provide new insights into the recently discovered multi-azimuthal angle (MAA) instability of neutrino oscillations in supernovae.

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.

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.

Neutrinos and rare isotopes

The close connection between neutrino physics and the physics explored at rare isotope facilities is explored. The duality between the Hamiltonian describing the self-interacting neutrino gas near the proto-neutron star in a core-collapse supernova and the BCS theory of pairing is elucidated. This many neutrino system is unique as it is the only many-body system driven by weak interactions. Its symmetries are discussed.

Flavor oscillations of supernova neutrinos

Neutrinos emitted by core-collapse supernovae (SNe) represent an important laboratory for both particle physics and astrophysics. While propagating in the dense SN environment, they can feel not only the presence of background matter (via ordinary Mikheev-Smirnov-Wolfenstein effects) but also of the gas of neutrinos and antineutrinos (via neutrino-neutrino interaction effects). The MSW effect would imprint on SN neutrinos a track of the shock-wave propagation and of the matter turbulences in the stellar envelope. Moreover, the neutrino-neutrino interactions appear to modify the flavor evolution of SN neutrinos in a collective way, completely different from the ordinary matter effects. In these conditions, the flavor evolution equations become highly nonlinear, sometimes resulting in surprising phenomena when the entire neutrino system oscillates coherently as a single collective mode. In this talk, I will present the recent results on supernova neutrino flavor conversions and I will discuss about the sensitivity of these effects to the ordering of the neutrino mass spectrum.

Instability in the Dense Supernova Neutrino Gas with Flavor-Dependent Angular Distributions

The usual description of self-induced flavor conversions for neutrinos (ν's) in supernovae is based on the simplified assumption that all the ν's of the different species are emitted "half-isotropically" by a common neutrinosphere, in analogy to a blackbody emission. However, realistic supernova simulations show that ν angular distributions at decoupling are far from being half-isotropic and, above all, are flavor dependent. We show that flavor-dependent angular distributions may lead to crossing points in the angular spectra of different ν species (where F(ν(e))=F(ν(x)) and F(ν(e))=F(ν(x))) around which a new multiangle instability can develop. To characterize this effect, we carry out a linearized flavor stability analysis for different supernova neutrino angular distributions. We find that this instability can shift the onset of the flavor conversions toward low radii and produce a smearing of the splitting features found with trivial ν emission models. As a result the spectral differences among ν's of different flavors could be strongly reduced.

Evolution of a dense neutrino gas in matter and electromagnetic field

We describe the system of massive Weyl fields propagating in a background matter and interacting with an external electromagnetic field. The interaction with an electromagnetic field is due to the presence of anomalous magnetic moments. To canonically quantize this system first we develop the classical field theory treatment of Weyl spinors in frames of the Hamilton formalism which accounts for the external fields. Then, on the basis of the exact solution of the wave equation for a massive Weyl field in a background matter we obtain the effective Hamiltonian for the description of spin–flavor oscillations of Majorana neutrinos in matter and a magnetic field. Finally, we incorporate in our analysis the neutrino self-interaction which is essential when the neutrino density is sufficiently high. We also discuss the applicability of our results for the studies of collective effects in spin–flavor oscillations of supernova neutrinos in a dense matter and a strong magnetic field.

Invariants of collective neutrino oscillations

We consider the flavor evolution of a dense neutrino gas by taking into account both vacuum oscillations and self interactions of neutrinos. We examine the system from a many-body perspective as well as from the point of view of an effective one-body description formulated in terms of the neutrino polarization vectors. We show that, in the single angle approximation, both the many-body picture and the effective one-particle picture possess several constants of motion. We write down these constants of motion explicitly in terms of the neutrino isospin operators for the many-body case and in terms of the polarization vectors for the effective one-body case. The existence of these constants of motion is a direct consequence of the fact that the collective neutrino oscillation Hamiltonian belongs to the class of Gaudin Hamiltonians. This class of Hamiltonians also includes the (reduced) BCS pairing Hamiltonian describing superconductivity. We point out the similarity between the collective neutrino oscillation Hamiltonian and the BCS pairing Hamiltonian. The constants of motion manifest the exact solvability of the system. Borrowing the well established techniques of calculating the exact BCS spectrum, we present exact eigenstates and eigenvalues of both the many-body and the effective one-particle Hamiltonians describing the collective neutrino oscillations. For the effective one-body case, we show that spectral splits of neutrinos can be understood in terms of the adiabatic evolution of some quasi-particle degrees of freedom from a high density region where they coincide with flavor eigenstates to the vacuum where they coincide with mass eigenstates. We write down the most general consistency equations which should be satisfied by the effective one-body eigenstates and show that they reduce to the spectral split consistency equations for the appropriate initial conditions.

Analysis of matter suppression in collective neutrino oscillations during the supernova accretion phase

The usual description of self-induced neutrino flavor conversions in core collapse supernovae (SNe) is based on the dominance of the neutrino density n_nu over the net electron density n_e. However, this condition is not met during the post-bounce accretion phase, when the dense matter in a SN is piled up above the neutrinosphere. As recently pointed-out, a dominant matter term in the anisotropic SN environment would dephase the flavor evolution for neutrinos traveling on different trajectories, challenging the occurrence of the collective behavior in the dense neutrino gas. Using the results from recent long term simulations of core-collapse SN explosions, based on three flavor Boltzmann neutrino transport in spherical symmetry, we find that both the situations of complete matter suppression (when n_e >> n_nu) and matter-induced decoherence (when n_e \gtrsim n_nu) of flavor conversions are realized during the accretion phase. The matter suppression at high densities prevents any possible impact of the neutrino oscillations on the neutrino heating and hence on the dynamics of the explosion. Furthermore, it changes the interpretation of the Earth matter effect on the SN neutrino signal during the accretion phase, allowing the possibility of the neutrino mass hierarchy discrimination at not too small values of the leptonic mixing angle \theta_{13} (i.e. \sin^2{\theta}_{13} \gtrsim 10^{-3}).

Towards the detection of light and heavy relic neutrinos

The standard Big Bang cosmology predicts that the universe is abundantly populated with neutrinos. As expected there are at least 114 neutrinos per cubic centimeter averaged over the whole space. Like the cosmic background radiation the cosmic neutrinos at present posses a very small kinetic energy due to expansion of the universe. This prediction is one of the cornerstones of modern cosmology. On the other hand the existence of cosmic neutrinos has not yet been confirmed by direct detection experiments. For now we only have a lower limit on the total mass of this free floating ghostly gas of neutrinos, but even so it is roughly equivalent to the total mass of all the visible stars in universe. There could be many more neutrinos at Earth because of condensation of neutrinos, now moving slowly under the gravitational pull of our galaxy. Here we discuss the possibility of detection of relic neutrinos in KATRIN and MARE experiments via neutrino capture on tritium and rhenium, respectively. We also examine single and double relic neutrino capture on double β -decaying nuclei which might be relevant in the context of the new generation double beta decay experiments. Further we explore feasibility of experiments for detection of heavy sterile neutrinos with masses in MeV region, which may have important astrophysical and cosmological implications.

Collective Neutrino Oscillations

We review the rich phenomena associated with neutrino flavor transformation in the presence of neutrino self-coupling. Our exposition centers on three collective neutrino oscillation scenarios: (a) a simple bipolar neutrino system that initially consists of monoenergetic νeand [Formula: see text], (b) a homogeneous and isotropic neutrino gas with multiple neutrino/antineutrino species and continuous energy spectra, and (c) a generic neutrino gas in an anisotropic environment. We use each of these scenarios to illustrate key facets of collective neutrino oscillations. We discuss the implications of collective neutrino flavor oscillations for core-collapse supernova physics and for the prospects of obtaining and/or constraining fundamental neutrino properties, such as the neutrino mass hierarchy and θ13from a future observed supernova neutrino signal.

Neutrinos and symmetries

Three facets of symmetries in neutrino physics are briefly reviewed: i) The SO(5) symmetry of the neutrino mass and and its connection to the see-saw mechanism; ii) SU(N flavor) symmetries of dense, self-interacting neutrino gases in astrophysical settings; iii) The neutrino mixing angle θ 13 and possible CP-violation in the neutrino sector.

A lower limit on the dark particle mass from dSphs

We use dwarf spheroidal galaxies as a tool to attempt to put precise lower limits on the mass of the dark matter particle, assuming it is a sterile neutrino. We begin by making cored dark halo fits to the line of sight velocity dispersions as a function of projected radius (taken from Walker et al. 2007) for six of the Milky Way's dwarf spheroidal galaxies. We test Osipkov-Merritt velocity anisotropy profiles, but find that no benefit is gained over constant velocity anisotropy. In contrast to previous attempts, we do not assume any relation between the stellar velocity dispersions and the dark matter ones, but instead we solve directly for the sterile neutrino velocity dispersion at all radii by using the equation of state for a partially degenerate neutrino gas (which ensures hydrostatic equilibrium of the sterile neutrino halo). This yields a 1:1 relation between the sterile neutrino density profile and the velocity dispersion profile, and therefore gives us an accurate estimate of the Tremaine-Gunn limit at all radii. By varying the sterile neutrino particle mass, we locate the minimum mass for all six dwarf spheroidals such that the Tremaine-Gunn limit is not exceeded at any radius (in particular at the centre). We find sizeable differences between the ranges of feasible sterile neutrino particle mass for each dwarf, but interestingly there exists a small range 270-280eV which is consistent with all dSphs at the 1-σ level.

Equilibrium configurations of 11 eV sterile neutrinos in MONDian galaxy clusters

Modified Newtonian dynamics (MOND) can fit a broad range of galaxy kinematic data, but struggles with clusters of galaxies. MONDian clusters need dark matter (DM), and here we test the 11 eV c−2 sterile neutrino (SN) – used to fit the first three acoustic peaks of the cosmic microwave background (CMB) – by investigating their equilibrium distributions in 30 groups and clusters over a wide range of temperatures. We do this by first taking the known SN density, necessary for hydrostatic equilibrium of the intracluster medium (or to produce the observed lensing map). Then, we solve for the SN velocity dispersion (VD), needed for their own hydrostatic equilibrium, through the equation of state for a partially degenerate neutrino gas. The VD is a unique, continuous function of radius determined by the density and mass of the SN particles. Knowing both the SN density and VD tells us the Tremaine–Gunn phase-space limit at all radii. We find that all 30 systems serendipitously reach the Tremaine–Gunn limit by the centre, which means a portion of the dynamical mass must always be covered by the brightest cluster galaxy. Interestingly, the typical fitted K-band mass-to-light ratio is unity and at most 1.2, which is very consistent – although leaving no margin for error – with stellar population synthesis models. Amidst the sample there are several special cases including the Coma cluster (for which DM was first proposed), NGC 720 (where geometrical evidence for DM was found) and the bullet cluster (where DM – of some kind – in clusters was directly proven to exist). We demonstrate that 11 eV c−2 SNs are unlikely to influence spiral galaxy rotation curves, as they do not influence even some very massive early-types (NGC 4125 and NGC 6482). Finally, we conclude that it is intriguing that the minimum mass of SN particle that can match the CMB is the same as the minimum mass found here to be consistent with equilibrium configurations of MONDian clusters of galaxies.