Neutrino Gas Research Articles

Chaos in inhomogeneous neutrino fast flavor instability

In dense neutrino gases, the neutrino-neutrino coherent forward scattering gives rise to a complex flavor oscillation phenomenon not fully incorporated in simulations of neutron star mergers (NSM) and core collapse supernovae (CCSNe). Moreover, it has been proposed to be chaotic, potentially limiting our ability to predict neutrino flavor transformations in simulations. To address this issue, we explore how small flavor perturbations evolve in the nonlinear regime of the neutrino quantum kinetic equation within a narrow centimeter-scale region inside a NSM and a toy neutrino distribution. Our findings reveal that paths in the flavor state space of solutions with similar initial conditions diverge exponentially, exhibiting chaos. This inherent chaos makes the microscopic scales of neutrino flavor transformations unpredictable. However, the domain-averaged neutrino density matrix remains relatively stable, with chaos minimally affecting it. This particular property suggests that domain-averaged quantities remain reliable despite the exponential amplification of errors. Published by the American Physical Society 2024

Once-in-a-lifetime encounter models for neutrino media: From coherent oscillations to flavor equilibration

Collective neutrino oscillations are typically studied using the lowest-order quantum kinetic equation, also known as the mean-field approximation. However, some recent quantum many-body simulations suggest that quantum entanglement among neutrinos may be important and may result in flavor equilibration of the neutrino gas. In this work, we develop new quantum models for neutrino gases in which any pair of neutrinos can interact at most once in their lifetimes. A key parameter of our models is γ=μΔz, where μ is the neutrino coupling strength, which is proportional to the neutrino density, and Δz is the duration over which a pair of neutrinos can interact each time. Our models reduce to the mean-field approach in the limit γ→0 and achieve flavor equilibration in time t≫(γμ)−1. These models demonstrate the emergence of coherent flavor oscillations from the particle perspective and may help elucidate the role of quantum entanglement in collective neutrino oscillations. Published by the American Physical Society 2024

Application of neural networks for the reconstruction of supernova neutrino energy spectra following fast neutrino flavor conversions

Neutrinos can undergo fast flavor conversions (FFCs) within extremely dense astrophysical environments, such as core-collapse supernovae (CCSNe) and neutron star mergers (NSMs). In this study, we explore FFCs in a neutrino gas, revealing that when the FFC growth rate significantly exceeds that of the vacuum Hamiltonian, all neutrinos (regardless of energy) share a common survival probability dictated by the energy-integrated neutrino spectrum. We then employ physics-informed neural networks (PINNs) to predict the asymptotic outcomes of FFCs within such a multienergy neutrino gas. These predictions are based on the first two moments of neutrino angular distributions for each energy bin, typically available in state-of-the-art CCSN and NSM simulations. Our PINNs achieve errors as low as ≲6% and ≲18% for predicting the number of neutrinos in the electron channel and the relative absolute error in the neutrino moments, respectively. Published by the American Physical Society 2024

Simple method for determining asymptotic states of fast neutrino-flavor conversion

Neutrino-neutrino forward scatterings potentially induce collective neutrino oscillation in dense neutrino gases in astrophysical sites such as core-collapse supernovae (CCSN) and binary neutron star mergers (BNSM). In this paper, we present a detailed study of fast neutrino-flavor conversion (FFC), paying special attention to asymptotic states, by linear stability analysis and local simulations with a periodic boundary condition. We find that asymptotic states can be characterized by two key properties of FFC: (1) the conservation of lepton number for each flavor of neutrinos and (2) the disappearance of ELN(electron neutrino-lepton number)-XLN(heavy-leptonic one) angular crossings in the spatial- or time-averaged distributions. The system which initially has the positive (negative) ELN-XLN density reaches a flavor equipartition in the negative (positive) ELN-XLN angular directions, and the other part compensates it to preserve the conservation laws. These properties of FFCs offer an approximate scheme determining the survival probability of neutrinos in asymptotic states without solving quantum kinetic equations. We also demonstrate that the total amount of flavor conversion can vary with species-dependent neutrino distributions for identical ELN-XLN ones. Our results suggest that even shallow or narrow ELN angular crossings have the ability to drive large flavor conversion, exhibiting the need for including the effects of FFCs in the modeling of CCSN and BNSM.

Applications of machine learning to detecting fast neutrino flavor instabilities in core-collapse supernova and neutron star merger models

Neutrinos propagating in a dense neutrino gas, such as those expected in core-collapse supernovae (CCSNe) and neutron star mergers (NSMs), can experience fast flavor conversions on relatively short scales. This can happen if the neutrino electron lepton number ($\nu$ELN) angular distribution crosses zero in a certain direction. Despite this, most of the state-of-the-art CCSN and NSM simulations do not provide such detailed angular information and instead, supply only a few moments of the neutrino angular distributions. In this study we employ, for the \emph{first} time, a machine learning (ML) approach to this problem and show that it can be extremely successful in detecting $\nu$ELN crossings on the basis of its zeroth and first moments. We observe that an accuracy of $\sim95\%$ can be achieved by the ML algorithms, which almost corresponds to the Bayes error rate of our problem. Considering its remarkable efficiency and agility, the ML approach provides one with an unprecedented opportunity to evaluate the occurrence of FFCs in CCSN and NSM simulations \emph{on the fly}. We also provide our ML methodologies on GitHub.

Nonstandard neutrino self-interactions can cause neutrino flavor equipartition inside the supernova core

We show that non-standard neutrino self-interactions can lead to total flavor equipartition in a dense neutrino gas, such as those expected in core-collapse supernovae. In this first investigation of this phenomenon in the multi-angle scenario, we demonstrate that such a flavor equipartition can occur on very short scales, and therefore very deep inside the newly formed proto-neutron star, with a possible significant impact on the physics of core-collapse supernovae. Our findings imply that future galactic core-collapse supernovae can appreciably probe non-standard neutrino self-interactions, for certain cases even when they are many orders of magnitude smaller than the Standard Model terms.

Collision-induced flavor instability in dense neutrino gases with energy-dependent scattering

We investigate the collision-induced flavor instability in homogeneous, isotropic, dense neutrino gases in the two-flavor mixing scenario with energy-dependent scattering. We uncover a simple expression of the growth rate of this instability in terms of the flavor-decohering collision rates and the electron lepton number distribution of the neutrino. This growth rate is common to the neutrinos and antineutrinos of different energies, and is independent of the mass splitting and vacuum-mixing angle of the neutrino, the matter density, and the neutrino density, although the initial amplitude of the unstable oscillation mode can be suppressed by a large matter density. Our results suggest that neutrinos are likely to experience collision-induced flavor conversions deep inside a core-collapse supernova even when both the fast and slow collective flavor oscillations are suppressed.

Slow and fast collective neutrino oscillations: Invariants and reciprocity

The flavor evolution of a neutrino gas can show ''slow'' or ''fast'' collective motion. In terms of the usual Bloch vectors to describe the mean-field density matrices of a homogeneous neutrino gas, the slow two-flavor equations of motion (EOMs) are $\dot{\mathbf{P}}_\omega=(\omega\mathbf{B}+\mu\mathbf{P})\times\mathbf{P}_\omega$, where $\omega=\Delta m^2/2E$, $\mu=\sqrt{2} G_{\mathrm{F}} (n_\nu+n_{\bar\nu})$, $\mathbf{B}$ is a unit vector in the mass direction in flavor space, and $\mathbf{P}=\int d\omega\,\mathbf{P}_\omega$. For an axisymmetric angle distribution, the fast EOMs are $\dot{\mathbf{D}}_v=\mu(\mathbf{D}_0-v\mathbf{D}_1)\times\mathbf{D}_v$, where $\mathbf{D}_v$ is the Bloch vector for lepton number, $v=\cos\theta$ is the velocity along the symmetry axis, $\mathbf{D}_0=\int dv\,\mathbf{D}_v$, and $\mathbf{D}_1=\int dv\,v\mathbf{D}_v$. We discuss similarities and differences between these generic cases. Both systems can have pendulum-like instabilities (soliton solutions), both have similar Gaudin invariants, and both are integrable in the classical and quantum case. Describing fast oscillations in a frame comoving with $\mathbf{D}_1$ (which itself may execute pendulum-like motions) leads to transformed EOMs that are equivalent to an abstract slow system. These conclusions carry over to three flavors.

Effects of energy-dependent scatterings on fast neutrino flavor conversions

Neutrino self-interactions in a dense neutrino gas can induce collective neutrino flavor conversions. Fast neutrino flavor conversions (FFCs), one of the collective neutrino conversion modes, potentially change the dynamics and observables in core-collapse supernovae and binary neutron star mergers. In cases without neutrino-matter interactions (or collisions), FFCs are essentially energy independent, and, therefore, the single-energy treatment has been used in previous studies. However, neutrino-matter collisions, in general, depend on neutrino energy, suggesting that energy-dependent features may emerge in FFCs with collisions. In this paper, we perform dynamical simulations of FFCs with isoenergetic scatterings (emulating nucleon scatterings) under multienergy treatment. We find that cancellation between in- and outscatterings happens in the high-energy region, which effectively reduces the number of collisions and then affects the FFC dynamics. In fact, the lifetime of FFCs is extended compared to the single-energy case, leading to large flavor conversions. Our result suggests that the multienergy treatment is mandatory to gauge the sensitivity of FFCs to collisions. We also provide a useful quantity to measure the importance of multienergy effects of collisions on FFCs.

Symmetry breaking induced by pairwise conversion of neutrinos in compact sources

A surprising consequence of non-linear flavor evolution is the spontaneous breaking of the initial symmetries of the neutrino gas propagating in a dense astrophysical environment. We explore the flavor conversion physics by taking into account the polar and azimuthal angular distributions of neutrinos and present the very first example of spontaneous symmetry breaking in the context of fast flavor mixing in the nonlinear regime. Intriguingly, we find that fast flavor mixing does not always develop in the proximity of the angular regions with vanishing electron lepton number, as commonly assumed, and large flavor mixing can rapidly spread through all neutrino modes. Such behavior cannot be predicted from the linear regime of the flavor evolution. These results can have major consequences on the physics of compact astrophysical objects.

Flavor isospin waves in one-dimensional axisymmetric neutrino gases

Flavor oscillations can occur on very short spatial and temporal scales in the dense neutrino media in a core-collapse supernova (CCSN) or binary neutron star merger (BNSM) event. Although the dispersion relations (DRs) of the fast neutrino oscillations can be obtained by linearizing the equations of motion (EoM) before the emergence of any significant flavor conversion, one largely depends on numerical calculations to understand this interesting phenomenon in the nonlinear regime. In this work we demonstrate that there exist nontrivial solutions to the flavor EoM that govern the fast oscillations in one-dimensional axisymmetric neutrino gases. These solutions represent a coherent flavor isospin wave similar to the magnetic spin wave in a lattice of magnetic dipoles. We also compute the DRs of such waves in some example cases which are closely related to the DRs of the fast neutrino oscillations obtained in the linear regime. This result sheds new light on the long-term behavior of fast neutrino oscillations which can have various implications for the CCSN and BNSM events.

Nonlinear evolution of fast neutrino flavor conversion in the preshock region of core-collapse supernovae

In environments with high dense neutrino gases, such as in core-collapse supernovae, the neutrinos can experience collective neutrino oscillation due to their self-interactions. In particular, fast flavor conversion driven by the crossings in the neutrino angular distribution can affect explosion mechanism, nucleosynthesis, and neutrino observation. We perform the numerical computation of nonlinear flavor evolution on the neutrino angular distribution with tiny crossings expected to be generated in the preshock region. We demonstrate that the fast instability is triggered and a cascade develops under a realistic three-flavor model considering muon production and weak magnetism in the supernova dynamics. The tiny crossing excites specific spatial modes, and then the flavor instability propagates into other modes which otherwise remain stable due to the nonlinear effects. Our results indicate that fast flavor conversion can rise in the preshock region and have a sufficient impact on the flavor contents.

Stationary solutions for fast flavor oscillations of a homogeneous dense neutrino gas

We present a method to find the stationary solutions for fast flavor oscillations of a homogeneous dense neutrino gas. These solutions correspond to collective precession of all neutrino polarization vectors around a fixed axis in the flavor space on average, and are conveniently studied in the co-rotating frame. We show that these solutions can account for the numerical results of explicit evolution calculations, and that even with the simplest assumption of adiabatic evolution, they can provide the average survival probabilities to good approximation. We also discuss improvement of these solutions and their use as estimates of the effects of fast oscillations in astrophysical environments.

Fast flavor oscillations of astrophysical neutrinos with 1, 2, …, ∞ crossings

In the early Universe, as well as in supernovae and merging neutron stars, neutrinos have such high densities that they affect each other and exhibit collective flavor oscillations. A crucial ingredient for fast collective flavor oscillations is that the electron lepton number (ELN) distribution changes its sign as a function of direction, i.e., has a zero crossing. We present a study in two spatial dimensions and time, focussing on the fast and linear regime, and show how fast flavor oscillations depend on the ELN and its crossings. We show that a large number of crossings can inhibit flavor oscillations. This may be a natural self-limiting mechanism that stabilizes the flavor content of the dense neutrino gas in a vast majority of scenarios, especially the early Universe, where the angular distributions for all flavors are very similar and crossings occur mainly due to fluctuations.

New Developments in Flavor Evolution of a Dense Neutrino Gas

Neutrino–neutrino refraction dominates the flavor evolution in core-collapse supernovae, neutron star mergers, and the early Universe. Ordinary neutrino flavor conversions develop on timescales determined by the vacuum oscillation frequency. However, when the neutrino density is large enough, collective flavor conversions may arise because of pairwise neutrino scattering. Pairwise conversions are deemed fast because they are expected to occur on timescales that depend on the neutrino–neutrino interaction energy (i.e., on the neutrino number density) and are regulated by the angular distributions of electron neutrinos and antineutrinos. The enigmatic phenomenon of fast pairwise conversions has been overlooked for a long time. However, because of the fast conversion rate, pairwise conversions could occur in the proximity of the neutrino decoupling region with yet-to-be-understood implications for the hydrodynamics of astrophysical sources and the synthesis of the heavy elements. We review the physics of this fascinating phenomenon and its implications for neutrino-dense sources.

Change of direction in pairwise neutrino conversion physics: The effect of collisions

Fast pairwise conversions of neutrinos may affect the flavor distribution in the core of neutrino-dense sources. We explore the interplay between collisions and fast conversions within a simplified framework that assumes angle-independent, direction-changing collisions in a neutrino gas that has no spatial inhomogeneity. Counter to expectations, we find that collisions may enhance fast flavor conversions instead of damping them. Our work highlights the need to take into account the feedback of collisions on the neutrino angular distributions self-consistently, in order to predict the flavor outcome in the context of fast pairwise conversions reliably.

Birefringence of electromagnetic waves in the relic neutrino gas

We reconsider the problem of the birefringence of electromagnetic (EM) waves in a medium consisting of a plasma and a νν̅-gas within the Standard Model of particle physics. The considered effect arises in such a medium due to the parity violation for the electroweak neutrino-electron interaction. Our recent calculations of the electroweak correction to the photon polarization operator in the electroweak plasma allow us to significantly improve some previous estimates of such effect in astrophysics. We estimate the rotary power for EM waves propagating in a non-relativistic plasma in the intergalactic space and interacting with the gas of relic neutrinos and antineutrinos there. We show that, in presence of a plasma, the EM wave birefringence effect in a νν̅-gas exceeds significantly that effect in a νν̅-gas in empty space considered earlier. These previous treatments of the birefringence relied on the calculations of the refraction index for on-shell photons in vacuum using the forward scattering amplitude γν→γν with virtual charged leptons in Feynman diagrams. The possibility to observe experimentally the new effect suggested here is discussed.

Turbulence fingerprint on collective oscillations of supernova neutrinos

We bring to light a novel mechanism through which turbulent matter density fluctuations can induce collective neutrino flavor conversions in core-collapse supernovae, i.e., the leakage of flavor instabilities between different Fourier modes. The leakage mechanism leaves its notable fingerprint on the flavor stability of a dense neutrino gas by coupling flavor conversion modes on different scales which in turn, makes the flavor instabilities almost ubiquitous in the Fourier space. The most remarkable consequence of this effect is in that it allows for the presence of significant flavor conversions in the deepest supernova regions even in the absence of the so-called fast modes. This is yet another crucial impact of turbulence on the physics of core-collapse supernovae which can profoundly change our understanding of neutrino flavor conversions in the supernova environment.

Exact solution of multiangle quantum many-body collective neutrino-flavor oscillations

I study the flavor evolution of a dense neutrino gas by considering vacuum contributions, matter effects and neutrino self-interactions. Assuming a system of two flavors in a uniform matter background, the time evolution of the many-body system in discretized momentum space is computed. The multi-angle neutrino-neutrino interactions are treated exactly and compared to both the single-angle approximation and mean field calculations. %The time unit chosen is $\mu_0^{-1}=(\frac{G_F}{2\sqrt{2}V})^{-1}$. The mono-energetic two neutrino beam scenario is solved analytically. I proceed to solve flavor oscillations for mono-energetic cubic lattices and quadratic lattices of two energy levels. In addition I study various configurations of twelve, sixteen, and twenty neutrinos. I find that when all neutrinos are initially of the same flavor, all methods agree. When both flavors are present, I find collective oscillations and flavor equilibration develop in the many body treatment but not in the mean field method. This difference persists in dense matter with tiny mixing angle and it can be ascribed to non-negligible flavor polarization correlations being present. Entanglement entropy is significant in all such cases. The relevance for supernovae or neutron stars mergers is contingent upon the value of the normalization volume $V$ and the large $N$ dependence of the timescale associated with oscillations. In future work, I intend to study this dependence using larger lattices and also include anti-neutrinos.

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

A dense neutrino gas, such as the one anticipated in the supernova environment, can experience fast neutrino flavor conversions on scales much shorter than those expected in vacuum probably provided that the angular distributions of $\nu_e$ and $\bar\nu_e$ cross each other. We perform a detailed investigation of the neutrino angular distributions obtained by solving the Boltzmann equations for fixed matter profiles of some representative snapshots during the post-bounce phase of core-collapse supernovae in multidimensional calculations of an $11.2\mathrm{M}_{\odot}$ and a $27\mathrm{M}_{\odot}$ progenitor models. Although the $11.2\mathrm{M}_{\odot}$ model features $\nu_e - \bar\nu_e$ angular crossings and the associated fast modes at different time snapshots, the $27\mathrm{M}_{\odot}$ model does not show any crossings within the decoupling region. We show that this can be understood by studying the multipole components of the neutrino distributions. In fact, there is a higher chance for the occurrence of $\nu_e - \bar\nu_e$ angular crossings for the zones where the multipole components of the neutrino distributions are strong enough. We also show that there can exist more than one crossings between the angular distributions of $\nu_e$ and $\bar{\nu}_e$. In addition, apart from the crossings within the neutrino decoupling region, there is a class of $\nu_e-\bar\nu_e$ angular crossings which appears very deep inside the proto-neutron star.