Single-angle Approximation Research Articles

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.

Collective neutrino oscillations with the halo effect in single-angle approximation

We perform a self-consistent calculation of collective neutrino oscillations including the effect of back scattered neutrinos (Halo effect) in the `single-angle' approximation, within a spherically symmetric supernova model. We find that due to the Halo effect the onset of flavor transformations is pushed to smaller radii, by a few kilometers. The celebrated phenomenon of the spectral split is found to be robust under the present inclusion of the Halo effect.

Neutrino spectral split in the exact many-body formalism

We consider the many-body system of neutrinos interacting with each other through neutral current weak force. Emerging many-body effects in such a system could play important roles in some astrophysical sites such as the core collapse supernovae. In the literature this many-body system is usually treated within the mean field approximation which is an effective one-body description based on omitting entangled neutrino states. In this paper, we consider the original many-body system in an effective two flavor mixing scenario under the single angle approximation and present a solution without using the mean field approximation. Our solution is formulated around a special class of many-body eigenstates which do not undergo any level crossings as the neutrino self interaction rate decreases while the neutrinos radiate from the supernova. In particular, an initial state which consists of electron neutrinos and antineutrinos of an orthogonal flavor can be entirely decomposed in terms of those eigenstates. Assuming that the conditions are perfectly adiabatic so that the evolution of these eigenstates follow their variation with the interaction rate, we show that this initial state develops a spectral split at exactly the same energy predicted by the mean field formulation.

Multi-angle calculation of the matter-neutrino resonance near an accretion disk

We perform a numerical study of the matter-neutrino resonance in a multi-angle calculation in the vicinity of an accretion disk. We assume thermally distributed neutrino and anti-neutrino fields emitted by two-dimensional disk that is homogeneous and isotropic; the electrons are assumed to be at constant density. We compare the result of this computation to that obtained using single-angle approximation. We investigate the robustness of matter-neutrino resonance in environment surrounding accretion disks by progressively relaxing the single angle approximation. We find that the multi-angle results in the present simplified model do not support a robust resonance mechanism as suggested by the single angle treatment. We also discuss the context under which matter-neutrino resonance may be important in future studies.

Matter-neutrino resonance transitions above a neutron star merger remnant

The Matter-Neutrino Resonance (MNR) phenomenon has the potential to significantly alter the flavor content of neutrinos emitted from compact object mergers. We present the first calculations of MNR transitions using neutrino self interaction potentials and matter potentials generated selfconsistently from a dynamical model of a three-dimensional neutron star merger. In the context of the single angle approximation, we find that Symmetric and Standard MNR transitions occur in both normal and inverted hierarchy scenarios. We examine the spatial regions above the merger remnant where propagating neutrinos will encounter the matter neutrino resonance and find that a significant fraction of the neutrinos are likely to undergo MNR transitions.

Neutrino magnetic moment,CPviolation, and flavor oscillations in matter

We consider collective oscillations of neutrinos, which are emergent nonlinear flavor evolution phenomena instigated by neutrino-neutrino interactions in astrophysical environments with sufficiently high neutrino densities. We investigate the symmetries of the problem in the full three flavor mixing scheme and in the exact many-body formulation by including the effects of CP violation and neutrino magnetic moment. We show that, similar to the two flavor scheme, several dynamical symmetries exist for three flavors in the single-angle approximation if the net electron background in the environment and the effects of the neutrino magnetic moment are negligible. Moreover, we show that these dynamical symmetries are present even when the CP symmetry is violated in neutrino oscillations. We explicitly write down the constants of motion through which these dynamical symmetries manifest themselves in terms of the generators of the SU(3) flavor transformations. We also show that the effects due to the CP-violating Dirac phase factor out of the many-body evolution operator and evolve independently of nonlinear flavor transformations if neutrino electromagnetic interactions are ignored. In the presence of a strong magnetic field, CP-violating effects can still be considered independently provided that an effective definition for neutrino magnetic moment is used.

Transition magnetic moments and collective neutrino oscillations: three-flavor effects and detectability

We demonstrate the non-negligible effect of transition magnetic moments on three-flavor collective oscillations of Majorana neutrinos in the core of type-II supernovae, within the single-angle approximation. We argue that data from a galactic supernova in conjunction with terrestrial experiments can potentially give us clues about the non-zero nature of neutrino transition magnetic moments if these are Majorana fermions, even if their values are as small as those predicted by the Standard Model augmented by nonzero neutrino Majorana masses.

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.

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.

Resonances driven by a neutrino gyroscope and collective neutrino oscillations in supernovae

We show that flavor evolution of a system of neutrinos with continuous energy spectra as in supernovae can be understood in terms of the response of individual neutrino flavor-isospins (NFIS's) to the mean field. In the case of a system initially consisting of nu_e and anti-nu_e with the same energy spectrum but different number densities, the mean field is very well approximated by the total angular momentum of a neutrino gyroscope. Assuming that NFIS evolution is independent of the initial neutrino emission angle, the so-called single-angle approximation, we find that the evolution is governed by two types of resonances driven by precession and nutation of the gyroscope, respectively. The net flavor transformation crucially depends on the adiabaticity of evolution through these resonances. We show that the results for the system of two initial neutrino species can be extended to a system of four species with the initial number densities of nu_e and anti-nu_e significantly larger than those of nu_x and anti-nu_x. Further, we find that when the dependence on the initial neutrino emission angle is taken into account in the multi-angle approximation, nutation of the mean field is quickly damped out and can be neglected. In contrast, precession-driven resonances still govern the evolution of NFIS's with different energy and emission angles just as in the single-angle approximation. Our pedagogical and analytic study of collective neutrino oscillations in supernovae provides some insights into these seemingly complicated yet fascinating phenomena.

Self-Induced Suppression of Collective Neutrino Oscillations in a Supernova

We investigate collective flavor oscillations of supernova neutrinos at late stages of the explosion. We first show that the frequently used single-angle (averaged coupling) approximation predicts oscillations close to, or perhaps even inside, the neutrinosphere, potentially invalidating the basic neutrino transport paradigm. Fortunately, we also find that the single-angle approximation breaks down in this regime; in the full multiangle calculation, the oscillations start safely outside the transport region. The new suppression effect is traced to the interplay between the dispersion in the neutrino-neutrino interactions and the vacuum oscillation term.

Supernova neutrinos and antineutrinos: ternary luminosity diagram and spectral split patterns

In core-collapse supernovae, the νe and ν̄e species may experience collective flavor swaps to non-electron species νx, within energy intervals limited by relatively sharp boundaries (``splits''). These phenomena appear to depend sensitively upon the initial energy spectra and luminosities. We investigate the effect of generic variations of the fractional luminosities (le, lē, lx) with respect to the usual ``energy equipartition'' case (1/6, 1/6, 1/6), within an early-time supernova scenario with fixed thermal spectra and total luminosity. We represent the constraint le+lē+4lx = 1 in a ternary diagram, which is explored via numerical experiments (in single-angle approximation) over an evenly-spaced grid of points. In inverted hierarchy, single splits arise in most cases, but an abrupt transition to double splits is observed for a few points surrounding the equipartition one. In normal hierarchy, collective effects turn out to be unobservable at all grid points but one, where single splits occur. Admissible deviations from equipartition may thus induce dramatic changes in the shape of supernova (anti)neutrino spectra. The observed patterns are interpreted in terms of initial flavor polarization vectors (defining boundaries for the single/double split transitions), lepton number conservation, and minimization of potential energy.

Collective neutrino oscillations in nonspherical geometry

The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the nonspherical example of coalescing neutron stars, presumably the central engines of short gamma-ray bursts, we use the Liouville equation to formulate the problem for general source geometries. Assuming the neutrino ensemble displays self-maintained coherence, the problem once more becomes effectively one-dimensional along the streamlines of the overall neutrino flux. This approach for the first time provides a formal definition of the ``single-angle approximation'' frequently used for supernova neutrinos and allows for a natural generalization to nonspherical geometries. We study the explicit example of a disk-shaped source as a proxy for coalescing neutron stars.