Neutrino Flavor Evolution in High Flux Astrophysical Environments

Abstract

We examine neutrino evolution in astrophysical environments where the neutrino flux is very large, including core-collapse supernovae and neutron star mergers. In these environments, the neutrino-neutrino and neutrino-antineutrino interactions are crucial. We include non-forward scattering of neutrinos and anti-neutrinos in a semi-classical treatment. Because of the large scale of neutrino momenta (2-10 MeV), the quantum evolution problem can be treated as a sum over incoherent paths in the and flavor of each neutrino. The phases between different neutrinos are essentially random because of the large kinetic terms. Momentum is conserved at each vertex, and important flavor symmetries are retained. Dynamics in the many-body neutrino system enable rapid equilibration in the energy and angular distributions of all flavors, and an equilibration of products of neutrino and anti-neutrino densities for each flavor at either large or zero background matter density. We also describe the evolution at moderate densities where the mass eigenstates differ for neutrinos and antineutrinos, and with time-varying background matter densities. The evolution maintains relevant symmetries and reduces to standard MSW oscillations in the appropriate limits. The rapid equilibration in energy and flavor can significantly impact energy deposition and nucleosynthesis in high-flux astrophysical environments, and potentially flavor energy relations in terrestrial supernovae neutrino observations.

Figures (10)

• Figure 1: Pictorial representation of the propagation represented by Eq. \ref{['eq:prop']}. Horizontal lines are neutrinos, dashed lines are anti-neutrinos, and color represents flavor. Vertical lines represent two-neutrino vertices. Only flavor evolution is indicated here, though the momenta are also changing at each vertex.
• Figure 2: Possible two neutrino final states conserving momentum and energy. Sample initial states momenta parallel and perpendicular to the total pair momentum are shown as circles. Possible two-neutrino final states conserving energy and momentum are shown as lines. The two final state neutrino each lie on one of the two lines. There is an additional azimuthal symmetry as well.
• Figure 3: Possible initial and final states in neutrino-neutrino (upper) and neutrino-antineutrino (lower) vertices, indicating azimuthal rotations and possible flavor changes. The sum of the two momenta and the individual magnitudes (kinetic energy) are conserved. The final states can either exchange the flavors in the upper panel or not. In the lower panel the momenta magnitudes can change (or not) between neutrino and antineutrino and the flavor of the pair can change. The dashed ovals are meant to indicate the possible azimuthal rotation of momenta in the final state, still preserving the total momenta.
• Figure 4: Pictorial representation of the calculations of observables at the black vertical bar from the squares of the relevant amplitudes. The path integral on the left and right is the same with phase information remaining from flavor amplitudes within each neutrino.
• Figure 5: Full semi-classical calculation for large N versus explicit many-body calculations of 10 neutrinos. Average of 10 many-body calculations are indicated by thick solid lines, with individual runs by fainter runs. Thick dashed lines are obtained by averages over many semiclassical runs with different samples of energies and momenta for 100 neutrinos. The full H calculation is an average over instances of fixed couplings, while the semiclassical runs resample the couplings at a rate of 1 $\mu^{-1}$.