How collective modes terminate in the dispersion relation of neutrino plasmas

Abstract

Neutrino plasmas support flavor waves, collective oscillations of flavor, that neutrinos can resonantly emit or absorb when they fulfill the Cherenkov condition. For massless neutrinos, this condition leads to singular features in the dispersion relation: Landau-damped modes, for example, disappear abruptly as their phase velocity approaches the speed of light. We investigate how these singularities change when nonzero neutrino masses introduce a spread in velocities. We classify singular behavior of the frequency as a function of wavevector into i) degeneracy points, where two modes merge, and ii) abrupt mode termination, when the frequency approaches a branch cut of the flavor dielectric function. For each class, we derive a local expansion and determine where such behavior can occur. Degeneracy points, frequently encountered in axially symmetric dispersion relations in the fast limit, are not generic. Nonzero neutrino masses lift the degeneracy along the symmetry axis; in three-dimensional wavevector space, there might still be degeneracy lines, not necessarily intersecting the symmetry axis. Abrupt mode termination, instead, persists generically, except for special energy distributions which are entire functions. As a byproduct of this study, we show that a collisionless plasma with a Lorentzian neutrino-frequency distribution is exactly equivalent to a monochromatic one with an effective collision rate. Approximating a general frequency distribution by a sum of Lorentzians therefore substantially simplifies the dispersion relation.