Theory of neutrino slow flavor evolution. Part II. Space-time evolution of linear instabilities

Abstract: Slow flavor evolution (defined as driven by neutrino masses and not necessarily ``slow'') is receiving fresh attention in the context of compact astrophysical environments. In Part~I of this series, we have studied the slow-mode dispersion relation following our recently developed analogy to plasma waves. The concept of resonance between flavor waves in the linear regime and propagating neutrinos is the defining feature of this approach. It is best motivated for weak instabilities, which probably is the most relevant regime in self-consistent astrophysical environments because these will try to eliminate the cause of instability. We here go beyond the dispersion relation alone (which by definition applies to infinite media) and consider the group velocities of unstable modes that determines whether the instability relaxes within the region where it first appears (absolute), or away from it (convective). We show that all weak instabilities are convective so that their further evolution is not local. Therefore, studying their consequences numerically in small boxes from given initial conditions may not always be appropriate.