Neutrino flavor instabilities intermediate between slow and fast

Abstract

The neutrino flavor composition in supernovae and neutron star mergers is shaped by flavor instabilities, which are commonly classified into three types: slow (SFI), fast (FFI), and collisional (CFI). The focus here is on mixed-type instabilities combining attributes of the standard varieties. We examine instability growth rates in two-dimensional parameter spaces (``phase diagrams'') whose axes correspond to instabilities of pure type. We find critical curves connecting the pure-type instability onset points. We also exhibit qualitative trends in the growth-rate spectra ${\gamma }_{\mathbf{k}}$, emphasizing the occurrence of crossovers and phase transitions in the fastest-growing Fourier mode $k_{\text{max}}$ and drawing attention to the distinction between spatial-mean ($\mathbf{k}=0$) and flavor-wave ($\mathbf{k}\ne 0$) instabilities. Our paper is a step toward understanding flavor instabilities as they actually occur in nature rather than in idealized limits.