Stability Condition of the Kelvin-Helmholtz Instability for the Two-Component Protogalaxy

Within the context of the evolution of two-component protogalaxies, we discuss the stability condition of the Kelvin-Helmholtz (KH) instability on a boundary where evaporation of a denser component (cloud) or condensation of a diffuser component (hot gas) is expected. It has been stressed that the stability condition for the KH instability may determine the global properties of protogalaxies. However, discontinuous phase transition layer was assumed between the two phases in previous studies, though that layer is never a step condition. It is known that when a density continuity on the boundary is concerned, the KH instability is stabilized by gravity if the well-known Richardson criterion is satisfied : J > 0.25, where J is called the Richardson number. Especially, for the physical parameters of the two-component model of a protogalaxy, we find that J is much smaller than 0.25. The Richardson criterion is the stable condition due to gravity (we do not judge whether the adopted condition becomes unstable). Then, the smallness of J means that we can neglect the stabilization due to the self-gravity of the denser cloud component. Our conclusion supports the justification of the stability condition for the cloud phase given by the previous study.