On the wave nature of the spiral structure of Galaxies II. The linear theory (Part 2)

Due to Landau effect a self gravitating thin disc consisting of differentially rotating population I and non-rotating population II is unstable against spiral waves of small amplitude. Leading and trailing spiral waves are dynamically equivalent in respect to instability: they increase with the same increment. The instability is caused by stars population II whose radial component of velocity is to the radial phase velocity of the wave. The spiral wave rotates with less angular velocity than that of population I. From any arbitrary disturbance asymptotically in time persists one (or a few) spiral mode. In addition to Landau instability the Jeans instability is possible. However, it can't, apparently, lead to formation of spiral arms. The character of Jeans instability essentially differs from that in single-component system. The relative perturbations in densities in different subsystems differs in magnitudes and are phase shifted: each subsystem thus forms their own spiral arms