Stability of Density Waves in a Self-Gravitating Stellar System with Uniform Rotation

The collective processes in a self‐gravitating system with uniform rotation are studied with particular emphasis on the stability of density waves. In addition to the classical Jeans instability, it is shown that the so‐called microinstability can also exist if the distribution is anisotropic and $\mathrm{\beta \hspace{0.17em}\equiv \hspace{0.17em}}\frac{\mathrm{longitudinal\; dispersion\; speed}}{\mathrm{transverse\; dispersion\; speed}}<\left(\right|\text{1 −}\frac{\sqrt{2}}{2}{\left|\right)}^{\frac{1}{2}}\text{≃ 0.54}$ . The critical wavelength is calculated as a function of β for nearly transversely propagated modes and is also estimated for the case that waves have arbitrary propagation direction and long wavelength. Finally, the stability of density waves associated with a system in the presence of the Kapteyn‐Eddington star stream is examined.