The Weakly Nonlinear-Theory Of Density Waves In A Stellar Disk

Quasilinear theory is applied to the adiabatic wave-star interaction of a differentially-rotating stellar disk of a galaxy. Under the influence of growing spiral waves the velocity dispersion of stars increases and the surface mass density becomes more peaked. The resulting distortion in phase space leads to a decrease in the growth rate of the waves, and as the result the Jeans instability should end after a few rotations of the system. The theory is confirmed by N-body computer simulations.