Analysis of small-scale vertical perturbation modes against the background of a pulsating disk model

This work investigates the problem of gravitational instability of small-scale vertical perturbation modes against the background of a pulsating composite model of disk- shaped self-gravitating systems. A non-stationary analog of the dispersion equation (NADE) has been derived in its general form for the vertical perturbation modes of the composite model. The results are presented in the form of critical diagrams of the initial virial ratio as a function of the model’s rotation parameter for various values of the superposition parameter for each of the considered vertical perturbation modes. The analysis of the results shows, in particular, that the small-scale nature of the vertical perturbation modes plays a destabilizing role, while the system’s rotation parameter, on the contrary, has a stabilizing effect.