A unified theory for the formation of galactic structures

Abstract

A new theory for the formation of the main structures of galaxies is proposed: these structures are viewed as low-frequency normal modes in disks consisting of precessing stellar orbits. Mathematically, the theory is based on an integral equation in the form of a classical eigenvalue problem, with the eigenvalues being equal to the angular velocities Ωp of the modes. Analysis of the general properties of the master integral equation (without finding concrete solutions) shows that it admits two types of solutions: barlike and spiral. The numerical algorithms are discussed and particular solutions of the integral equation are presented. If resonance interaction can be neglected, the bar mode represents a neutral perturbation of the disk. This mode can be amplified by the effect of the long-range gravitational field of the mode on stars located in the vicinity of the corotation and outer-Lindblad resonances. Spiral perturbations are waves with zero total angular momentum, and spiral modes are excited at the inner-Lindblad resonance. The approach proposed is compared to currently accepted mechanisms for the formation of galactic structures. In particular, Toomre's application of the swing amplification mechanism to explain the formation of global modes is critically discussed. In addition, we show that it is not correct to simulate the real stellar velocity dispersion in a galaxy using softened gravity.