Small-amplitude density waves in galactic discs with radial gradients

Stellar discs of highly flattened giant galaxies, including that of the Mil ky Way, are studied by linear theory to determine the stability of such dis cs against small-amplitude gravity perturbations. In order to understand th e physics of the problem better, the simplest theoretical model is applied. That is, the local disc is studied by employing the method of particle orb it theory. In this purely Lagrangian method, an approximate solution of the Newtonian equations of the motion of stars is obtained using a general tec hnique based upon the perturbation method. In the second order of Lindblad' s epicyclic theory, expressions are found for the unperturbed motions of st ars in a stationary system with an axially symmetric mass distribution. The n, expressions are found for the perturbed motions of stars when the small non-axisymmetric gravity perturbation is additionally taken into account. T he perturbed terms are obtained as second-order oscillations. To describe t he ordered behaviour of a medium near its quasi-equilibrium state, these eq uations for the trajectories of stars are used to obtain the dispersion rel ation that connects the frequency of excited collective oscillations with t he wavenumber throughout the disc, including resonant regions. Using the di spersion relation, a new class of gradient microinstabilities of a non-unif ormly rotating disc inherent in an inhomogeneous system is discussed. The L andau mechanism of excitation of spiral density waves works at the corotati on resonance between stars and hydrodynamically (Jeans) stable perturbation s (e.g. those produced by a bar-like structure, a spontaneous perturbation and/or a companion galaxy). A physical aetiology of the gradient microinsta bilities of collisionless stellar discs is explained. Such instabilities ca n develop only if the inhomogeneous and non-uniformly rotating disc of star s is Jeans-stable. Certain astronomical implications of the theory for actu al galaxies are explored as well. In particular, the development of these i nstabilities of a stellar disc can result directly in the formation of diff erent observable structural features, e.g, spiral arms and collisionless dy namical relaxation of the system on the Hubble time-scale.