Theory for the instability of radial orbits in the collisionless gravitating systems and its applications.
Abstract
The integral equations for the low frequency modes in a gravitating cylinder, disk and sphere are derived. The analytic theory for the instability of radial orbits (the important instability of the collisionless gravitating systems) is suggested. The orbits elongated in the radius direction arise naturally and become dominant with the formation of various star systems as a result of the collapse of a cloud rarefied strongly at first. Galaxies, its separate components, clusters of galaxies and so on refer to these systems. In its background the instability concerned has the Jeans classic nature. In this paper it consists in the deformation of the system due to the gravitational attraction between the elongated orbits. This kind of the Jeans instability has an interesting feature. In particular, as seen from the theory, even in the limit of pure radial orbits the instability develops only for the definite additional condition, namely, the precession of orbits with the small angular momenta in the gravitational potential of the given star system should proceed in the direction of the star rotation on such orbits. The finite dispersion of the orbit precession velocities stabilizes the instability under consideration. Simple formulae expressing the relation between the precession angular velocity dispersion necessary minimally for stability and instability increment for the pure radial orbits are obtained. The marked distinction is proved for the elliptical deformation of the disk systems and ellipsoidlike deformations of the spherical systems with the orbits elongated radially. This fact is connected directly with involving the instability of radial orbits into the formation of barred spiral galaxies and elliptical galaxies. The possibility for explaining the ellipticity of thin planetary rings as a manifestation of the corresponding instability in the systems with orbits close to circular form is discussed in brief.
 Publication:

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki
 Pub Date:
 May 1992
 Bibcode:
 1992ZhETF.101.1409P
 Keywords:

 Celestial Mechanics;
 Cylindrical Bodies;
 Disks (Shapes);
 Gravitational Effects;
 Orbital Mechanics;
 Spheres;
 Stability;
 Barred Galaxies;
 Elliptical Galaxies;
 Integral Equations;
 Planetary Rings;
 Astrophysics