Other
Scientific paper
May 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992jetp...74..755p&link_type=abstract
Sov. Phys. - JETP, Vol. 74, No. 5, p. 755 - 763
Other
3
Scientific paper
The author derives integral equations for the low-frequency modes in a gravitating cylinder, disk, and sphere. An analytic theory is proposed for the instability of radial orbits. Radially extended orbits arise naturally, and they become the dominant type of orbit as a heterogeneous population of stellar systems is produced by collapse of an initially highly tenuous cloud. Such systems include galaxies, their individual components, clusters of galaxies, and so forth. Based on this theory, the instability in question harks back to the classical Jeans instability; in the present case, it entails the deformation of a system by virtue of the gravitational attraction of orbits that extend toward one another. This embodiment of the Jeans instability has a very interesting feature: the theory predicts that even in the limit of perfectly radial orbits, instability will only develop under one additional condition - that the precession of low angular momentum orbits in the gravitational potential of a particular stellar system take place in the same direction as the stars' orbital motion. The final dispersion of orbital precession rates will remove the instability. Here the author obtains simple equations for the relationship between the minimum scatter in angular precession rates necessary for stability and the instability growth factor for exactly radial orbits. He demonstrates the importance of disk and ellipsoidal deformation of spherical systems with radially extended orbits, which relates directly to the role played by radial orbit instability in the formation of barred spirals and elliptical galaxies. Finally, it is briefly discussed the possible explanation of ellipticity of thin planetary rings as a manifestation of the appropriate instability in systems with quasicircular orbits.
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