Does Jean's theorem apply only to spherical systems

Details Does Jean's theorem apply only to spherical systems Does Jean's theorem apply only to spherical systems

Oct 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982mnras.201...15b&link_type=abstract

Monthly Notices of the Royal Astronomical Society, vol. 201, Oct. 1982, p. 15-19.

Astronomy and Astrophysics

Astronomy

32

Jeans Theory, Orbital Mechanics, Stellar Motions, Stellar Systems, Vlasov Equations, Astrodynamics, Equations Of Motion, Fourier Series, Kepler Laws

Scientific paper

It is argued that Jean's theorem is valid only for special potentials, and should not be used as a basis for a discussion of general stellar systems. A steady-state potential supports both regular and irregular orbits. For regular orbits, which are quasi-periodic and have from three to five isolating integrals, the time-averaged phase-space density contributed by a particle is constant at the intersection of the hypersurfaces in phase space that are picked out by the isolating integrals. So the distribution function of a system that supports only regular orbits satisfies Jean's theorem. For irregular orbits, the phase-space density that is contributed is not constant at the intersection of the hypersurfaces defined by its isolating integrals. So the distribution functions of systems involving such orbits do not obey Jean's theorem or the Vlasov equation.

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