Astronomy and Astrophysics – Astronomy
Scientific paper
May 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993mnras.262..401h&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 262, no. 2, p. 401-428.
Astronomy and Astrophysics
Astronomy
81
Distribution Functions, Elliptical Galaxies, Galactic Rotation, Integrals, Stellar Motions, Stellar Systems, Celestial Mechanics, Integral Equations, Integral Transformations
Scientific paper
The new method presented for finding distribution functions, which depend only on the classical integrals of energy and angular momentum for stellar systems with known axisymmetric densities, is the analog for the axisymmetric case of Eddington's classical solution for the isotropic distribution function, depending only on energy, of a known spherical density. It is required that density be expressed as a function of the potential and of a radial coordinate. Our solution is also an integral which is derived directly from the density, and hence can be used with complicated densities. A numerical quadrature is generally required to evaluate this solution, but contour integrals can be computed accurately by numerical quadrature; this is preferable to an explicit evaluation if the latter is an infinite series, such as is obtained using Fricke's method. We give several examples, including some for which our distribution functions are new. Our method can be extended simply to the related problems of finding anisotropic distribution functions for spherical or disk systems.
Hunter Charles
Qian Edward
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