A completely analytical family of anisotropic Plummer models

Details A completely analytical family of anisotropic Plummer models A completely analytical family of anisotropic Plummer models

Jan 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987mnras.224...13d&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 224, Jan. 1, 1987, p. 13-39.

Astronomy and Astrophysics

Astronomy

111

Astronomical Models, Mass Distribution, Mass To Light Ratios, Stellar Systems, Eddington Approximation, Energy Distribution, Poisson Equation, Spherical Coordinates

Scientific paper

In spherical stellar systems, a given mass density allows an infinity of distribution functions. This indeterminacy is illustrated with a one-parameter family of anisotropic models. They all satisfy the Plummer law in the mass density, but have different velocity dispersions. Moreover, the stars are not confined to a particular subset of the total accessible phase space. This family is explored analytically in detail (the moments, various energy distributions, the line profiles can all be calculated). Even when both the mass density and the velocity dispersion profiles are required to be the same, a degeneracy in the model space persists, which can be shown with a three-parameter generalization of the above family. The observational consequence of the degeneracy are studied by calculating the observable line profiles obtained with different distribution functions. This provides an estimate of the accuracy needed in the observed shape of the line profiles in order to be of use in the determination of the distribution function.

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