Other
Scientific paper
Sep 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982mnras.200..951b&link_type=abstract
Monthly Notices of the Royal Astronomical Society, vol. 200, Sept. 1982, p. 951-964.
Other
88
Brightness Distribution, Elliptical Galaxies, Galactic Structure, Star Distribution, Boltzmann Distribution, Density Distribution, Distribution Functions, Energy Distribution, Galactic Evolution, Galactic Nuclei, Isothermal Processes, Phase-Space Integral, Velocity Distribution
Scientific paper
The distribution function f(E) that self-consistently generates a galaxy whose surface density profile conforms to de Vaucouleurs' (1948, 1959) r to the 1/4th law is calculated. This distribution function is such that the number N(E)dE of stars with binding energies near E is well approximated by the Boltzmann formula N(E) = exp(-beta E) over the range of values of E for which there is secure observational support for de Vaucouleurs' law. It is noted that King (1966, 1978) models do not have N(E) curves of this form. The surface density and velocity dispersion properties are given of a galaxy whose N(E) curve is exactly given by the Boltzmann formula at all possible binding energies. As with the r to the 1/4th model, this new model has only two fitting parameters - a radius and a surface density - yet it fits the photometry of the standard elliptical NGC 3379 even better than the r to the 1/4th model. It is contended that a fundamental understanding of the structure of the spheroidal components is more likely to be found in terms of some special form of N(E) than in terms of the distribution function f(E).
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