Statistics – Computation
Scientific paper
Nov 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987ap%26ss.138..323p&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 138, no. 2, Nov. 1987, p. 323-332.
Statistics
Computation
Computational Astrophysics, Elliptical Galaxies, Energy Distribution, Exponential Functions, Galactic Structure, Stellar Systems, Density Distribution, Gravitational Collapse, Phase-Space Integral, Self Consistent Fields
Scientific paper
Some analytical relations for the phase space functions of a self-consistent spherical stellar system are derived. The integral constraints on the distribution function by imposing a given ρ(r) density distribution and N(E) fractional energy distribution are determined. For the case of radially-anisotropic velocity distribution in the E→0 limit the constraint by an exponential N(E) implies that f(E,J2) tends to zero in the order (-E)3/2. This lends analytical support to the use of the Stiavelli and Bertin (1985) distribution function for modeling elliptical galaxies. Maximum phase space density constraint confirms the necessity of high collapse factors to produce such a distribution function. Limits on the steepness of an exponential N(E) for the case when ρ(r) resembles the emissivity law of ellipticals are also derived.
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