Properties of a Spherical Galaxy with Exponential Energy Distribution
Abstract
Some analytical relations for the phase space functions of a selfconsistent spherical stellar system are derived. The integral constraints on the distribution function by imposing a given ϱ(r) density distribution andN(E) fractional energy distribution are determined. For the case of radiallyanisotropic velocity distribution in theE→0 limit the constraint by an exponentialN(E) implies thatf(E, J ^{2}) 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 exponentialN(E) for the case when ϱ(r) resembles the emissivity law of ellipticals are also derived.
 Publication:

Astrophysics and Space Science
 Pub Date:
 November 1987
 DOI:
 10.1007/BF00637853
 Bibcode:
 1987Ap&SS.138..323P
 Keywords:

 Computational Astrophysics;
 Elliptical Galaxies;
 Energy Distribution;
 Exponential Functions;
 Galactic Structure;
 Stellar Systems;
 Density Distribution;
 Gravitational Collapse;
 PhaseSpace Integral;
 Self Consistent Fields;
 Astrophysics