Properties of a spherical galaxy with exponential energy distribution

Research output: Article

Abstract

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{variant}(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{variant}(r) resembles the emissivity law of ellipticals are also derived.

Original languageEnglish
Pages (from-to)323-332
Number of pages10
JournalAstrophysics and Space Science
Volume138
Issue number2
DOIs
Publication statusPublished - nov. 1987

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energy distribution
distribution functions
galaxies
energy
function space
stellar systems
space density
elliptical galaxies
emissivity
density distribution
velocity distribution
slopes
distribution
modeling

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

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abstract = "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{variant}(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{variant}(r) resembles the emissivity law of ellipticals are also derived.",
author = "K. Petrovay",
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T1 - Properties of a spherical galaxy with exponential energy distribution

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N2 - 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{variant}(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{variant}(r) resembles the emissivity law of ellipticals are also derived.

AB - 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{variant}(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{variant}(r) resembles the emissivity law of ellipticals are also derived.

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