### 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, 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 exponential N(E) for the case when ρ{variant}(r) resembles the emissivity law of ellipticals are also derived.

Original language | English |
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Pages (from-to) | 323-332 |

Number of pages | 10 |

Journal | Astrophysics and Space Science |

Volume | 138 |

Issue number | 2 |

DOIs | |

Publication status | Published - nov. 1987 |

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### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

**Properties of a spherical galaxy with exponential energy distribution.** / Petrovay, K.

Research output: Article

*Astrophysics and Space Science*, vol. 138, no. 2, pp. 323-332. https://doi.org/10.1007/BF00637853

}

TY - JOUR

T1 - Properties of a spherical galaxy with exponential energy distribution

AU - Petrovay, K.

PY - 1987/11

Y1 - 1987/11

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.

UR - http://www.scopus.com/inward/record.url?scp=34250107742&partnerID=8YFLogxK

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U2 - 10.1007/BF00637853

DO - 10.1007/BF00637853

M3 - Article

AN - SCOPUS:34250107742

VL - 138

SP - 323

EP - 332

JO - Astrophysics and Space Science

JF - Astrophysics and Space Science

SN - 0004-640X

IS - 2

ER -