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Anisotropic distribution functions for spherical galaxies

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Abstract

A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular momentum. It requires the density to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the angular momentum. The products of the density and its radial and transverse velocity dispersions can be also expressed as a sum of products of functions of the potential and of the radial coordinate. Several examples are given, including some of new anisotropic distribution functions. This device can be extended further to the related problem of finding two-integral distribution functions for axisymmetric galaxies.

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References

  • Baes M., Dejonghe H. (2005) The dynamical structure of isotropic spherical galaxies with a central black hole. Astron. Astrophys. 432: 411–422

    Article  ADS  Google Scholar 

  • Binney J. (1980) The radius-dependence of velocity dispersion in elliptical galaxies. Monthly Notices Roy. Astron. Soc. 190: 873–880

    ADS  Google Scholar 

  • Binney J., Tremaine S. (1987) Galactic Dynamics. Princeton University, Princeton

    Google Scholar 

  • Bouvier P. (1962) Sur le structure des amas globulaires. Archi. des Sci. (Genéve) 15: 163–173

    MathSciNet  Google Scholar 

  • Bouvier P. (1963) Distribution des vitesses dans un système sphérique quau permanent. Archives des Sciences (Genéve) 16: 195–210

    Google Scholar 

  • Camm G.L. (1952) Self-gravitating star systems. II. Monthly Notices Roy. Astron. Soc. 112, 155–176

    MATH  MathSciNet  ADS  Google Scholar 

  • Cuddeford P. (1991) An analytic inversion for anisotropic spherical galaxies. Monthly Notices Royal Astron. Soc. 253: 414–426

    MathSciNet  ADS  Google Scholar 

  • Dehnen W. (1993) A family of potential-density pairs for spherical galaxies and bulges. Monthly Notices Roy. Astron. Soc. 265: 250–256

    ADS  Google Scholar 

  • Dejonghe H. (1986) Stellar dynamics and the description of stellar systems. Phys. Rep. 133: 217–313

    Article  MathSciNet  ADS  Google Scholar 

  • Dejonghe H. (1987) A completely analytical family of anisotropic Plummer. Monthly Notices Roy. Astron. Soc. 224: 13–39

    MATH  ADS  Google Scholar 

  • Dejonghe H., Merritt D. (1988) Radial and nonradial stability of spherical stellar systems. Astrophys. J. 328: 93–102

    Article  ADS  Google Scholar 

  • Eddington A.S. (1916) The distribution of stars in globular clusters. Monthly Notices Roy. Astron. Soc. 76: 572–585

    ADS  Google Scholar 

  • Evans N.W. (1993) Simple galaxy models with massive haloes. Monthly Notices Roy. Astron. Soc. 260: 191–201

    ADS  Google Scholar 

  • Fricke W. (1952) Dynamische Begründung der Geschwindigkeitsverteilung im Sternsystem. Astron. Nachr. 280: 193–216

    MATH  MathSciNet  ADS  Google Scholar 

  • Hénon M. (1959a) L’amas isochrone: I. Annales d’Astrophysique 22: 126–139

    ADS  Google Scholar 

  • Hénon M. (1959b) II. Le calcul des orbites. Annales d’Astrophysique 22: 491–498

    ADS  Google Scholar 

  • Hernquist L. (1990) An analytical model for spherical galaxies and bulges. Astrophys. J. 356: 359–364

    Article  ADS  Google Scholar 

  • Hunter C. (1975) Determination of the distribution function of an elliptical galaxy. Astron. J. 80: 783–793

    Article  ADS  Google Scholar 

  • Hunter C., Qian E. (1993) Two-integral distribution functions for axisymmetric galaxies. Monthly Notices Roy. Astron. Soc. 262: 401–428

    MathSciNet  ADS  Google Scholar 

  • Jiang Z. (2000) Flattened Jaffe models for galaxies. Monthly Notices Roy. Astron. Soc. 319: 1067–1078

    Article  Google Scholar 

  • Kalnajs A.J. (1976) Dynamics of flat galaxies. III. Equilibrium models. Astrophys. J. 205: 751–761

    MathSciNet  ADS  Google Scholar 

  • Kent S.M., Gunn J.E. (1982) The dynamics of rich clusters of galaxies. I – The Coma cluster. Astron. J. 87: 945–971

    Article  ADS  Google Scholar 

  • Kutuzov, S.A., Ossipkov, L.P.: A generalized model for the three-dimensional gravitational potential of stellar systems. Pis’ma v Astronomicheskij Zhurnal 57, 28–37 (1980) (English translations: Soviet Astron. Lett. 24, 17–22 (1981))

  • Kuzmin G.G., Veltmann Ü.-I.K. (1967a) Hydrodynamic models of spherical stellar systems. W. Struve Tartu Astrofüüs. Obs. Publ. 36: 3–47

    Google Scholar 

  • Kuzmin G.G., Veltmann Ü.-I.K. (1967b) Lindblad diagram and isochronic models. W. Struve Tartu Astrofüüs. Obs. Publ. 36: 470–507

    Google Scholar 

  • Kuzmin, G.G., Veltmann, Ü.-I.K.: Generalized isochrone models for spherical stellar systems. Dynamics of Galaxies and Star Clusters, Nauka, Alma-Ata, pp. 82–87 (1973) (English translations: Galactic Bulges (IAU Symp. 153), Kluwer, Dordrecht, pp. 363–366 (1993))

  • Kuzmin G.G., Veltmann Ü.-I.K., Tenjes P. L. Quasi-isothermal models of spherical stellar systems. Application to the galaxies M 87 and M 105. W. Struve Tartu Astrofüüs. Obs. Publ. 51: 232–242 (1986)

  • Louis P.D. (1993) Models for spherical stellar systems with isotropic cores and anisotropic haloes. Monthly Notices of the Royal Astronomical Society 261: 283–298

    ADS  Google Scholar 

  • Lynden-Bell D. (1962) Stellar dynamics: exact solution of the self-gravitation equation. Monthly Notices Roy. Astron. Soc. 123: 447–458

    MATH  MathSciNet  ADS  Google Scholar 

  • Merritt D. (1985) Spherical stellar systems with spheroidal velocity distributions. Astron. J. 90: 1027–1037

    Article  ADS  Google Scholar 

  • Ogorodnikov K.F. (1965) Dynamics of Stellar Systems, Pergamon Press. London

    MATH  Google Scholar 

  • Ossipkov, L.P.: Some problems of the theory of self-consistent models for star clusters. Star Clusters, Urals University Press, Sverdlovsk, pp. 72–89 (1979a)

  • Ossipkov, L.P.: Spherical systems of gravitating bodies with an ellipsoidal velocity distribution. Pis’ma v Astronomicheskij Zhurnal, 5, 77–80 (1979b) (English translations: Soviet Astronomy Letters 5, 42–44)

  • Plummer H.C. (1911) On the problem of distribution in globular star clusters. Monthly Notices Roy. Astron. Soc. 71: 460–470

    ADS  Google Scholar 

  • Qian E., Hunter C. (1995) Anisotropic distribution functions for spherical galaxies. Astron. Astrophys. Trans. 7: 201–206

    Google Scholar 

  • Saha P.(1993) Designer basis functions for potentials in galactic dynamics. Monthly Notices Roy. Astron. Soc. 262: 1062–1064

    ADS  Google Scholar 

  • Shiveshwarkar S.W. (1936) Remarks on some theorems in the dynamics of a steady stellar system. Monthly Notices Roy. Astron. Soc. 96: 749–757

    MATH  ADS  Google Scholar 

  • Tremaine S. et al. (1994) A family of models for spherical stellar systems. Astron. J. 107: 634–644

    Article  ADS  Google Scholar 

  • Veltmann Ü.-I.K. (1961) Constructing models for spherical star systems with given space density. Tartu Astron. Obs. Publ. 33: 387–415

    Google Scholar 

  • Veltmann Ü.-I.K. (1965) On phase density of spherical stellar systems. W. Struve Tartu Astrofüüs. Obs. Publ., 35: 5–26

    Google Scholar 

  • Veltmann Ü.-I.K.: Phase space models for star clusters. Star Clusters, Urals University Press, Sverdlovsk, pp. 50–71 (1979)

  • Veltmann Ü.-I.K. (1981) Gravitational potential, space density and phase density of star clusters. W. Struve Tartu Astrofüüs.Obs. Publ. 48: 232–261

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, Guangzhou, 510275, China

    Zhenglu Jiang

  2. Saint Petersburg State University, Staryj Peterhof, Saint Petersburg, 198504, Russia

    Leonid Ossipkov

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  1. Zhenglu Jiang
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  2. Leonid Ossipkov
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Correspondence to Zhenglu Jiang.

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Jiang, Z., Ossipkov, L. Anisotropic distribution functions for spherical galaxies. Celestial Mech Dyn Astr 97, 249–265 (2007). https://doi.org/10.1007/s10569-006-9062-5

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  • DOI: https://doi.org/10.1007/s10569-006-9062-5

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