Flattened γ models for galaxies

Jiang, Zhuhan; Ossipkov, L. P.

doi:10.1080/10556790600896008

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…Since the mass density of the system is defined by the integration of the DF over the velocity, the problem of finding a DF is that of solving an integral equation (see [8,9,10,11,12,13] and the references therein). At present we have at disposal a variety of self-consistent galaxy models: [14,15,16,17,18,19,20,21,22,23,24,25]. Now, even though for most systems under consideration Newtonian gravity is believed to be dominant, general relativistic corrections might play an important role in their evolution.…”

Section: Introductionmentioning

confidence: 99%

Kinetic theory of collisionless self-gravitating gases. II. Relativistic corrections in galactic dynamics

Ramos-Caro

Agón

Pedraza³

2012

Phys. Rev. D

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In this paper we study the kinetic theory of many-particle astrophysical systems imposing axial symmetry and extending our previous analysis in Phys. Rev. D 83, 123007 (2011).Starting from a Newtonian model describing a collisionless self-gravitating gas, we develop a framework to include systematically the first general relativistic corrections to the matter distribution and gravitational potentials for general stationary systems. Then, we use our method to obtain particular solutions for the case of the Morgan & Morgan disks. The models obtained are fully analytical and correspond to the post-Newtonian generalizations of classical ones. We explore some properties of the models in order to estimate the importance of post-Newtonian corrections and we find that, contrary to the expectations, the main modifications appear far from the galaxy cores. As a by-product of this investigation we derive the corrected version of the tensor virial theorem. For stationary systems we recover the same result as in the Newtonian theory. However, for time dependent backgrounds we find that there is an extra piece that contributes to the variation of the inertia tensor.

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Section: Introductionmentioning

confidence: 99%

Kinetic theory of collisionless self-gravitating gases. II. Relativistic corrections in galactic dynamics

Ramos-Caro

Agón

Pedraza³

2012

Phys. Rev. D

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“…It is worthwhile to mention that such equipotential extensions have been studied for the Jaffe (1983) spherical model (e.g. Jiang 2000; Jiang et al 2002a; Jiang, Fang & Moss 2002b) and for the spherical γ model (Jiang & Ossipkov 2006). The γ model was found independently by Kuzmin, Veltmann & Tenjes (1986), Dehnen (1993), Saha (1993) and Tremaine et al (1994).…”

Section: Application To the Prolate Modelsmentioning

confidence: 99%

Two-integral distribution functions for axisymmetric stellar systems with separable densities

Jiang¹,

Ossipkov

2007

Monthly Notices of the Royal Astronomical Society

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We show different expressions of distribution functions (DFs) which depend only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known axisymmetric densities. The density of the system is required to be a product of functions separable in the potential and the radial coordinates, where the functions of the radial coordinate are powers of a sum of a square of the radial coordinate and its unit scale. The even part of the two-integral DF corresponding to this type of density is in turn a sum or an infinite series of products of functions of the energy and of the magnitude of the angular momentum about the axis of symmetry. A similar expression of its odd part can be also obtained under the assumption of the rotation laws. It can be further shown that these expressions are in fact equivalent to those obtained by using Hunter & Qian's contour integral formulae for the system. This method is generally computationally preferable to the contour integral method. Two examples are given to obtain the even and odd parts of their two-integral DFs. One is for the prolate Jaffe model and the other for the prolate Plummer model.It can be also found that the Hunter-Qian contour integral formulae of the two-integral even DF for axisymmetric systems can be recovered by use of the Laplace-Mellin integral transformation originally developed by Dejonghe.

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“…In the literature, there are a number of different axisymmetric models for galaxies (e.g. Miyamoto 1971; Bagin 1972; Miyamoto & Nagai 1975; Nagai & Miyamoto 1976; Kutuzov & Ossipkov 1980, 1986, 1988; Evans 1993, 1994; Kutuzov 1995; Jiang 2000; Jiang & Moss 2002; Jiang et al 2002; Jiang & Ossipkov 2006; Ossipkov & Jiang 2007) and different integral transformation techniques are used to obtain the solution of the problem of finding the two‐integral DFs of axisymmetric stellar systems (e.g. Lynden‐Bell 1962; Hunter 1975; Kalnajs 1976; Dejonghe 1986) but there is a fatal obstacle of requiring not only the validity of these transformations of the density but also the complex analyticity of a density‐related integral kernel to complex arguments.…”

Section: Introductionmentioning

confidence: 99%

Two-integral distribution functions for axisymmetric systems

Jiang¹,

Ossipkov

2007

Monthly Notices of the Royal Astronomical Society

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Some formulae are presented for finding two-integral distribution functions (DFs) which depends only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known axisymmetric densities. They come from an combination of the ideas of Eddington and Fricke and they are also an extension of those shown by Jiang and Ossipkov for finding anisotropic DFs for spherical galaxies. The density of the system is required 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 about the axis of symmetry. The product of the density and its radial velocity dispersion can be also expressed as a sum of products of functions of the potential and of the radial coordinate. It can be further known that the density multipied by its rotational velocity dispersion is equal to a sum of products of functions of the potential and of the radial coordinate minus the product of the density and the square of its mean rotational velocity. These formulae can be applied to the Binney and the Lynden-Bell models. An infinity of the odd DFs for the Binney model can be also found under the assumption of the laws of the rotational velocity

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Flattened γ models for galaxies

Abstract: Using the equipotential method we introduce a class of flattened γ models for galaxies and study the properties of their potential-density pairs and two-integral distribution functions.

Cited by 5 publications

References 8 publications

Kinetic theory of collisionless self-gravitating gases. II. Relativistic corrections in galactic dynamics

Kinetic theory of collisionless self-gravitating gases. II. Relativistic corrections in galactic dynamics

Two-integral distribution functions for axisymmetric stellar systems with separable densities

Two-integral distribution functions for axisymmetric systems

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