2007/06/30 by Zhenglu Jiang, Zhuhan Jiang, Leonid Ossipkov +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Angular momentum #Classical mechanics #Coordinate system #Dispersion (optics) #Distribution (mathematics) #Geometry #Mathematical analysis #Mechanics #Physics #Product (mathematics) #Quantum and Classical Electrodynamics #Quantum mechanics #Rotational symmetry #Scientific Research and Discoveries #Symmetry (geometry) #Total angular momentum quantum number #astro-ph #math-ph #math.MP
paper · pdf · doi:10.1111/j.1365-2966.2007.11992.x
published as Monthly Notices of the Royal Astronomical Society, Vol 379, issue 3, 2007,p1133-1142
openalex publication_date 2007/06/30 · arxiv created 2007/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Some formulae are presented for finding two-integral 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. They come from a 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 multiplied 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.