Open AccessStellar dynamics in razor‐thin discs with massive nuclear black holes
Author(s) -
Jalali Mir Abbas
Publication year - 1999
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1999.02947.x
Subject(s) - physics , phase space , circular orbit , classical mechanics , orbit (dynamics) , harmonic oscillator , conformal map , elliptic orbit , hamiltonian system , astrophysics , mathematical analysis , mathematics , quantum mechanics , engineering , thermodynamics , aerospace engineering
The bifurcations of orbit‐averaged dynamics are studied in a class of razor‐thin discs with central black holes. The model used here consists of a perturbed harmonic oscillator Hamiltonian augmented with a − GM r potential. Through a sequence of conformal and canonical transformations, we reduce the phase‐space flows of the system to a set of non‐linear differential equations on a sphere. Based on the critical points of the averaged system, we classify orbit families and reveal the existence of six types of periodic motions: circular , long ‐ and short‐axis elliptical , long ‐ and short‐axis radial and inclined radial orbits. Long‐axis elliptical orbits and their surrounding tubes have significant features: whilst they keep stars away from the centre, they elongate in the same direction as the density profile. These properties are helpful in the construction of self‐consistent equilibria.