1996/12/07 by S. Sridhar, J. Touma, Jihad Touma · 30 citations
Engineering · Physics and Astronomy · #Astrophysical Phenomena and Observations #Astrophysics #Celestial mechanics #Classical mechanics #Galaxy #Gravitation #Gravitational potential #Integrable system #Mass distribution #Mathematical physics #Mechanics #Physics #Relativity and Gravitational Theory #Rotational symmetry #Sports Dynamics and Biomechanics #astro-ph
paper · pdf · doi:10.1093/mnras/287.1.l1
published in Monthly Notices of the Royal Astronomical Society 287(1), L1-L4 (Oxford University Press) · 4 pages, 2 figures, submitted to MNRAS
arxiv created 1996/12/07 · openalex publication_date 1997/05/01 · arxiv updated 2016/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present cuspy, non-axisymmetric, scale-free mass models of discs, whose gravitational potentials are of Stäckel form in parabolic coordinates. A black hole may be added at the centre, without in any way affecting the Stäckel form ; the dynamics in these potentials is, of course, fully integrable. The surface density Σdisc ∝ 1/ry, where 0 < γ < 1 corresponds to steep cusps for which the central force diverges. Thus cusps, black holes, and non-axisymmetry are not a sure recipe for chaos, as is generally assumed. A new family of orbits, lens orbits, emerges to replace the box orbits of models of elliptical galaxies that have constant-density cores. Loop orbits are conspicuous by their absence. Both lenses and bananas (the other family of orbits) can be elongated in the direction of the density distribution, a property that is favourable for the construction of non-axisymmetric, self-consistent equilibrium models of elliptical galaxies.