Cusps without chaos

Abstract

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, ${\Sigma }_{disc}\propto 1/r^{\gamma }$, where $0<\gamma <1$ 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 boxlets (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.

4 pages, 2 figures, submitted to MNRAS

Cited by in corpus (20)

• Rates of tidal disruption of stars by massive central black holes
• Elliptical Galaxy Dynamics
• The loss cone problem in axisymmetric nuclei
• Orbits Around Black Holes in Triaxial Nuclei
• Relativistic and Newtonian core-shell models: analytical and numerical results
• Long-Lived Triaxiality in the Dynamically Old Elliptical Galaxy NGC 4365: A Limit on Chaos and Black Hole Mass
• Dark Halo Shapes and the Fate of Stellar Bars
• Dynamical Modeling of the Stellar Nucleus of M31
• On the Orbit Structure of the Logarithmic Potential
• Can galactic nuclei be non-axisymmetric? --- The parameter space of power-law discs
• Stellar Dynamics around a Massive Black Hole I: Secular Collisionless Theory
• Density cusps: restrictions on non-axisymmetric models
• Probing a regular orbit with spectral dynamics
• Classification of Stellar Orbits in Axisymmetric Galaxies
• Separable triaxial potential-density pairs in MOND
• Integrable models of galactic discs with double nuclei
• The pendulum dilemma of fish orbits
• Self-consistent axisymmetric Sridhar-Touma models
• The curvature condition for self-consistent scale-free galaxies
• Building galaxy models with Schwarzschild method and spectral dynamics