Cusps without chaos
Abstract
We present cuspy, nonaxisymmetric, scalefree mass models of discs, whose gravitational potentials are of Stackel form in parabolic coordinates. A black hole may be added at the centre, without in any way affecting the Stackel form; the dynamics in these potentials is, of course, fully integrable. The surface density Sigma_disc~1/r^gamma, where 0<gamma<1 corresponds to steep cusps for which the central force diverges. Thus cusps, black holes, and nonaxisymmetry 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 constantdensity 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 nonaxisymmetric, selfconsistent equilibrium models of elliptical galaxies.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 1997
 DOI:
 10.1093/mnras/287.1.L1
 arXiv:
 arXiv:astroph/9612067
 Bibcode:
 1997MNRAS.287L...1S
 Keywords:

 GALAXIES: ELLIPTICAL AND LENTICULAR;
 CD;
 GALAXIES: KINEMATICS AND DYNAMICS;
 GALAXIES: STRUCTURE;
 Astrophysics
 EPrint:
 4 pages, 2 figures, submitted to MNRAS