Eccentric Stellar Discs with Strong Density Cusps and Separable Potentials

Details Eccentric Stellar Discs with Strong Density Cusps and Separable Potentials Eccentric Stellar Discs with Strong Density Cusps and Separable Potentials

2000-01-04

arxiv.org/abs/astro-ph/0001042v1

Astronomy and Astrophysics

Astrophysics

5 pages, submitted to MNRAS

Scientific paper

We introduce a class of eccentric discs with "strong" density cusps whose potentials are of St\"ackel form in elliptic coordinates. Our models exhibit some striking features: sufficiently close to the location of the cusp, the potential and surface density distribution diverge as $\Phi \propto r^{-1}$ and $\Sigma \propto r^{-2}$, respectively. As we move outward from the centre, the model takes a non-axisymmetric, lopsided structure. In the limit, when $r$ tends to infinity, the isocontours of $\Phi$ and $\Sigma$ become spherically symmetric. It is shown that the configuration space is occupied by three families of regular orbits: {\it eccentric butterfly}, {\it aligned loop} and {\it horseshoe} orbits. These orbits are properly aligned with the surface density distribution and can be used to construct self-consistent equilibrium states.

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