Eccentric Stellar Discs with Strong Density Cusps and Separable Potentials

Abstract

We introduce a class of eccentric discs with "strong" density cusps whose potentials are of Stäckel 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 $Φ\propto r^{-1}$ and $Σ\propto r^{-2}$, 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 $Φ$ and $Σ$ 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.