Eccentric stellar discs with strong density cusps and separable potentials

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 ∝ r and Σ ∝ r, 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: eccentric butterfly, aligned loop and horseshoe orbits. These orbits are properly aligned with the surface density distribution and can be used to construct self-consistent equilibrium states.