DENSITY CUSPS - RESTRICTIONS ON NON-AXISYMMETRICAL MODELS

Galactic nuclei are now generally thought to have density cusps in the ir centres, and the evidence is mounting that as a consequence they ar e unlikely to be triaxial. Self-consistent stellar dynamical models of non-axisymmetric cusps would be an interesting counterargument to thi s conclusion. We consider 2D analogues of triaxial cusps: a sequence o f non-axisymmetric, cuspy discs first described by Sridhar & Touma. Sc ale-free models with potential Phi proportional to r(alpha) are examin ed in detail. It is shown analytically for 0 < alpha less than or simi lar to 0.43 that self-consistent models with positive phase-space dens ity do not exist. Numerical solutions of the combined Vlasov and Poiss on equations suggest that the whole sequence of models with 0 < alpha < 1 are also unphysical. Together with existing work on cusps, we conc lude on purely theoretical grounds that galactic nuclei are not expect ed to be triaxial.