Can galactic nuclei be non-axisymmetric? The parameter space of power-law discs

The shape of a cusped galactic nucleus is constrained by the range of shape s of orbits in its gravitational potential. It is shown for scale-free non- axisymmetric discs that while a plausible elongated density model requires at least some orbits to spend more time near the major axis than anywhere e lse, both regular boxlets and tube orbits generally cross the major axis to o fast for self-consistency. If galaxies host inner nuclear discs or flat b ars with a cuspy surface light profile (gamma = \d log mu/d log r\ > 0), th eir ellipticity 1- b/a cannot be greater than about gamma/2. Discs or bars with a shallow central profile (gamma less than or equal to 0.3) should not be strongly elliptical.