  Dense and narrow rings have been discovered recently around the small Centaur
object Chariklo and the dwarf planet Haumea, while being suspected around the
Centaur Chiron. They are the first rings observed in the Solar System elsewhere
than around giant planets. Contrarily to the latters, gravitational fields of
small bodies may exhibit large non-axisymmetric terms that create strong
resonances between the spin of the object and the mean motion of rings
particles. Here we show that modest topographic features or elongations of
Chariklo and Haumea explain why their rings are relatively far away from the
central body, when scaled to those of the giant planets. Lindblad-type
resonances actually clear on decadal time-scales an initial collisional disk
that straddles the corotation resonance (where the particles mean motion
matches the spin rate of the body). The disk material inside the corotation
radius migrates onto the body, while the material outside the corotation radius
is pushed outside the 1/2 resonance, where the particles complete one
revolution while the body completes two rotations. Consequently, the existence
of rings around non-axisymmetric bodies requires that the 1/2 resonance resides
inside the Roche limit of the body, favoring fast rotators for being surrounded
by rings.
