  We analyze the excitation spectrum of a superfluid Bose-Einstein condensate
rotating in a ring trap. We identify two important branches of the spectrum
related to outer and inner edge surface modes that lead to the instability of
the superfluid. Depending on the initial circulation of the annular condensate,
either the outer or the inner modes become first unstable. This instability is
crucially related to the superfluid nature of the rotating gas. In particular
we point out the existence of a maximal circulation above which the superflow
decays spontaneously, which cannot be explained by invoking the average speed
of sound.
