We study the stability of an equilibrium model of prominences in rapidly rotating stars. A prominence is represented by an axisymmetric equatorial current sheet embedded in a massless and perfectly conducting coronal plasma. There is an equilibrium between gravity, centrifugal force and Lorentz force acting on the prominence. The energy method of Bernstein et al., in the form presented by Lepeltier & Aly, is used to derive sufficient stability conditions. Using existing observational values for the masses, dimensions and coronal locations of the prominences, we find that surface fields of a few hundred Gauss are required to hold them in a stable equilibrium. The free magnetic energy present in stable equilibrium models is sufficient to feed medium-sized flares but probably not the very energetic ones.
We discuss the question of what makes stellar prominences so different from their solar counterparts and what allows them to be detected. We also examine the role of the corotation radius in their formation.