Prominence support in potential field configurations around rotating stars

We present a general method for determining the locations of stable gravitational centrifugal potential minima within arbitrary potential magnetic field configurations surrounding rotating single stars. We show that stable locations exist both inside and outside the corotation radius of a single star, for even the simplest field configurations. We show that for prominence formation to occur at significant distances above the equatorial plane, as observed in stars such as AB Dor and PZ Tel, the field must show significant departures from a simple dipole to distances as great as four or more stellar radii from the star. We demonstrate that the radial-field distribution derived from a Zeeman-Doppler image of AB Dor yields sufficient field complexity at large distances for prominence sheets to form outside the corotation radius at latitudes that transit the stellar disc, assuming an axial inclination of 60 degrees to the line of sight.