Prominence support in potential field configurations around rotating stars

We present a general method for determining the locations of stable gravita tional centrifugal potential minima within arbitrary potential magnetic fie ld configurations surrounding rotating single stars. We show that stable lo cations exist both inside and outside the corotation radius of a single sta r, 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 significan t departures from a simple dipole to distances as great as four or more ste llar radii from the star. We demonstrate that the radial-field distribution derived from a Zeeman-Doppler image of AB Dor yields sufficient field comp lexity at large distances for prominence sheets to form outside the corotat ion radius at latitudes that transit the stellar disc, assuming an axial in clination of 60 degrees to the line of sight.