The shape of buoyant coronal loops in a magnetic field and the eruption of coronal transients and prominences

The equilibrium and non-equilibrium properties of a coronal loop embedded in a stratified isothermal atmosphere are investigated. The shape of the loop is determined by a balance between magnetic tension, buoyancy, and external pressure gradients. The footpoints of the loop are anchored in the photosphere; if they are moved too far apart, no equilibrium is possible and the loop erupts upwards. This critical separation is independent of the pressure differential between the loop and the external medium if the loop has enhanced magnetic field, but varies if instead the loop pressure is increased. The maximum width is proportional to the larger of the gravitational scale-height and the length-scale of the ambient field. In some circumstances, it is shown that multiple solutions exist for the tube path. These results may be relevant to the eruption of prominences during the preflare phase of two-ribbon flares and to the onset of coronal loop transients. Such eruptions may occur if the footpoint separation, internal pressure or internal magnetic field are too great.