The magnetic non-equilibrium of buoyant flux tubes in the solar corona

The equilibrium shape of a slender flux tube in the stratified solar atmosphere is studied. The path is determined by a balance between the downwards magnetic tension, which depends on the curvature of the loop, and the upwards buoyancy force. Previous results for untwisted slender tubes are extended to include twisted tubes embedded in an external magnetic field.The path of an untwisted tube in an atmosphere with an ambient magnetic field is calculated. For a given footpoint separation, the height of the tube is lowered by increasing the strength of the external magnetic field. If the footpoints are slowly moved apart, the tube rises, until a threshold separation is reached beyond which there is no possible equilibrium height. This threshold width does not depend on the strength of the external field.The effects of twisting up a curved loop are studied, using an extension of results obtained for slender curved tubes with a straight axis. It is shown that for a twisted tube of given width, there can be two possible values of the equilibrium height. If, however, the tube is twisted more than a certain amount or if the footpoints are too widely separated there is no equilibrium. The critical footpoint separation for non-equilibrium is smaller for a twisted tube that an untwisted one.Twisting a tube or moving its feet apart is thus likely to result in non-equilibrium, causing the tube to rise indefinitely under the influence of the unbalanced buoyant force. It is suggested that this phenomenon could be important in the preflare stage of a large two-ribbon solar flare, by causing the initial slow rise of an active region filament. As well as being involved in the onset of an erupting prominence, this non-equilibrium may also be relevant to the formation of coronal loop transients.