A time-dependent three-dimensional magnetohydrodynamic model of the coronal mass ejection

We present a theoretical magnetohydrodynamic (MHD) model describing the time-dependent expulsion of a three-dimensional coronal mass ejection (CME) out of the solar corona. The model relates the white-light appearance of the CME to its internal magnetic field, which takes the form of a closed bubble, filled with a partly anchored, twisted magnetic flux rope, and embedded in an otherwise open background held. The model is constructed by solving in closed form the time-dependent ideal MHD equations for a gamma = 4/3 polytrope making use of a similarity assumption and the application of a mathematical stretching transformation in order to treat a complex field geometry with three-dimensional variations. The density distribution frozen into the expanding CME magnetic field is obtained. The scattered white light integrated along the line of sight shows the conspicuous three features often associated with CMEs as observed with white-light coronagraphs: a surrounding high-density region, an internal low-density cavity, and a high-density core. We also show how the orientation of this three-dimensional structure relative to the line of sight can give rise to a variety of different geometric appearances in white light. These images generated from a CME model in a realistic geometry offer an opportunity to directly compare theoretical predictions on CME shapes with observations of CMEs in white light. The mathematical methods used in the model construction have general application and are described in the Appendices.