Fitting Technique to Obtain the 3D CME Geometric Parameters and Uncertainty Analysis.

This study introduces a fitting technique to obtain the 3-D geometric parameters of coronal mass ejections (CME) and their uncertainties. CMEs are large-scale eruptions carrying plasma and magnetic field from the Sun and often show a two front structure consisting of the ejecta and the shock. The graduated cylindrical shell model (GCS model) is used to recreate the morphology of the ejecta and the spheroid model is used to recreate the shock in 3-D. Both models depend on a number of free parameters. The GCS model depends on six free parameters which are responsible for its propagation direction, orientation and shape; these are longitude, latitude, tilt angle, aspect ratio (related to cross-section size of the flux rope), half angle and leading height and describe the morphology of the CME in 3-D along its radial, toroidal and poloidal dimension. Although studies that focus on the radial and toroidal dimension of the CMEs can be found in the literature, there is not much information on their poloidal dimension, which leaves room for misunderstandings and not accurate interpretation of the size of a flux rope. The spheroid shock model depends on four free parameters, which are longitude, latitude, aspect ratio (related to the radius of the spheroid) and height. The fitting technique we present uses the MPFIT minimization IDL routine and combines multi-viewpoint white light observations from the two STEREO and SOHO spacecraft with the GCS and spheroid shock point clouds in order to obtain the best values of the geometric parameters along with their uncertainties. Using this technique we examine the cases of halo, partial halo and limb CMEs as viewed from the Earth. This method only needs two input parameters, a set of selected points defining the fronts and a set of initial guesses in order to minimize the chi-square between the observations and the models which automate the fitting process. Space weather predictions will be benefited by a robust, fast and straightforward way to estimate the CME geometric parameters along with their uncertainties.