Quantifying the Toroidal Flux of Pre-existing Flux Ropes of CMEs

In past decades, much progress has been achieved on the origin and evolution of coronal mass ejections (CMEs). In-situ observations of the counterparts of CMEs, especially magnetic clouds (MCs) near the Earth, have provided measurements of the structure and total flux of CME flux ropes. However, it has been difficult to measure these properties in the erupting CME flux rope, in particular in the pre-existing flux rope. In this work, we propose a model to estimate the toroidal flux of the pre-existing flux rope by subtracting the flux contributed by magnetic reconnection during the eruption from the flux measured in the MC. The flux by the reconnection is derived from geometric properties of two-ribbon flares based on a quasi-2D reconnection model. We then apply the model to four CME/flare events and find that the ratio of toroidal flux in the pre-existing flux rope to that of the associated MC lies in the range of 0.40--0.88. It indicates that the toroidal flux of the pre-existing flux rope has an important contribution to that of the CME flux rope and is usually at least as large as the flux arising from the eruption process for the selected events.