Coronal mass ejections (CMEs) are large-scale explosions of the coronal magnetic field. It is believed that magnetic reconnection significantly builds up the core structure of CMEs, a magnetic flux rope, during the eruption. However, the quantitative evolution of the flux rope, particularly its toroidal flux, is still unclear. In this paper, we study the evolution of the toroidal flux of the CME flux rope for four events. The toroidal flux is estimated as the magnetic flux in the footpoint region of the flux rope, which is identified by a method that simultaneously takes the coronal dimming and the hook of the flare ribbon into account. We find that the toroidal flux of the CME flux rope for all four events shows a two-phase evolution: a rapid increasing phase followed by a decreasing phase. We further compare the evolution of the toroidal flux with that of the Geostationary Operational Environmental Satellites soft X-ray flux and find that they are basically synchronous in time, except that the peak of the former is somewhat delayed. The results suggest that the toroidal flux of the CME flux rope may be first quickly built up by the reconnection mainly taking place in the sheared overlying field and then reduced by the reconnection among the twisted field lines within the flux rope, as enlightened by a recent 3D magnetohydrodynamic simulation of CMEs.
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