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We investigated the frequency distributions of flares with and withoutcoronal mass ejections (CMEs) as a function of flare parameters (peak flux,fluence, and duration of soft X-ray flares). We used CMEs observed by the LargeAngle and Spectrometric Coronagraph (LASCO) on board the Solar and HeliosphericObservatory (SOHO) mission and soft X-ray flares (C3.2 and above) observed bythe GOES satellites during 1996 to 2005. We found that the distributions obey apower-law of the form: dN/dX~X^-alpha, where X is a flare parameter and dN isthe number of events recorded within the interval [X, X+dX]. For the flareswith (without) CMEs, we obtained the power-law index alpha=1.98+-0.05(alpha=2.52+-0.03) for the peak flux, alpha=1.79+-0.05 (alpha=2.47+-0.11) forthe fluence, and alpha=2.49+-0.11 (alpha=3.22+-0.15) for the duration. Thepower-law indices for flares without CMEs are steeper than those for flareswith CMEs. The larger power-law index for flares without CMEs supports thepossibility that nanoflares contribute to coronal heating.Comment: 4 pages, 2 figures embedded, accepted for publication in ApJ

Different Power-Law Indices in the Frequency Distributions of Flares with and without Coronal Mass Ejections