Different Power-law Indices in the Frequency Distributions of Flares   with and without Coronal Mass Ejections
  We investigated the frequency distributions of flares with and without coronal 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 Large Angle and Spectrometric Coronagraph (LASCO) on board the Solar and Heliospheric Observatory (SOHO) mission and soft X-ray flares (C3.2 and above) observed by the GOES satellites during 1996 to 2005. We found that the distributions obey a power-law of the form: dN/dX~X^-alpha, where X is a flare parameter and dN is the number of events recorded within the interval [X, X+dX]. For the flares with (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) for the fluence, and alpha=2.49+-0.11 (alpha=3.22+-0.15) for the duration. The power-law indices for flares without CMEs are steeper than those for flares with CMEs. The larger power-law index for flares without CMEs supports the possibility that nanoflares contribute to coronal heating. 
S. Yashiro, S. Akiyama, N. Gopalswamy, and R. A. Howard