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 Geostationary Operational Environmental Satellite (GOES) during 1996-2005. We found that the distributions obey a power law of the form dN/dX proportional to 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 = 1.98 +/- 0.05 (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.