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 ∝ X^-α, 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 α = 1.98 ± 0.05 (α = 2.52 ± 0.03) for the peak flux, α = 1.79 ± 0.05 (α = 2.47 ± 0.11) for the fluence, and α = 2.49 ± 0.11 (α = 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.