THE DISTRIBUTION OF FLARE PARAMETERS AND IMPLICATIONS FOR CORONAL HEATING

Assuming that solar hard X-ray flares are caused by bremsstrahlung fro m a distribution of accelerated electrons impinging on a thick target, we determine the relationship between the total flare energy released in the corona and observable flare parameters. It is shown that for t he more numerous smaller flares to be energetically more important tha n larger ones, there must be an anticorrelation between observed flux and one or more of the photon spectral index, the total flare duration , the ratio of the total energy that goes into heating the corona to t he energy that goes into acceleration of electrons, and the reciprocal of the low-energy cutoff of the accelerated electron spectrum. Using a new statistical test which properly takes account of data truncation due to observational selection effects, we find that neither spectral index nor duration show an anticorrelation with flux in ISEE 3/ICE ha rd X-ray data. Using a nonparametric method, we obtain single distribu tions of peak flux, spectral index, duration, and fluence, corrected f or selection biases. The functional forms of these distributions do no t support coronal heating by numerous small flares without very specif ic behavior by yet unobserved parameters.