Effects of Temperature Bias on Nanoflare Statistics

Abstract

Statistics of solar flares, microflares, and nanoflares have been gathered over an energy range of some 8 orders of magnitude, over E~1024-1032 ergs. Frequency distributions of flare energies are always determined in a limited temperature range, e.g., at T~1-2 MK if the 171 and 195 Å filters are used from an extreme ultraviolet telescope (the Solar and Heliospheric Observatory/EUV Imaging Telescope or the Transitional Region and Coronal Explorer). Because the electron temperature Te and the thermal energy E=3nekBTeV are statistically correlated in flare processes, statistics in a limited temperature range introduce a bias in the frequency distribution of flare energies, N(E)~E-aE. We demonstrate in this Letter that the power-law slope of nanoflare energies, e.g., aE~1.9, as determined in a temperature range of T~1.1-1.6 MK (195 Å), corresponds to a corrected value of a'E~1.4 in an unbiased, complete sample. This corrected value is in much better agreement with predictions from avalanche models of solar flares. However, it also implies that all previously published power-law slopes of EUV nanoflares, covering a range of aE~1.8-2.3, correspond to unbiased values of aE<2, which then poses a serious challenge to Parker's hypothesis of coronal heating by nanoflares.