Effects of temperature bias on nanoflare statistics

Statistics of solar flares, microflares, and nanoflares have been gathered over an energy range of some 8 orders of magnitude, over E approximate to 10(24)-10(32) ergs. Frequency distributions of flare energies are always determined in a limited temperature range, e.g., at T approximate to 1-2 MK if the 171 and 195 Angstrom 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 and the thermal energy E = 3n(e)k(B)T(e)V are statistically correlated in flare processes, statistics in a limited temperature range introduce a bias in the frequency distribution of flare energies, N(E) proportional to E-aE. We demonstrate in this Letter that the power-law slope of nanoflare energies, e.g., a(E) approximate to 1.9, as determined in a temperature range of T approximate to 1.1-1.6 MK (195 Angstrom), corresponds to a corrected value of a(E)' approximate to 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 a(E) approximate to 1.8-2.3, correspond to unbiased values of a(E) < 2, which then poses a serious challenge to Parker's hypothesis of coronal heating by nanoflares.