Time Variability of the “Quiet” Sun Observed withTRACE. II. Physical Parameters, Temperature Evolution, and Energetics of Extreme‐Ultraviolet Nanoflares

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Abstract
We present a detailed analysis of the geometric and physical parameters of 281 EUV nanoflares, simultaneously detected with the TRACE telescope in the 171 and 195 Å wavelengths. The detection and discrimination of these flarelike events is detailed in the first paper in this series. We determine the loop length l, loop width w, emission measure EM, the evolution of the electron density ne(t) and temperature Te(t), the flare decay time τdecay, and calculate the radiative loss time τloss, the conductive loss time τcond, and the thermal energy Eth. The findings are as follows: (1) EUV nanoflares in the energy range of 1024-1026 ergs represent miniature versions of larger flares observed in soft X-rays (SXR) and hard X-rays (HXR), scaled to lower temperatures (Te 2 MK), lower densities (ne 109 cm-3), and somewhat smaller spatial scales (l ≈ 2-20 Mm). (2) The cooling time τdecay is compatible with the radiative cooling time τrad, but the conductive cooling timescale τcond is about an order of magnitude shorter, suggesting repetitive heating cycles in time intervals of a few minutes. (3) The frequency distribution of thermal energies of EUV nanoflares, N(E) ≈ 10-46(E/1024)-1.8 (s-1 cm-2 ergs-1) matches that of SXR microflares in the energy range of 1026-1029, and exceeds that of nonthermal energies of larger flares observed in HXR by a factor of 3-10 (in the energy range of 1029-1032 ergs). Discrepancies of the power-law slope with other studies, which report higher values in the range of a = 2.0-2.6 (Krucker & Benz; Parnell & Jupp), are attributed to methodical differences in the detection and discrimination of EUV microflares, as well as to different model assumptions in the calculation of the electron density. Besides the insufficient power of nanoflares to heat the corona, we find also other physical limits for nanoflares at energies 1024 ergs, such as the area coverage limit, the heating temperature limit, the lower coronal density limit, and the chromospheric loop height limit. Based on these quantitative physical limitations, it appears that coronal heating requires other energy carriers that are not luminous in EUV, SXR, and HXR.