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4.2 Thermal energy

Electron energy distributions can be inferred from X-ray spectra with high spectral resolution, e.g., Figure 7View Image. The quasi-thermal part, observed mostly in coronal sources, reaches temperatures of several ten MK. For simplicity, it is often modeled with a single temperature, sometimes with an additional much hotter, but smaller second component. In reality, the distribution of the emission measure with temperature (called differential emission measure, DEM) can easily exceed a factor two in the temperature range (McTiernan et al., 1999Chifor et al., 2007Aschwanden, 2007). The quasi-thermal population may be directly heated coronal material or evaporated chromospheric material heated by precipitating particles accelerated by the flare. As the coronal emission measure greatly increases during a flare, most of the thermal flare plasma must origin from the chromosphere. The first X-ray emissions appear to be purely thermal, but already contain more material than expected in the corona of quiescent active regions. Thus the thermal X-ray plasma is generally assumed to be evaporated chromospheric material. The thermal energy Eth of this plasma is thus of flare origin and amounts to
3∑ ∫ Eth = -- nαkBT αdV , (4 ) 2 α
where α refers to the plasma species, n, T, and V refer to density, temperature, and volume. Assuming a homogeneous source having equal temperatures among species and approximate equality between electron and ion density,
√ ----- Eth = 3kBT ℳV , (5 )
where ℳ is the observed emission measure of soft X-rays. The observations suggest that Ekin is larger by a factor of 1 – 10 than Eth for plasma at T > 10 MK (Emslie et al., 2004aSaint-Hilaire and Benz, 2005). The factor concurs with the expectation that heating to coronal temperature is not a loss-free process. The result is also consistent with the observations in white light suggesting that a major part of the precipitated energy is lost to low-temperature plasma not observable in X-rays (Section 4.4).
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