4.2 Thermal energy
Electron energy distributions can be inferred from X-ray spectra with high spectral resolution, e.g.,
Figure 7. 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., 1999; Chifor et al., 2007; Aschwanden, 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
where 
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,
where 
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., 2004a; Saint-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).
. 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., 1999; Chifor et al., 2007; Aschwanden, 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
where 
