High-temperature differential emission measure and altitude variations in the temperature and density of solar flare coronal X-ray sources

The detailed knowledge of plasma heating and acceleration region properties presents a major observational challenge in solar flare physics. Using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI), the high temperature differential emission measure, DEM(T ), and the energy-dependent spatial structure of solar flare coronal sources are studied quantitatively. The altitude of the coronal X-ray source is observed to increase with energy by ∼ +0.2 arcsec/keV between 10 and 25 keV. Although an isothermal model can fit the thermal X-ray spectrum observed by RHESSI, such a model cannot account for the changes in altitude, and multithermal coronal sources are required where the temperature increases with altitude. For the first time, we show how RHESSI imaging information can be used to constrain the DEM(T ) of a flaring plasma. We develop a thermal bremsstrahlung X-ray emission model with inhomogeneous temperature and density distributions to simultaneously reproduce: i) DEM(T ), ii) altitude as a function of energy, and iii) vertical extent of the flaring coronal source versus energy. We find that the temperature-altitude gradient in the region is ∼ +0.08 keV/arcsec (∼ 1.3 MK/Mm). Similar altitude-energy trends in other flares suggest that the majority of coronal X-ray sources are multi-thermal and have strong vertical temperature and density gradients with a broad DEM(T ).