FOXSI-2 Solar Microflares. I. Multi-instrument Differential Emission Measure Analysis and Thermal Energies

In this paper we present the differential emission measures (DEMs) of two sub-A class microflares observed in hard X-rays (HXRs) by the FOXSI-2 sounding rocket experiment, on 2014 December 11. The second Focusing Optics X-ray Solar Imager (FOXSI) flight was coordinated with instruments X-ray Telescope (Hinode/XRT) and Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA), which provided observations in soft X-rays and Extreme Ultraviolet. This unique data set offers an unprecedented temperature coverage, useful for characterizing the plasma temperature distribution of microflares. By combining data from FOXSI-2, XRT, and AIA, we determined a well-constrained DEM for the microflares. The resulting DEMs peak around 3 MK and extend beyond 10 MK. The emission measures determined from FOXSI-2 were lower than 10²⁶ cm^-5 for temperatures higher than 5 MK; faint emission in this range is best measured in HXRs. The coordinated FOXSI-2 observations produce one of the few definitive measurements of the distribution and the amount of plasma above 5 MK in microflares. We utilize the multi-thermal DEMs to calculate the amount of thermal energy released during both the microflares as ∼5.0 × 10²⁸ erg for Microflare 1 and ∼1.6 × 10²⁸ erg for Microflare 2. We also show the multi-thermal DEMs provide more comprehensive thermal energy estimates than isothermal approximation, which systematically underestimates the amount of thermal energy released.