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 FOXSI (Focusing Optics X-ray Solar Imager) flight was coordinated with instruments Hinode/XRT and SDO/AIA, which provided observations in soft X-rays (SXR) and Extreme Ultraviolet (EUV). This unique dataset 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 3MK and extend beyond 10MK. The emission measures determined from FOXSI-2 were lower than 10 26cm-5 for temperatures higher than 5MK; 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 5MK in microflares. We utilize the multi-thermal DEMs to calculate the amount of thermal energy released during both the microflares as ~ 5.0 x 10 28 ergs for Microflare 1 and ~ 1.6 x 10 28 ergs for Microflare 2. We also show the multi-thermal DEMs provide a more comprehensive thermal energy estimates than isothermal approximation, which systematically underestimates the amount of thermal energy released.