Benchmark Test of Differential Emission Measure Codes and Multi-Thermal Energies in Solar Active Regions

We compare the ability of 11 Differential Emission Measure (DEM) forward-fitting and inversion methods to constrain the properties of active regions and solar flares by simulating synthetic data using the instrumental response functions of SDO/AIA, SDO/EVE, RHESSI, and GOES/XRS. The codes include the single-Gaussian DEM, a bi-Gaussian DEM, a fixed-Gaussian DEM, a linear spline DEM, the spatial synthesis DEM, the Monte-Carlo Markov chain DEM, the regularized DEM inversion, the Hinode/XRT method, a polynomial spline DEM, an EVE+GOES, and an EVE+RHESSI method. Averaging the results from all 11 DEM methods, we find the following accuracies in the inversion of physical parameters: the EM-weighted temperature $T_w^{fit}/T_w^{sim}=0.9\pm0.1$, the peak emission measure $EM_p^{fit}/EM_p^{sim}=0.6\pm0.2$, the total emission measure $EM_t^{fit}/EM_t^{sim}=0.8\pm0.3$, and the multi-thermal energies $E_{th}^{fit}/EM_{th}^{sim}=1.2\pm0.4$. We find that the AIA spatial synthesis, the EVE+GOES, and the EVE+RHESSI method yield the most accurate results.