Investigating the Reliability of Coronal Emission Measure Distribution Diagnostics using Three-dimensional Radiative Magnetohydrodynamic Simulations

Determining the temperature distribution of coronal plasmas can provide stringent constraints on coronal heating. Current observations with the Extreme ultraviolet Imaging Spectrograph (EIS) on board Hinode and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory provide diagnostics of the emission measure distribution (EMD) of the coronal plasma. Here we test the reliability of temperature diagnostics using three-dimensional radiative MHD simulations. We produce synthetic observables from the models and apply the Monte Carlo Markov chain EMD diagnostic. By comparing the derived EMDs with the "true" distributions from the model, we assess the limitations of the diagnostics as a function of the plasma parameters and the signal-to-noise ratio of the data. We find that EMDs derived from EIS synthetic data reproduce some general characteristics of the true distributions, but usually show differences from the true EMDs that are much larger than the estimated uncertainties suggest, especially when structures with significantly different density overlap along the line of sight. When using AIA synthetic data the derived EMDs reproduce the true EMDs much less accurately, especially for broad EMDs. The differences between the two instruments are due to the: (1) smaller number of constraints provided by AIA data and (2) broad temperature response function of the AIA channels which provide looser constraints to the temperature distribution. Our results suggest that EMDs derived from current observatories may often show significant discrepancies from the true EMDs, rendering their interpretation fraught with uncertainty. These inherent limitations to the method should be carefully considered when using these distributions to constrain coronal heating.