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Using a Differential Emission Measure and Density Measurements in an Active Region Core to Test a Steady Heating Model

The frequency of heating events in the corona is an important constraint on the coronal heating mechanisms. Observations indicate that the intensities and velocities measured in active region cores are effectively steady, suggesting that heating events occur rapidly enough to keep high temperature active region loops close to equilibrium. In this paper, we couple observations of Active Region 10955 made with XRT and EIS on \textit{Hinode} to test a simple steady heating model. First we calculate the differential emission measure of the apex region of the loops in the active region core. We find the DEM to be broad and peaked around 3\,MK. We then determine the densities in the corresponding footpoint regions. Using potential field extrapolations to approximate the loop lengths and the density-sensitive line ratios to infer the magnitude of the heating, we build a steady heating model for the active region core and find that we can match the general properties of the observed DEM for the temperature range of 6.3 $<$ Log T $<$ 6.7. This model, for the first time, accounts for the base pressure, loop length, and distribution of apex temperatures of the core loops. We find that the density-sensitive spectral line intensities and the bulk of the hot emission in the active region core are consistent with steady heating. We also find, however, that the steady heating model cannot address the emission observed at lower temperatures. This emission may be due to foreground or background structures, or may indicate that the heating in the core is more complicated. Different heating scenarios must be tested to determine if they have the same level of agreement.