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

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