The soft X-ray intensity of loops in active region cores and the corresponding footpoint, or moss, intensity observed in the EUV remain steady for several hours of observation. The steadiness of the emission has prompted many to suggest that the heating in these loops must also be steady, although no direct comparison between the observed X-ray and EUV intensities and the steady heating solutions of the hydrodynamic equations has yet been made. In this paper we perform these simulations and simultaneously model the X-ray and EUV moss intensities in one active region core with steady uniform heating. To perform this task, we introduce a new technique to constrain the model parameters using the measured EUV footpoint intensity to infer a heating rate. Using an ensemble of loop structures derived from magnetic field extrapolation of photospheric field, we associate each field line with an EUV moss intensity, then determine the steady uniform heating rate on that field line that reproduces the observed EUV intensity within 5% for a specific cross-sectional area, or filling factor. We then calculate the total X-ray filter intensities from all loops in the ensemble and compare this to the observed X-ray intensities. We complete this task iteratively to determine the filling factor that returns the best match to the observed X-ray intensities. We find that a filling factor of 8% and loops that expand with height provides the best agreement with the intensity in two X-ray filters, although the simulated SXT Al12 intensity is 147% the observed intensity and the SXT AlMg intensity is 80% the observed intensity. From this solution we determine the required heating rate scales as 0.29L−0.95. Finally, we discuss the future potential of this type of modeling, such as the ability to use density measurements to fully constrain filling factor, and its shortcomings, such as the requirement to use potential field extrapolations to approximate the coronal field.
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