We present new measurements of the dependence of the Extreme Ultraviolet radiance on the total magnetic flux in active regions as obtained from the Atmospheric Imaging Assembly ( AIA ) and the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory ( SDO ) .
Using observations of nine active regions tracked along different stages of evolution , we extend the known radiance - magnetic flux power-law relationship ( I \propto \Phi ^ { \alpha } ) to the AIA 335 Å passband , and the \ion Fe18 93.93 Å spectral line in the 94 Å passband .
We find that the total unsigned magnetic flux divided by the polarity separation ( \Phi / D ) is a better indicator of radiance for the \ion Fe18 line with a slope of \alpha = 3.22 \pm 0.03 .
We then use these results to test our current understanding of magnetic flux evolution and coronal heating .
We use magnetograms from the simulated decay of these active regions produced by the Advective Flux Transport ( AFT ) model as boundary conditions for potential extrapolations of the magnetic field in the corona .
We then model the hydrodynamics of each individual field line with the Enthalpy-based Thermal Evolution of Loops ( EBTEL ) model with steady heating scaled as the ratio of the average field strength and the length ( \bar { B } / L ) and render the \ion Fe18 and 335 Å emission .
We find that steady heating is able to partially reproduce the magnitudes and slopes of the EUV radiance - magnetic flux relationships and discuss how impulsive heating can help reconcile the discrepancies .
This study demonstrates that combined models of magnetic flux transport , magnetic topology and heating can yield realistic estimates for the decay of active region radiances with time .