Modeling coronal response in decaying active regions with magnetic flux transport and steady heating

We present new measurements of the dependence of the extreme ultraviolet (EUV) 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. Using observations of nine active regions tracked along different stages of evolution, we extend the known radiance-magnetic flux power-law relationship (I proportional to Phi(alpha)) to the AIA 335 angstrom passband, and the Fe XVIII 93.93 angstrom spectral line in the 94 angstrom passband. We find that the total unsigned magnetic flux divided by the polarity separation (Phi/D) is a better indicator of radiance for the Fe XVIII line with a slope of alpha = 3.22 +/- 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 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 model with steady heating scaled as the ratio of the average field strength and the length ((B) over bar /L) and render the Fe XVIII and 335 angstrom 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.