Abstract: Coronal heating generally increases with increasing magnetic field strength: the EUV/X-ray corona in active regions is 10–100 times more luminous and 2–4 times hotter than that in quiet regions and coronal holes, which are heated to only about 1.5 MK, and have fields that are 10–100 times weaker than that in active regions. From a comparison of a nonlinear force-free model of the three-dimensional active region coronal field to observed extreme-ultraviolet loops, we find that (1) umbra-to-…