The Long-Term Evolution of AR 7978: Testing Coronal Heating Models

We derive the dependence of the mean coronal heating rate on the magnetic flux density. Our results are based on a previous study of the plasma parameters and the magnetic flux density (B) in the active region NOAA 7978 from its birth to its decay, throughout five solar rotations using the Solar and Heliospheric Observatory Michelson Doppler Imager, Yohkoh Soft X-Ray Telescope (SXT), and Yohkoh Bragg Crystal Spectrometer (BCS). We use the scaling laws of coronal loops in thermal equilibrium to derive four observational estimates of the scaling of the coronal heating with B (two from SXT and two from BCS observations). These results are used to test the validity of coronal heating models. We find that models based on the dissipation of stressed, current-carrying magnetic fields are in better agreement with the observations than models that attribute coronal heating to the dissipation of MHD waves injected at the base of the corona. This confirms, with smaller error bars, previous results obtained for individual coronal loops, as well as for the global coronal emission of the Sun and cool stars. Taking into account that the photospheric field is concentrated in thin magnetic flux tubes, both SXT and BCS data are in best agreement with models invoking a stochastic buildup of energy, current layers, and MHD turbulence.