Coronal Heating of an Active Region Observed by the Solar Dynamics Observatory

A realistic model of Alfven wave turbulence for coronal loops in an observed active region is constructed. An important question is whether turbulent heating leads to thermally stable loops, as seems to be required by the observations (Klimchuk et al. 2010). We use data from the Solar Dynamics Observatory (SDO) for an active region observed on 2010 May 5. Coronal images obtained with the Atmospheric Imager Assembly (AIA) in several EUV passbands show the presence of coronal loops with temperatures in the range 1-3 MK. Our goal is to determine whether these loops may be heated by Alfven wave turbulence, and if so, to predict the observational signatures of such waves and turbulence. Using data from the Heliospheric and Magnetic Imager (HMI), we construct a three-dimensional (3D) magnetic model of the region, and select field lines that match eleven of the observed loops (image 1). This provides us with the magnetic field strength B0(s) along each loop. Using a modified version of the reduced MHD code developed in our previous paper (van Ballegooijen et al. 2011), we construct 3D time-dependent MHD models for the Alfven waves in each loop and derive estimates of the heating rate averaged over time and cross-sectional area of the loop. Then we iteratively adjust the coronal temperature and density for each loop in order to satisfy the requirements of energy balance. This ensures that the rate of energy loss from the modeled coronal loops is consistent with the volumetric heating rate predicted by the Alfven wave turbulence model. The results of this modeling are compared with the observed fine structures of the coronal loops. We find that the Alfven wave turbulence model can reproduce the observed characteristics of the hotter loops in the active region core, but the cooler loops at the periphery of the region have large expansion factors and are predicted to be thermally unstable.