Observations of Non-thermal Velocity and Comparison with Alfvén Wave Turbulence Model in Solar Active Regions

We present a study of spectral line width measurements from the Extreme Ultraviolet Imaging Spectrometer (EIS) on {\it Hinode}. We used spectral line profiles of Fe {\sc xvi} 262.984 Å, Fe {\sc xiv} 264.787 Å, Fe {\sc xiv} 270.519 Å, Fe {\sc xiv} 274.203 Å, and Fe {\sc xv} 284.160 Å, and studied 11 active regions. Previous studies of spectral line widths have shown that in hot loops in the cores of active regions, the observed non-thermal velocities are smaller than predicted from models of reconnection jets in the corona or shock heating associated with Alfvén waves. The observed line widths are also inconsistent with models of chromospheric evaporation due to coronal nanoflares. We show that recent advances in higher resolution Alfvén wave turbulence modeling enables us to obtain non-thermal velocities similar to those measured in active regions. The observed non-thermal velocities for the 11 active regions in our study are in the range of 17$-$30 $\rm km ~ s^{-1}$, consistent with the spectral line non-thermal widths predicted from our model of 16 interacting flux tubes, which are in the range of ~15$-$37 $\rm km ~ s^{-1}$.