Observations of Non-thermal Velocity and Comparison with Alfv\'en 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 {\AA}, Fe {\sc xiv} 264.787 {\AA}, Fe {\sc xiv} 270.519 {\AA}, Fe {\sc xiv} 274.203 {\AA}, and Fe {\sc xv} 284.160 {\AA}, 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 Alfv\'{e}n 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 Alfv\'{e}n 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 $\rm km ~ s^{-1}$.