Synthetic Fe XIII 1074.7 nm Observations of Torsional Alfv\'{e}n Waves in Coronal Waveguides
Torsional Alfv\'{e}n waves are a promising mechanism for transporting energy through the solar atmosphere, with implications for coronal heating and solar wind acceleration. Recently, signatures of torsional Alfv\'{e}n waves have been observed with the Daniel K. Inouye Solar Telescope. We aim to investigate the effects of line of sight integration and plasma conditions on the observable properties of the torsional mode. Here we present three-dimensional magnetohydrodynamic simulations of multiple coronal waveguides, driven by a combination of transverse kink and torsional wave drivers, considering two plasma regimes representative of active region (AR) and quiet Sun (QS) conditions. Synthetic observables of the Fe~\textsc{xiii}~1074.7~nm coronal emission line are produced using the pyCELP forward-modelling framework to enable direct comparison with spectroscopic observations. In the QS regime, red-blue Doppler asymmetries are associated with the driven torsional waves, though their observed amplitudes are substantially reduced by line-of-sight integration. In contrast, the AR regime exhibits red-blue Doppler asymmetries even in the absence of an imposed torsional driver, which may be misidentified as the $m=0$ torsional Alfv\'{e}n mode. In the AR setup, the red-blue Doppler asymmetries arise from strong phase mixing, generating shear flows and localised vorticity between waveguides where emission is strongest. The differences between the two regimes are governed by the location of peak emission, which is determined by the degree of density inhomogeneity. Our results support the identification of torsional Alfv\'{e}n wave signatures in the quiet Sun (a weakly inhomogeneous environment), but caution should be exercised when interpreting spectroscopic observations in strongly inhomogeneous environments such as active regions.