Non-equilibrium Ionization Effects on Extreme-Ultraviolet Emissions Modulated by Standing Sausage Modes in Coronal Loops

Forward-modeling the emission properties in various passbands is important for confidently identifying magnetohydrodynamic waves in the structured solar corona. We examine how Non-equilibrium Ionization (NEI) affects the Extreme Ultraviolet (EUV) emissions modulated by standing fast sausage modes (FSMs) in coronal loops, taking the Fe IX 171 \AA\ and Fe XII 193 \AA\ emission lines as examples. Starting with the expressions for linear FSMs in straight cylinders, we synthesize the specific intensities and spectral profiles for the two spectral lines by incorporating the self-consistently derived ionic fractions in the relevant contribution functions. We find that relative to the case where Equilibrium Ionization (EI) is assumed, NEI considerably impacts the intensity modulations, but shows essentially no effect on the Doppler velocities or widths. Furthermore, NEI may affect the phase difference between intensity variations and those in Doppler widths for Fe XII 193 \AA\ when the line-of-sight is oblique to the loop axis. While this difference is $180^\circ$ when EI is assumed, it is $\sim 90^\circ$ when NEI is incorporated for the parameters we choose. We conclude that in addition to viewing angles and instrumental resolutions, NEI further complicates the detection of FSMs in spectroscopic measurements of coronal loops in the EUV passband.