Forward Modelling of Standing Slow Modes in Flaring Coronal Loops

Standing slow mode waves in hot flaring loops are exclusively observed in spectrometers and are used to diagnose the magnetic field strength and temperature of the loop structure. Due to the lack of spatial information, the longitudinal mode cannot be effectively identified. In this study, we simulate standing slow mode waves in flaring loops and compare the synthesized line emission properties with SUMER spectrographic and SDO/AIA imaging observations. We find that the emission intensity and line width oscillations are a quarter period out of phase with Doppler shift velocity both in time and spatial domain, which can be used to identify a standing slow mode wave from spectroscopic observations. However, the longitudinal overtones could be only measured with the assistance of imagers. We find emission intensity asymmetry in the positive and negative modulations, this is because the contribution function pertaining to the atomic emission process responds differently to positive and negative temperature variations. One may detect \textbf{half} periodicity close to the loop apex, where emission intensity modulation is relatively small. The line-of-sight projection affects the observation of Doppler shift significantly. A more accurate estimate of the amplitude of velocity perturbation is obtained by de-projecting the Doppler shift by a factor of $1-2\theta/\pi$ rather than the traditionally used $\cos\theta$. \textbf{If a loop is heated to the hotter wing, the intensity modulation could be overwhelmed by background emission, while the Doppler shift velocity could still be detected to a certain extent.