Line-of-sight geometrical and instrumental resolution effects on intensity perturbations by sausage modes

Context. Diagnostics of magnetohydrodynamic (MHD) waves in the solar atmosphere is a topic that often encounters interpretation problems, partly because of the high complexity of the solar atmospheric medium. Forward modelling can significantly guide interpretation, bridging the gap between numerical simulations and observations, and increasing the reliability of mode identification for applying MHD seismology. Aims. We determine the characteristics of the fast MHD sausage mode in the corona on the modulation of observable quantities, such as line intensity and spectral line broadening. Effects of the line-of-sight angle and of spatial, temporal, and spectral resolutions are considered. Methods. We take a cylindrical tube that simulates a loop in a low-β coronal environment with an optically thin background and let it oscillate with the fast sausage mode. A parametric study is performed. Results. Longitudinal structuring of the intensity modulation is obtained and set by the nodal structure of the radial velocity. The modulation is strongly dependent on the contribution function of the spectral line. Under the assumption of equilibrium ionisation, the intensity variation can be very low (≲4% for Fe ix 171) or significant (35% for Fe xii 193). Most of this variation disappears when considering the radiative relaxation times of the ions, due to the fast timescales of the sausage mode in the corona. Regardless of the ionisation state of the plasma, the variation in spectral line broadening can be significant, even for low intensity modulation. The nature of this broadening is not thermal but is mostly turbulent. This places spectrometers in clear advantage over imaging instruments for the detection of the sausage mode. The modulation of all quantities can considerably decrease with the line-of-sight angle with respect to the perpendicular to the tube axis. The spatial and temporal resolution are the main factors affecting modulation, erasing longitudinal structuring when these are on the order of the mode's wavelength or the mode's period, placing high constraints on instrumentation. Significant variability in all quantities can still be obtained when viewing at an angle of up to 30, with pixel size resolutions up to one-third of the mode's wavelength, or temporal resolution of one fifth of the mode's period. Modulation is only weakly dependent on spectral resolution due to the mode's inherent symmetry.