Aims. We determine the dependence of the observed properties of fast magnetoacoustic axisymmetric oscillations (the sausage mode) of a thick and dense flaring coronal loop, modelled by a magnetic cylinder, on the parameters of the equilibrium plasma configuration. The plasma inside and outside the cylinder is of low-beta, and penetrated by a straight magnetic field. The plasma density has a smooth profile across the magnetic field.
Methods. We use three-dimensional ideal magnetohydrodynamic equations to model numerically the development of the perturbations of the cylindrical equilibrium, considering both leaky and trapped regimes.
Results. Short-period sausage oscillations, trapped by the cylinder, are qualitatively consistent with the analytical results obtained in the models of a plasma slab or a cylinder with a step-function transverse profile. The period of trapped sausage oscillations is determined by the ratio of the phase speed, with the value between the internal and external Alfvén speeds, to the wavelength. Longer-period sausage oscillations are leaky, and their decay times are longer for higher density contrasts between the internal and external media. Leaky sausage oscillations have longer periods than trapped sausage oscillations of the same cylinder. In the coronal conditions, sausage oscillations are essentially compressible and transverse, hence produce modulation of the thermal optically thin emission intensity and periodic Doppler broadening of emission lines. However, if the oscillating plasma non-uniformity is poorly spatially resolved, the variation in the emission intensity is weak and proportional to the actual amplitude of the oscillation squared. The latter variation property is connected with the transverse nature of the oscillation, causing the conservation of mass in the transverse cross-section of the oscillating plasma structure.