Fast-sausage oscillations in coronal loops with smooth boundary

Abstract

Aims. The effect of the transition layer (shell) in nonuniform coronal loops with a continuous radial density profile on the properties of fast-sausage modes are studied analytically and numerically. Methods. We modeled the coronal waveguide as a structured tube consisting of a cord and a transition region (shell) embedded within a magnetic uniform environment. The derived general dispersion relation was investigated analytically and numerically in the context of frequency, cut-off wave number, and the damping rate of fast-sausage oscillations for various values of loop parameters. Results. The frequency of the global fast-sausage mode in the loops with a diffuse (or smooth) boundary is determined mainly by the external Alfvén speed and longitudinal wave number. The damping rate of such a mode can be relatively low. The model of coronal loop with diffuse boundary can support a comparatively low-frequency, global fast-sausage mode of detectable quality without involving extremely low values of the density contrast. The effect of thin transition layer (corresponds to the loops with steep boundary) is negligible and produces small reductions of oscillation frequency and relative damping rate in comparison with the case of step-function density profile. Seismological application of obtained results gives the estimated Alfvén speed outside the flaring loop about 3.25 Mm/s.