Cross-sectional area and intensity variations of sausage modes

Context. The observations obtained using the Rapid Oscillations in the Solar Atmosphere instrument ( ROSA) show variations in both cross-sectional area and intensity for magnetic pores in the photosphere. Aims. We study the phase behaviour between cross-sectional area and intensity variations for sausage modes in a photospheric context. We aim to determine the wave mode by looking at the phase difference between the cross-sectional area and intensity variations. Methods. We used a straight cylinder as a model for the flux tube. The plasma is uniform both inside and outside the flux tube with a possible jump in the equilibrium values at the boundary, the magnetic field is directed along the flux tube. We derived analytic expressions for the cross-sectional area variation and the total intensity variation. Using these analytic expressions, we calculated the phase differences between the cross-sectional area and the intensity variations. These phase differences were then used to identify the wave mode. Results. We found that for slow sausage modes the cross-sectional area and intensity variations are always in phase, while for fast sausage modes the variations are in antiphase.