The effect of density stratification on the amplitude profile of transversal coronal loop oscillations

Context. Measuring how the density of the plasma in the Sun's corona varies along fine structures such as coronal loops using emission measure is very difficult as the exact value of the line of sight filling factor and the correct amount of background subtraction are unknown. Aims. To investigate if magnetohydrodynamic (MHD) wave theory can be used to complement existing observational methods to obtain diagnostic information about the density structure of coronal loops by measuring the amplitude profile of the fundamental standing mode of the fast kink wave. Methods. Analytical and numerical approaches are used to show how the amplitude profile of the fundamental fast kink mode changes by varying the amount of density stratification in a coronal loop. Results. Increasing the amount of density stratification in a coronal loop will increase the difference in amplitude profile from one of constant longitudinal density. For a semi-circular TRACE 171 angstrom temperature loop of length 200 Mm and density scale height, H = 50 Mm, the maximum change in amplitude profile is of the order of 50 km. It is also found that the amplitudes of these oscillations are effectively negligible at altitudes lower than the transition region. Conclusions. The effect of density stratification on the amplitude profile of the fundamental standing kink mode of a TRACE 171 angstrom temperature loop may be very subtle. Unfortunately, the observational signatures of this effect are likely to be well below the resolution of the best currently available extreme-ultraviolet (EUV) imagers. Only loops with homogeneous magnetic fields have been addressed here, but inhomogeneous magnetic fields may well dominate over the effect of density stratification on the amplitude profile.