Transverse Oscillations of Longitudinally Stratified Coronal Loops System

The collective transverse coronal loop oscillations seem to be detected in the observational studies. In this regard, Luna et al. (2009, ApJ, 692, 1582) modeled the collective kinklike normal modes of several cylindrical loops system using the T-matrix theory. This paper investigates the effects of longitudinal density stratification along the loop axis, on the collective kinklike modes of system of coronal loops. The coronal loops system is modeled as cylinders of parallel flux tubes, with two ends of each loop at the dense photosphere. The flux tubes are considered as uniform magnetic fields, with stratified density along the loop axis which changes discontinuously at the lateral surface of each cylinder. The MHD equations are reduced to solve a set of two coupled dispersion relations for frequencies and wave numbers, in the presence of stratification parameter. The fundamental and first overtone frequencies and longitudinal wave numbers are computed. The previous results are verified for unstratified coronal loops system. Finally we would conclude that increased longitudinal density stratification parameter will result in increase of the frequencies. The frequencies ratios, first overtones to fundamentals, are very sensitive functions of density scale height parameter. Therefore, stratification should be included in dynamics of coronal loops systems. For the unstratified coronal loops system, these ratios are the same as monoloop ones.