Effect of gravitational stratification, longitudinal temperature inhomogeneity, radiative cooling and background plasma flow on torsional Alfvén oscillations of a coronal loop

Torsional Alfvén waves (TAWs) play a significant role in the dynamics of the solar atmosphere. A detailed study of the TAWs can provide valuable insights into various aspects of the internal structure of the solar atmosphere, and the coronal heating problem. In this paper, the effect of longitudinal structuring (such as gravitational stratification, temperature inhomogeneity, radiative cooling, and background plasma flow) on the characteristics of the standing TAWs in coronal plasma loops, which can be exploited in both temporal and spatial coronal seismology applications, is investigated. The governing equation for TAWs in a dynamic and stratified coronal plasma is reduced to a time-dependent partial differential equation. Analytical dispersion relations of the differential equation are extracted and solved numerically under various scenarios by imposing the necessary and sufficient boundary conditions. The numerical results indicate that the fundamental and first overtone mode frequencies and their ratios and the spatial anti-node shift of the first overtone mode are sensitive functions of gravitational stratification and scaled time of radiative cooling. The magnitude values of these quantities are strongly influenced by the magnitude of the temperature inhomogeneity parameter and are slightly affected by the scaled background plasma flow speed. Tuning the parameters that affect the oscillatory properties of the standing TAWs and matching them with observations can enhance our understanding of the coronal structures and their evolution and serve as a diagnostic tool in coronal seismology.