Oscillatory motions in intense flux tubes

The detailed nature of oscillatory motions in intense flux tubes is examined. We consider states of constant β (the ratio of gas to magnetic pressure) and analyse the character of motions that can occur in such tubes. We include heat exchange between the tube and the ambient medium using Newton's law of cooling. Adopting a linear analysis, we present results for both polytropic and real atmospheres. In the latter case, we use a height dependent radiation exchange time constant. For purposes of comparison with earlier studies, results for the adiabatic case are also given. Growth rates, oscillation frequencies and eigenvectors of the fundamental modes are calculated for different values of the initial magnetic field strength, parametrized by β, and initial tube radius. The latter quantity influences heat exchange, particularly in the optically thick layers. It is found that for the solar stratification, oscillatory behaviour occurs for $$\beta\lt\beta_\text c$$, where β_c denotes some critical value, which depends upon the radius of the tube. Moreover, in the solar case the oscillations are overstable with periods and growth rates typically in the ranges 650–1500 s and 625–1150 s respectively. An interesting feature of the solutions is the existence of a bifurcation at $$\beta=\beta_\text c$$ from overstability into two purely unstable modes. Results depicting the height dependence of the eigenvectors (in general complex) and their phases are presented as well. We also examine the sensitivity of the results on boundary conditions. Lastly, some of the observational consequences of the study are pointed out.