Abstract
Context. Flows are omnipresent and govern the dynamics of plasma. Solar tornadoes are a class of apparently rotating prominences that might be formed by thermal instability. In spectroscopic studies on thermal instability, background flow is commonly neglected.
Aims. We here determine the effect of background flow on thermal instability in cylindrical magnetic field configurations. How various parameters affect the distribution of eigenmodes in the magnetohydrodynamic (MHD) spectrum is also explored. We investigate whether discrete thermal modes exist.
Methods. In an analytical study, we extended upon the literature by including a generic background flow in a cylindrical coordinate system. The non-adiabatic MHD equations are linearised, Fourier-analysed, and examined to understand how a background flow changes the continua. An approximate expression for discrete thermal modes is derived using a Wentzel-Kramers-Brillouin (WKB) analysis. The analytical results are then verified for a benchmark equilibrium using the eigenvalue code Legolas. The eigenfunctions of discrete thermal modes are visualised in 2D and 3D.
Results. The thermal continuum is Doppler-shifted due to the background flow, just like the slow and Alfvén continua. Discrete modes are altered because the governing equations contain flow-related terms. An approximate expression to predict the appearance of discrete thermal modes based on the equilibrium parameters is derived. All analytical expressions match the numerical results. The distribution of the density perturbations of the discrete thermal modes is not a uniform or singular condensation, due to the shape of the eigenfunctions and the dependence of the assumed waveform on the coordinates and wavenumbers. A 3D visualisation of the total velocity field shows that the helical field is heavily influenced by the radial velocity perturbation.
Conclusions. We derived analytic expressions for non-adiabatic MHD modes of a cylindrical equilibrium with background flow and verified them using a coronal equilibrium. However, the equations are valid for and can be applied in other astrophysical environments.