Why Are Solar Filaments Filamentary?

Zirker, Engvold & Martin (1998) argued that the existence of solar prominences (filaments) should be conditioned by ubiquitous counter-streaming flows. Motivated by this, we address the thermal condensation instability in magnetized plasmas with shear flows in relation to filamentary structure formation in solar prominences. We establish a magnetohydrodynamic (MHD) model with radiative cooling, plasma heating and anisotropic thermal conduction and put it in the form of an eigenvalue problem, which is numerically solved to yield eigenfrequencies and eigenfunctions.

For a shear velocity less than the Alfven velocity of the background plasma, the eigenvalue with the maximum growth rate is found to correspond to a thermal condensation mode, for which the density and temperature variations are anti-phased (of opposite signs). Only when the shear velocity in the k-direction is near zero, the eigenfunctions for the condensation mode are of smooth sinusoidal forms. Otherwise each eigenfunction for density and temperature is singular and of a discrete form like delta functions.

Our results indicate that any non-uniform velocity field with a magnitude larger than a millionth of the Alfven velocity can generate discrete eigenfunctions of the condensation mode. We therefore suggest that filamentary condensation (condensation at discrete layers or threads) should be quite a natural and universal process whenever a thermal condensation instability arises in magnetized plasmas.