Why Are Cool Structures in the Universe Usually Filamentary?

Small-scale shear flows are ubiquitous in the universe, and astrophysical plasmas are often magnetized. We study the thermal condensation instability in magnetized plasmas with shear flows in relation to filamentary structure formation in cool structures in the universe, representatively solar prominences and supernova remnants. A linear stability analysis is extensively performed in the framework of magnetohydrodynamics (MHD) with radiative cooling, plasma heating and anisotropic thermal conduction to find the eigenfrequencies and eigenfunctions for the unstable modes. 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 condensation at discrete layers or threads should be quite a natural and universal process whenever a thermal instability arises in magnetized plasmas.