A Clue to the Filamentary Nature of Solar Filaments

It is generally accepted that solar prominences, also known as filaments, are formed through thermal condensation instability from hot coronal plasmas. Within solar prominences (filaments), counter-streaming subscale flows are frequently observed. It is quite surprising that thermal instability in magnetized plasmas with such shear flows has never been earnestly studied despite extensive research on thermal instability in various astrophysical contexts. In this paper, we have investigated this unexplored territory of thermal instability and have unexpectedly gained hints on why solar filaments are filamentary.

We have performed linear stability analysis of magnetized plasmas with shear flows within the framework of magnetohydrodynamics (MHD), incorporating radiative cooling, phenomenological plasma heating, and anisotropic thermal conduction. Our approach formulates an eigenvalue problem, which we solve numerically to derive eigenfrequencies and eigenfunctions.

Our findings reveal that, for shear speeds less than the Alfven speed of the background plasma, the dominant mode corresponds to an isobaric thermal condensation mode. Most remarkably, the eigenfunctions associated with this mode display a distinctive, discrete structure resembling delta functions, especially when the shear velocity in the k-direction exceeds 10⁻⁵ of the Alfven speed. We identify that these delta function-like spikes coincide with the zeroes of the coefficients of the second-order derivative terms in the differential equation of the eigenvalue problem.

In contrast, for shear speeds exceeding the Alfven speed (a rare occurrence in reality), we observe an isentropic Kelvin-Helmholtz instability, incompatible with thermal condensation.

Our investigation underscores that any non-uniform velocity field with a magnitude surpassing 10⁻⁵ of the Alfven speed triggers the discrete eigenfunction characteristic of the condensation mode. Consequently, filamentary condensation at discrete layers or threads, emerges as a natural and universal process whenever thermal condensation instability arises in magnetized plasmas with shear flows.