Are Filaments Cylindrical or Sheet-Like?

Abstract

Rapid cooling and collapse in a thermally unstable medium can lead to filamentary structures that are comparable to those observed in old supernova remnants. Here, simple formulae are derived for the shape of a filament forming in this manner. The cross-sectional shape of a filament will flatten and the ratio of major to minor axes (aspect ratio) increases in proportion to the density as it becomes sheet-like. Thus the aspect ratio of observed filaments is expected to be of the same order as the temperature change during the collapse, T₁/T₀. In very old remnants the filaments may appear to be tubes or sheets depending on perspective with aspect ratios less than 10. This model predicts a correlation between optical morphology and the temperature of the shock-heated gas. For T₁ between 10⁵K and 10⁶K, the thin sheet that forms is likely to split up through asymmetric warping disturbances, leading to several parallel striations, consistent with observations in the Cygnus Loop. Above 10⁶K, the instability may cause the sheet to degenerate before it has cooled to 10⁴K. Hence, an absence of well-defined filaments is expected near X-ray emitting regions.