The Gravitational Instability of Adiabatic Filaments

Filamentary structures, or long and narrow streams of material, arise in many areas of astronomy. Here we investigate the stability of such filaments by performing an eigenmode analysis of adiabatic and polytropic fluid cylinders, which are the cylindrical analog of spherical polytropes. We show that these cylinders are gravitationally unstable to perturbations along the axis of the cylinder below a critical wavenumber k(crit) few, where k(crit) is measured relative to the radius of the cylinder. Below this critical wavenumber, perturbations grow as <CDATA <i , where tau is time relative to the sound-crossing time across the diameter of the cylinder, and we derive the growth rate sigma(u) as a function of wavenumber. We find that there is a maximum growth rate sigma(max) similar to 1 that occurs at a specific wavenumber k(max) similar to 1, and we derive the growth rate sigma(max) and the wavenumbers k(max) and k(crit) for a range of adiabatic indices. To the extent that filamentary structures can be approximated as adiabatic and fluidlike, our results imply that these filaments are unstable without the need to appeal to magnetic fields or external media. Further, the objects that condense out of the instability of such filaments are separated by a preferred length scale, form over a preferred timescale, and possess a preferred mass scale.