The hydrodynamic stability of gaseous cosmic filaments
  Virial shocks at edges of cosmic-web structures are a clear prediction of standard structure formation theories. We derive a criterion for the stability of the post-shock gas and of the virial shock itself in spherical, filamentary and planar infall geometries. When gas cooling is important, we find that shocks become unstable, and gas flows uninterrupted towards the center of the respective halo, filament or sheet. For filaments, we impose this criterion on self-similar infall solutions. We find that instability is expected for filament masses between $10^{11}-10^{13}M_\odot Mpc^{-1}.$ Using a simplified toy model, we then show that these filaments will likely feed halos with $10^{10}M_{\odot}\lesssim M_{halo}\lesssim 10^{13}M_{\odot}$ at redshift $z=3$, as well as $10^{12}M_{\odot}\lesssim M_{halo}\lesssim 10^{15}M_{\odot}$ at $z=0$.   The instability will affect the survivability of the filaments as they penetrate gaseous halos in a non-trivial way. Additionally, smaller halos accreting onto non-stable filaments will not be subject to ram-pressure inside the filaments. The instreaming gas will continue towards the center, and stop either once its angular momentum balances the gravitational attraction, or when its density becomes so high that it becomes self-shielded to radiation. 
Yuval Birnboim, Dan Padnos and Elad Zinger
astro-ph.GA astro-ph.CO