2004MNRAS.349.1509N

We determine the critical size l_critof a filament of cold (T ∼ 10⁴ K) gas that is in radiative equilibrium with X-ray emitting gas at temperatures T_out∼ 10⁶ -10⁸ K. Filaments smaller than l_crit will be rapidly evaporated, while longer ones will induce the condensation of the ambient medium. At fixed pressure P, l_critincreases as T ^11/4 _out, while at fixed T_out, it scales as P ^–1. It scales as f ^1/2 , where f is the factor by which the magnetic field depresses the thermal conductivity below Spitzer's benchmark value. For plausible values of f, l_critis similar to the lengths of observed filaments. In a cluster such as Perseus, the value of l_critincreases by over an order of magnitude between the centre and a radius of 100 kpc. If the spectrum of seed filament lengths l is strongly falling with l, as is natural, then these results explain why filaments are only seen within a few kiloparsecs of the centres of clusters, and are not seen in clusters that have no cooling flow. We calculate the differential emission measure as a function of temperature for the interface between filaments and ambient gas of various temperatures. We discuss the implications of our results for the origin of the galaxy luminosity function.