Cold filaments in galaxy clusters: effects of heat conduction
  We determine the critical size l_crit of a filament of cold (T~10^4 K) gas that is in radiative equilibrium with X-ray emitting gas at temperatures T_out~10^6 - 10^8 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_crit increases as T_out^(11/4), while at fixed T_out it scales as 1/P. 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_crit is similar to the lengths of observed filaments. In a cluster such as Perseus, the value of l_crit increases 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. 
Carlo Nipoti and James Binney (Oxford University)