2002MNRAS.335L..71F

On the basis of the universal gas fraction in clusters of galaxies, we estimate that the effective thermal conductivity required to balance radiative cooling in the cores, where the gas temperature is 3-10 keV, is about one tenth of the Spitzer rate. This confirms that thermal conduction can be important for the energy balance provided that it is not highly suppressed by magnetic fields in the gas. We determine the global effective conductivity in a sample of 29 clusters using published X-ray data on the inferred cooling rates and show that most lie between one and one tenth of the Spitzer rate. More work on the profiles in cooling flow clusters is required to test the conduction hypothesis further. We examine the possibility that conduction operates during galaxy formation, and show that it provides a simple explanation for the upper-mass cut-off in galaxy masses.