Conduction and cooling flows

Chandra and XMM-Newton observations have confirmed the presence of large temperature gradients within the cores of many relaxed clusters of galaxies. Here we investigate whether thermal conduction operating over those gradients can supply sufficient heat to offset radiative cooling. Narayan & Medredev and Gruzinov have noted, using published results on cluster temperatures, that conduction within a factor of a few of the Spitzer rate is sufficient to balance bremsstrahlung cooling. From a detailed study of the temperature and emission measure profiles of Abell 2199 and Abell 1835, we find that the heat flux required by conduction is consistent with or below the rate predicted by Spitzer in the outer regions of the core. Conduction may therefore explain the lack of observational evidence for large mass cooling rates inferred from arguments based simply on radiative cooling, provided that conductivity is suppressed by no more than a factor of 3 below the full Spitzer rate. To stem cooling in the central 20 kpc however, would necessitate conductivity values of at least a factor of 2 larger than the Spitzer values, which we consider implausible. This may provide an explanation for the observed star formation and optical nebulosities in cluster cores. The solution is likely to be time-dependent. We briefly discuss the possible origin of the cooler gas and the implications for massive