Thermal equilibrium of molecular clouds in cooling flow clusters

In many clusters of galaxies there is evidence for cooling flows in the central regions. The ultimate fate of the gas which cools is still unknown. A possibility is that a fraction of the gas forms cold molecular clouds. We investigate the minimum temperature which can be reached by clouds in cooling flows by computing the cooling function due to H2, HD and CO molecules. As an example, we determine the minimum temperature achievable by clouds in the cooling flows of the Centaurus, Hydra and PKS 0745-191 clusters. Our results suggest that clouds can reach very low temperatures - less than 10 K - which would explain the non-detection of CO in these clusters.