  New X-ray observations with XMM-Newton show a lack of spectral evidence for
large amounts of cooling and condensing gas in the centers of galaxy clusters
believed to harbour strong cooling flows. The paper reexplores the cooling flow
scenario in the light of the new observations. We explore the diagnostics of
the temperature structure of cooling cores with XMM-spectroscopy, tests for
intracluster X-ray absorption towards central AGN, the effect of metal
abundance inhomogeneities, and the implications of high resolution images in
the centers of clusters. We find no evidence of intrinsic absorption in the
center of the cooling flows of M87 and the Perseus cluster. We further consider
the effect of cluster rotation in cooling flow regions in the frame of cosmic
structure evolution models. Also the heating of the core regions of clusters by
jets from a central AGN is reconsidered. We find that the power of the AGN jets
as estimated by their interaction effects with the intracluster medium in
several examples is more then sufficient to heat the cooling flows and to
reduce the mass deposition rates. We explore in more detail which requirements
such a heating model has to fulfill to be consistent with all observations,
point out the way such a model could be constructed, and argue that such model
building seems to be successful. In summary it is argued that most
observational evidence points towards much lower mass deposition rates than
previously inferred in the central region of clusters thought to contain strong
cooling flows.
