Scaling Relation to Understand Non-Detection of Cold Gas at the Cluster Center

Recent XMM-Newton observations of clusters of galaxies have indicated the soft X-ray spectra to be inconsistent with the simple isobaric cooling flow model. There is almost no feature of the cold gas expected from the model. This shows that we have not yet understood the physics of the hot gas in clusters of galaxies well. A quantitative evaluation of the behavior of gas cooling is important not only for understanding the clusters, themselves, but also for studying cosmology and galaxy formation. To clarify the problem of this reported discrepancy, we have studied scaling relations for clusters of galaxies based on the self-similarity assumption. We also propose an observational strategy to solve this problem