High Resolution X-Ray Spectroscopic Constraints on Cooling-Flow Models

clusters and groups of galaxies. We demonstrate the failure of the standard cooling-ow model to describe the soft X-ray spectrum of clusters of galaxies. We also em-phasize several new developments in the study of the soft X-ray spectrum of cooling ows. Although there is some uncertainty in the expected mass deposition rate for any individual cluster, we show that high resolution RGS spectra robustly demon-strate that the expected line emission from the isobaric cooling- ow model is absent below 1/3 of the background temperature rather than below a xed temperature in all clusters. Furthermore, we demonstrate that the best-resolved cluster spectra are inconsistent with the predicted shape of the dierential luminosity distribution and the measured distribution is tilted to higher temperatures. These observations create several ne-tuning challenges for current theoretical explanations for the soft X-ray cooling- ow problem. Comparisons between these observations and other X-ray mea-surements are discussed. 1. The Cooling-Flow Model A long-standing theoretical prediction is that the intra-cluster medium in the cores of galaxy clusters should cool by emitting X-rays in less than a Hubble time (Fabian &amp