Comparing the temperatures of galaxy clusters from hydrodynamical N-body simulations to Chandra and XMM-Newton observations

Theoretical studies of the physical processes guiding the formation and evolution of galaxies and galaxy clusters in the X-ray region are mainly based on the results of numerical hydrodynamical N-body simulations, which in turn are often directly compared with X-ray observations. Although trivial in principle, these comparisons are not always simple. We demonstrate that the projected spectroscopic temperature of thermally complex clusters obtained from X-ray observations is always lower than the emission-weighed temperature, which is widely used in the analysis of numerical simulations. We show that this temperature bias is mainly related to the fact that the emission-weighted temperature does not reflect the actual spectral properties of the observed source. This has important implications for the study of thermal structures in clusters, especially when strong temperature gradients, such as shock fronts, are present. Because of this bias, in real observations shock fronts appear much weaker than what is predicted by emission-weighted temperature maps, and may not even be detected. This may explain why, although numerical simulations predict that shock fronts are a quite common feature in clusters of galaxies, to date there are very few observations of objects in which they are clearly seen. To fix this problem we propose a new formula, the spectroscopic-like temperature function, and show that, for temperatures higher than 3 keV, it approximates the spectroscopic temperature to better than a few per cent, making simulations more directly comparable to observations.