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We briefly review our current knowledge of the space density of distant X-ray clusters as measured by several ROSAT serendipitous surveys. We compare old and new determinations of the cluster X-ray Luminosity Function (XLF) at increasing redshifts, addressing the controversial issue of the evolution of its high end. We use complete subsamples, drawn from the ROSAT Deep Cluster Survey (RDCS), to quantify the statistical significance of the XLF evolution out to z ~1. A consistent observational picture emerges in which the bulk of the cluster population shows no significant evolution out to z ~1, whereas the most luminous systems (L_x >~ L* [0.5-2 keV] =~ 5x10^44 erg/s) were indeed rarer, at least at z >0.5, in keeping with the original findings of the EMSS. We also report on the recent spectroscopic identification of four clusters in the RDCS lying beyond z =1, the most distant X-ray clusters known to date, which set an interesting lower limit on the space density of clusters at z >1.
We show that the most distant X-ray detected cluster known to date, ClJ1001 at z=2.506, hosts a strong overdensity of radio sources. Six of them are individually detected (within 10) in deep 0.75 resolution VLA 3GHz imaging, with S(3GHz)>8uJy. Of the
Investigating X-ray luminous galaxy clusters at z>~1 provides a fundamental constraint on evolutionary studies of the largest virialized structures in the Universe, the baryonic matter in form of the hot ICM, their galaxy populations, and the effects
We present the first three galaxy clusters of a larger sample of the most X-ray luminous galaxy clusters selected from the ROSAT Bright Survey. This project, which is a systematic search for strong lensing, aims at arc statistics, mass determinations
Considerable progress has been made over the last decade in the study of the evolutionary trends of the population of galaxy clusters in the Universe. In this review we focus on observations in the X-ray band. X-ray surveys with the ROSAT satellite,
We analyse cosmological hydrodynamical simulations of galaxy clusters to study the X-ray scaling relations between total masses and observable quantities such as X-ray luminosity, gas mass, X-ray temperature, and $Y_{X}$. Three sets of simulations ar