Sensitive, wide-area X-ray surveys which would be possible with the WFXT will detect huge samples of virialized objects spanning the mass range from sub-groups to the most massive clusters, and extending in redshift to beyond z=2. These samples will
be an excellent dataset for carrying out many traditional cosmological tests using the cluster mass function and power spectrum. Uniquely, WFXT will be able not only to detect clusters but also to make detailed X-ray measurements for a large number of clusters and groups right from the survey data. Very high quality measurements of the cluster mass function and spatial correlation over a very wide range of masses, spatial scales, and redshifts, will be useful for expanding the cosmological discovery space, and in particular, in searching for departures from the concordant Lambda-CDM cosmological model. Finding such departures would have far-reaching implications on our understanding of the fundamental physics which governs the Universe.
We discuss the central role played by X-ray studies to reconstruct the past history of formation and evolution of supermassive Black Holes (BHs), and the role they played in shaping the properties of their host galaxies. We shortly review the progres
s in this field contributed by the current X-ray and multiwavelength surveys. Then, we focus on the outstanding scientific questions that have been opened by observations carried out in the last years and that represent the legacy of Chandra and XMM, as for X-ray observations, and the legacy of the SDSS, as for wide area surveys: 1) When and how did the first supermassive black holes form? 2) How does cosmic environment regulate nuclear activity (and star formation) across cosmic time? 3) What is the history of nuclear activity in a galaxy lifetime? We show that the most efficient observational strategy to address these questions is to carry out a large-area X-ray survey, reaching a sensitivity comparable to that of deep Chandra and XMM pointings, but extending over several thousands of square degrees. Such a survey can only be carried out with a Wide-Field X-ray Telescope (WFXT) with a high survey speed, due to the combination of large field of view and large effective area, i.e., grasp, and sharp PSF. We emphasize the important synergies that WFXT will have with a number of future groundbased and space telescopes, covering from the radio to the X-ray bands and discuss the immense legacy value that such a mission will have for extragalactic astronomy at large.
While the exceptional sensitivity of Chandra and XMM-Newton has resulted in revolutionary studies of the Galactic neighborhood in the soft (<10 keV) X-ray band, there are many open questions. We discuss these issues and how they would be addressed by very wide-area (> 100 sq. deg.) X-ray surveys.
We present soft (0.5-2 keV) X-ray luminosity functions (XLFs) in the Great Observatories Origins Deep Survey (GOODS) fields, derived for galaxies at z~0.25 and 0.75. SED fitting was used to estimate photometric redshifts and separate galaxy types, re
sulting in a sample of 40 early-type galaxies and 46 late-type galaxies. We estimate k-corrections for both the X-ray/optical and X-ray/NIR flux ratios, which facilitates the separation of AGN from the normal/starburst galaxies. We fit the XLFs with a power-law model using both traditional and Markov-Chain Monte Carlo (MCMC) procedures. The XLFs differ between z<0.5 and z>0.5, at >99% significance levels for early-type, late-type and all (early and late-type) galaxies.We also fit Schechter and log-normal models to the XLFs, fitting the low and high redshift XLFs for a given sample simultaneously assuming only pure luminosity evolution. In the case of log-normal fits, the results of MCMC fitting of the local FIR luminosity function were used as priors for the faint and bright-end slopes (similar to ``fixing these parameters at the FIR values except here the FIR uncertainty is included). The best-fit values of the change in log L* with redshift were dlogL* = 0.23 +/- 0.16 dex (for early-type galaxies) and 0.34 +/- 0.12 dex (for late-type galaxies), corresponding to (1+z)^1.6 and (1+z)^2.3. These results were insensitive to whether the Schechter or log-normal function was adopted.
