| Abstract
| - We relate the star formation from cold baryons condensing in virialized structures to the X-ray properties of the associated diffuse, hot baryonic component. Our computations use the standard ‘semi-analytic’ models to include and connect three sectors of the complex astrophysics involved: first, the formation of dark matter haloes through accretion and merging, after the standard hierarchical clustering; secondly, the star formation governed, after the current ‘recipes’, by radiative cooling and by feedback of the supernova energy into the hot baryonic component; thirdly, and novel, the hydrodynamics and thermodynamics of the hot phase, rendered with our Punctuated Equilibria model. So we relate the X-ray observables concerning the intracluster medium (namely, the luminosity—temperature relation, the luminosity functions, the source counts) to the thermal energy of the gas pre-heated and expelled by supernovae following star formation, and then accreted during the subsequent merging events. Our main results are as follows. At fluxes fainter than FX≈10−15 erg cm−2 s−1 the X-ray counts of extended extragalactic sources (as well as the faint end of the luminosity function, their contribution to the soft X-ray background, and the LX−T correlation at the group scales) increase considerably if the star formation rate is high for z>1 as indicated by growing optical/infrared evidence. Specifically, the counts in the range 0.5-2 keV are increased by factors |4 when the the feedback is decreased and the star formation is enhanced as to yield a flat shape of the star formation rate for 2<z<4. Such faint fluxes are well within the reach of next generation X-ray observatories like AXAF and XMM. So very faint X-ray counts will soon constitute a new means of gaining information about the stellar processes (formation, and supernova feedback) at z>2, and a new way to advance the understanding of the galaxy formation.
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