The history of cosmic baryons: X-ray emission versus star formation rate

We relate the star formation from cold baryons condensing in virialized str uctures to the X-ray properties of the associated diffuse, hot baryonic com ponent. 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 s tandard hierarchical clustering; secondly, the star formation governed, aft er the current 'recipes', by radiative cooling and by feedback of the super nova energy into the hot baryonic component; thirdly, and novel, the hydrod ynamics and thermodynamics of the hot phase, rendered with our Punctuated E quilibria model. So we relate the X-ray observables concerning the intraclu ster medium (namely, the luminosity-temperature relation, the luminosity fu nctions, 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 F-X approximate to 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 t o the soft X-ray background, and the L-X - T correlation at the group scale s) increase considerably if the star formation rate is high for z > 1 as in dicated by growing optical/infrared evidence. Specifically, the counts in t he range 0.5-2 keV are increased by factors similar to 4 when the the feedb ack is decreased and the star formation is enhanced as to yield a flat shap e of the star formation rate for 2 < z < 4. Such faint fluxes are well within the reach of next generation X-ray observ atories 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 understandin g of the galaxy formation.