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Astron. Astrophys. 350, 725-742 (1999)

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1. Introduction

An important test of cosmological models is to check whether they can reproduce the wide variety of astrophysical objects we observe in the present universe. Several studies have already shown that the usual hierarchical scenarios (such as the standard CDM model) provide predictions which agree reasonably well with observations for galaxies (Valageas & Schaeffer 1999a; Kauffmann et al. 1993; Cole et al. 1994), Lyman-[FORMULA] clouds (Valageas et al. 1999a; Petitjean et al. 1992; Miralda-Escude et al. 1996; Riediger et al. 1998), quasars and reionization constraints (Valageas & Silk 1999a,b; Gnedin & Ostriker 1997; Haiman & Loeb 1998). However, within this framework the simplest model leads for clusters to a temperature - X-ray luminosity relation [FORMULA] (Kaiser 1986) which disagrees with observations (Ponman et al. 1996). It has been argued (Evrard & Henry 1991; Cavaliere et al. 1997; Ponman et al. 1998) that this discrepancy could be explained by a "preheating" of the gas which would raise its entropy before clusters form. Indeed, this entropy "floor" would lead to a maximum density for the ICM which would break the previous self-similar scaling and provide a steeper relation [FORMULA]. On the other hand, it has also been suggested (Blanchard et al. 1992; Blanchard & Prunet 1997) that the overcooling problem linked to galaxy formation (i.e. the fact that a small fraction of the baryonic content of the universe has been converted into stars while simple estimates show that most of the baryons should have been able to cool by now) requires a reheating of the IGM in order to prevent the gas from cooling and falling into the dark matter potential wells. Thus, it is important to obtain a good handle on the "entropy history" of the universe since it may play a key role in structure formation processes, for galaxies as well as for clusters.

In this article, we present an analytic model to derive the evolution of the entropy of the gas. To this order, we use a description developed in Valageas & Silk (1999a,b) to study the reheating and reionization history of the universe by the radiation emitted by stars and quasars. This model also provides a consistent description of galaxies (Valageas & Schaeffer 1999a), Lyman-[FORMULA] clouds (Valageas et al. 1999a) and clusters (Valageas & Schaeffer 1999b). Thus, it ensures that we obtain a realistic scenario. Then, as detailed in Sect. 2 we add to this simple model an additional source of heating which corresponds to a direct energy input into the IGM from supernovae or quasars. We also describe the modifications induced by entropy considerations. Next, in Sect. 3 we present the numerical results we obtain for an open universe for both supernova and quasar heating. Finally, in Sect. 4 we point out the feedback of such an entropy production onto structure formation, for galaxies, quasars and clusters. We also describe the cluster temperature - X-ray luminosity relation we obtain from these scenarios.

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© European Southern Observatory (ESO) 1999

Online publication: October 14, 1999