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

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5. Conclusion

In this article we have described an analytic model for structure formation processes which deals in a consistent fashion with quasars, galaxies, Lyman-[FORMULA] absorbers and underdense regions within the IGM. This allows us to obtain the reheating and reionization history of the universe, as well as the evolution of the entropy of the gas. We considered three scenarios, with different efficiency factors for the transfer of energy from supernovae or quasars into the IGM. Thus, we have shown that the energy provided by quasars is sufficient to reheat the universe and raise the mean entropy of the IGM up to the value required to match the "floor" level observed in cool clusters. This is an upper bound on the entropy production and this value allows to explain the behaviour of the cluster [FORMULA] relation. On the other hand, the supernova heating scenario would require an efficiency factor of order unity ([FORMULA]). Thus, the IGM is more likely to have been reheated by quasars than by supernovae .

Of course, a more realistic treatment would account for the details of the quasar interaction with their gaseous environment. However, our study already shows that quasar-driven outflows can provide an important heating mechanism. On the other hand, a detailed model of the inhomogeneous character of this reheating is probably necessary in order to evaluate its effects on Lyman-[FORMULA] clouds since most of the opacity may come from clouds located far away from quasars which have not been reheated.

We showed that the feedback of entropy production onto structure formation may partly account for the decline at lowzof the comoving star formation rate and of the quasar luminosity function, in addition to cluster observations . This is an interesting prospect since it links different processes to the same phenomenon and it gives additional weight to the hypothesis of such a reheating scenario. Moreover, it provides a narrow range for the reheating of the IGM ([FORMULA] K) since we must satisfy the contradictory constraints arising from clusters (which require a large reheating so as to modify the [FORMULA] relation) and from galaxies and quasars (which require a small reheating so that galaxy formation is not too much inhibited). Thus, it is important to simultaneously address these processes in order to check the validity of a given scenario. On the other hand, the reionization process of the universe is almost not modified which means that our results for the ionization state of the gas and the background UV flux should be quite robust.

Then, we found that although both scenarios, normalized to the current value of the entropy measured in cool clusters, are very similar, the reheating due to quasars occurs a bit earlier ([FORMULA]) than for supernovae ([FORMULA]) because of the sharp drop at [FORMULA] of the quasar luminosity function. This might give a clue to discriminate these two sources of energy from observations. However, it is clear that further work is needed in order to get stronger constraints on the possible efficiency of these reheating processes, for instance through very detailed numerical simulations. Nevertheless, despite the small discrepancies we get for the star formation rate or the quasar luminosity function as compared with observations, it appears quite remarkable that a simple analytic model like ours, which necessarily involves some approximations (e.g. we do not take into account the scatter of the galaxy or quasar properties, nor the inhomogeneity of the supernova or quasar heating), provides such a good description of structure formation processes. Indeed, we note that at [FORMULA] we describe objects which span a wide range in density, from [FORMULA] for voids and low-column density Lyman-[FORMULA] absorbers up to [FORMULA] for old galaxies, as well as in mass, from [FORMULA] for Lyman-[FORMULA] clouds up to [FORMULA] for clusters. The fact that we can build a unified consistent model for this broad variety of structures strongly suggests that hierarchical scenarios like ours, with adequate models for galaxy formation and radiative processes, provide a realistic description of the actual universe.

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© European Southern Observatory (ESO) 1999

Online publication: October 14, 1999
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