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Astron. Astrophys. 347, 1-20 (1999)

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1. Introduction

An important goal of cosmology is to describe the structure formation processes which led to the wide variety of astrophysical objects we observe in the present universe, from Lyman-[FORMULA] clouds to galaxies and clusters. Several studies have shown that the usual hierarchical scenarios (like the standard CDM model) can provide predictions which agree reasonably well with observations for galaxies as well as for Lyman-[FORMULA] clouds. This corresponds to objects at [FORMULA]. However, it is possible to constrain the earlier evolution of the universe by studying the reheating and reionization history implied by such models. Indeed, observations show that the universe is highly photo-ionized by [FORMULA] and a large reionization redshift could imprint a signature on the CMB radiation. Moreover, future missions such as NGST could for instance detect quasars at high redshifts [FORMULA].

In this article, we present an analytic model for the reheating and reionization history of the universe, adopting a CDM power spectrum in a critical density and in an open universe. Similar studies have been performed previously via numerical simulations (e.g. Gnedin & Ostriker 1997) and analytic approaches (e.g. Haiman & Loeb 1997; Haiman & Loeb 1998) based on the Press-Schechter prescription (Press & Schechter 1974). However, previous analytic models were often developed for this specific purpose (i.e. they were not derived from a model already checked in detail against observations of galaxies or Lyman-[FORMULA] clouds) and neglected the clumping of the gas (except for the presence of virialized objects used to count galaxies). Thus, the main motivations of our present study are to:

  • describe these early stages of structure formation through a self-consistent model which has already been applied to galaxies (Valageas & Schaeffer 1998) and to Lyman-[FORMULA] clouds (Valageas et al.1999a).

  • take into account the broad range of density fluctuations within the IGM through our description of Lyman-[FORMULA] clouds.

  • use this feature to constrain our model against several observations: notably the QSO number counts and the Gunn-Peterson test (for HI and HeII).

  • develop a simple analytic model which can predict many properties of the universe (galaxy and quasar luminosity functions, temperature and ionization state of the IGM, intensity and spectrum of the UV background radiation and fraction of matter within stars) and provide a complementary tool to numerical simulations.

Consideration of the various objects involved in our work (beyond the just-virialized halos which are usually studied) is made possible because of a specific description of the density field based on the assumption that the many-body correlation functions obey the scaling model detailed in Balian & Schaeffer (1989) and checked numerically in Colombi et al. (1997). This allows one to define the various mass functions of interest, as described in Valageas & Schaeffer (1997; also in Valageas et al.1999b), and to go beyond the scope of the usual Press-Schechter approximation (Press & Schechter 1974). The main advantage of our approach is thus to provide a globally consistent picture of structure formation in the universe, within the framework of a hierarchical scenario.

This article is organized as follows. In Sect. 2 we describe our prescription for mass functions. Next, in Sect. 3 we review our model for galaxy formation, described in more detail in Valageas & Schaeffer (1998) while in Sect. 4 we deal with our prescription for quasars. In Sect. 5 we summarize the relevant aspects of our model for Lyman-[FORMULA] clouds (Valageas et al. 1999a). We describe the calculation of the evolution of the IGM properties (temperature, UV background radiation, ionization state) in Sect. 6 and in Sect. 7. Finally, in Sect. 8 and Sect. 9 we present our results for the case of an open universe and then for a critical universe.

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© European Southern Observatory (ESO) 1999

Online publication: June 18, 1999
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