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

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9. Critical universe

We now consider the case of a critical universe [FORMULA] with a CDM power-spectrum (Davis et al.1985) normalized to [FORMULA]. We also choose [FORMULA] and [FORMULA] km s-1 Mpc- 1. Thus, as in the previous case of an open universe our model is consistent with the studies described in VS II and Valageas et al. (1999a).

9.1. Quasar luminosity function

We first present our results for the redshift evolution of the quasar luminosity function in Fig. 18.

[FIGURE] Fig. 18. The evolution with redshift of the B-band quasar luminosity function in comoving Mpc-3, as in Fig. 1. The data points are from Pei (1995).

We can check that our results are similar to those obtained previously for an open universe and they again agree reasonably with observations. This is not very surprising since we use the same physical model so that we recover a similar behaviour. We present in Fig. 19 the quasar number counts we obtain from our model.

[FIGURE] Fig. 19. The quasar cumulative V-band number counts. The dashed line shows the counts of quasars with a magnitude brighter than V located at redshifts [FORMULA] while the solid line corresponds to [FORMULA].

We can see that our results are similar to those displayed previously in Fig. 2 and that our predictions are still marginally consistent with the lack of observation in the HDF.

9.2. Reheating

We present in Fig. 20 the redshift evolution of the IGM temperature [FORMULA], the virial temperature [FORMULA] of the smallest objects which can cool at a given time, and the mass averaged temperature [FORMULA].

[FIGURE] Fig. 20. The redshift evolution of the IGM temperature [FORMULA] (solid curve), the virial temperature [FORMULA] (upper dashed curve) and the mass averaged temperature [FORMULA] (lower dashed curve), as in Fig. 3.

We can see that our results are again very close to those obtained for an open universe. Indeed, the structure formation process is quite similar and it must agree with the same observations (quasar and galaxy luminosity functions, Lyman-[FORMULA] column density distribution) at low z.

9.3. Reionization

We display in Fig. 21 the redshift evolution of the background radiation and the comoving star formation rate.

[FIGURE] Fig. 21. The redshift evolution of the UV flux [FORMULA] (upper panel) and of the comoving star formation rate [FORMULA] (lower panel) for the case of an open universe. The dashed line in the lower panel shows the effect of the absorption of high energy photons by the neutral hydrogen present in the IGM and in Lyamn-[FORMULA] clouds.

We can check that we recover the behaviour obtained previously for an open universe. However, the reionization redshift [FORMULA] is smaller than previously. This is related to the lower normalization [FORMULA] of the power-spectrum as compared to the previous case. This leads to fewer bright quasars at high z (compare Fig. 18 and Fig. 1) and to a smaller radiative output.

We can also check that the hydrogen and helium reionization process is close to our previous results (as for the reheating). Thus, for most practical purposes both critical and open cosmologies allow reasonable reheating and reionization histories which are very similar. In fact, the uncertainties involved in the galaxy and quasar formation processes are probably too large to favour significantly one of these two possible scenarios (as compared to the other). However, both models are consistent with present observations.

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© European Southern Observatory (ESO) 1999

Online publication: June 18, 1999
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