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Astron. Astrophys. 320, 365-377 (1997)

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8. Conclusions

The ensemble properties of clusters (and groups) are potentially useful for the determination of the various ingredients of cosmological models. However, in practice there are several problems which must be addressed in order to fruitfully use this method. As clusters are the result of the non-linear collapse of the largest fluctuations, one might think that their physical properties would be difficult to understand, and that any modeling would suffer from this limitation. This is even more important when one is trying to account for the evolution of the ensemble properties. The optical properties are certainly difficult to model: as pointed out by Frenk et al. (1990), projection effects can alter both the optical richness and inferred velocity dispersions. Other problems that make the modeling of cluster evolution difficult are 1) evolution of the member galaxies; 2) merging; 3) environmental effects likely to have played a major - but yet unclear - role in the galaxy formation history. Therefore any conclusions inferred from optical observations should be regarded as only tentative.

On the other hand, X-ray observations appear to provide a more reliable test of cosmological models because they are much less subject to these optical biases. Nevertheless, a substantial uncertainty remains in the modeling of cluster X-ray luminosities because the luminosity depends mainly on the cluster core properties. As we have emphasized, the gas temperature is better understood from a theoretical point of view, and present day data are of a good enough quality to allow reliable modeling. We find that the temperature distribution function indicates a power spectrum index of the order of [FORMULA] and a bias parameter of about of 1.7, in agreement with other power spectrum determinations. Notably, this conflicts with the standard CDM prediction of [FORMULA] on cluster scales. We have also investigated the case of non-gaussian fluctuations: we show that the local data implied by a given sprectrum can be reproduced by any other spectrum, provided that the distribution function of the fluctuations is adequatly chosen. Therefore, only specific models can be further investigated. Calculations of the luminosity evolution of cluster remains more uncertain, mainly because this needs to model the cluster core. One way to avoid this problem would be to obtain a temperature limited rather than flux limited sample of clusters, but this seems rather difficult to achieve. Nevertheless, information from the redshift distribution of flux limited clusters allows one to remove this difficulty. We find that the redshift distribution of the EMSS clusters can be fitted with a moderate positive evolution of the [FORMULA] (clusters of a given temperature were brighter in the past) whereas a strong negative evolution is needed in the case [FORMULA] (Oukbir & Blanchard, 1996).

Using the best-fit model to the cluster X-ray data, we have estimated the predicted cluster number counts as well as the contribution of clusters to the X-ray background in the case [FORMULA] and [FORMULA]. We confirm previous results: clusters could represent a significant fraction of the faint sources, and are expected to contribute about 10% of the X-ray background at energies of the order of a few keV. Since our modeling matches the local data as well as the high redshift observations, there is not a noticeable difference among the two models in the X-ray counts and the contribution of clusters to the X-ray background: within self-consistent modeling, these two quantities cannot provide stringent constraints on the various models. Further observations will help to remove the substantial uncertainty in the temperature distribution function and therefore will allow a better evaluation of the characteristics of the spectrum, while redshift information will lead to unambiguous information on the mean density of the universe (Oukbir & Blanchard, 1996).

Note added in proof: Recently, as a part of the Wide Angle ROSAT Pointed Survey Scharf et al. 1996 have given the sky density of extended objects at fluxes greater than [FORMULA] in the 0.5-2 keV band. They find a value in the range 2.8 to 4.0 ([FORMULA] 0.4) deg-2, in excellent agreement with our predictions.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998