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

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5. Evolution with redshift

In the above section, we have shown that the local X-ray data allow one to fully determine the power spectrum of the density fluctuations. Oukbir & Blanchard (1996) used a similar analysis to constrain the same quantity in the case of an open universe (see also Oukbir & Blanchard 1992, Viana & Liddle 1995, Eke et al. 1996). Within our framework, the models are then completely specified and we can now predict the temperature distribution function of galaxy clusters at any redshift. In principle this is a powerful test of the mean density of the universe, since Oukbir & Blanchard (1996) demonstrated that the evolution of the comoving number density of X-ray temperature selected galaxy clusters depends solely on [FORMULA]. Nevertheless, such information is not yet available and we can only investigate the evolution of the luminosity function. The most straightforward way to achieve this is to use the observed [FORMULA] relation. However, this correlation is determined only at low redshift. On the other hand, the standard scaling relation, [FORMULA], predicts the evolution with the redshift of the [FORMULA] relation; but as we have discussed in Sect. 3.2, this relation is not in agreement with local data. Actually, there is only little information concerning the temperature of high redshift galaxy clusters and the existing data seem to indicate that the [FORMULA] correlation is independent of redshift (Henry et al. 1994). However, due to the small number of clusters and to the large error bars on the temperatures, the uncertainties are quite high and do not lead to robust constraints. Investigating the possible evolution of the [FORMULA] relation, Oukbir & Blanchard (1996) determined the parameters which best fit the observed redshift distribution of the EMSS clusters (Gioia & Luppino 1994). In the case of the [FORMULA] universe, they found that a non-evolving [FORMULA] relation is in acceptable agreement with the observations, although a slight positive evolution [FORMULA] better fits the data (here, [FORMULA] is the luminosity that a cluster of given temperature would have at [FORMULA] according to the local [FORMULA] correlation). This latter relation is the one we will use in the following.

The observed evolution of the X-ray cluster population has been investigated and discussed in detail (Gioia et al. 1990, Edge et al. 1990, Henry et al. 1992, Luppino & Gioia 1995). The situation, however, is not very clear: the first results suggested a strong negative evolution, in the sense that for a given luminosity, fewer clusters were observed at high redshifts. On the other hand, Ebeling et al. (1995) claim that previous investigations were undermined by non-uniform selection procedures and they found no convincing evidence for any evolution within a sample of X-ray selected intermediate redshift ROSAT clusters, up to [FORMULA]. In fact, due to the extended nature of these objects, the interpretation of an X-ray selected cluster sample is not straightforward: apparent fluxes have to be corrected by a factor which depends on the assumed geometry of the source. This procedure has been used both by Gioia et al. (1990) and Henry et al. (1992), as well as by Luppino & Gioia (1995). The correction is very large for low redshift clusters and becomes moderate at higher redshifts. For instance, the mean correction factor used by Gioia & Luppino (1994) is 7; it could be as high as 15 for clusters with redshifts smaller than 0.15, but is less than 1.5 in the highest redshift bins. It seems therefore possible that a moderate systematic error in this correction could alter the inferred luminosity function.

It is interesting to compare our best fitting model with the observed luminosity function at high redhifts. This is presented in Fig. 3, where the luminosity function has been computed assuming the above mentioned evolutionary law for the [FORMULA] relation. The most impressive aspect of the observations is the fast apparent evolution of the slope of the observed luminosity function over the moderate redshift range from [FORMULA] to [FORMULA], which is not reproduced by the models. This is manifest by the fact that the model curve at [FORMULA] is already steeper than the data at this redshift; we have already noted this earlier in our discussion of Fig. 1. However, the models remains consistent with the data, when the uncertainty are taken into account. It is also interesting to note that the data from higher redshifts, shown in the inset, demonstrate similar or less evolution than the models; as pointed out by Gioia & Luppino (1994), the difference between [FORMULA] and [FORMULA] is consistent with no-evolution. From all of this, it seems reasonable to us to conclude that the observations are globally consistent with a moderate negative evolution, and that this evolution is weaker than previously estimated.

[FIGURE] Fig. 3. The X-ray temperature-luminosity function at different redshifts. The triangles show the EMSS data at [FORMULA] and the squares correspond to [FORMULA] ; the solid curve shows the model redshift-zero luminosity function, while the dashed line shows the result for a redshift of 0.33. The model has been normalized to the local temperature function, and the luminosity functions have been constructed by application of [FORMULA] to this local temperature function. The small inset shows the integrated number of clusters as a function of in-band luminosity. The slightly higher data point corresponds to a redshift of 0.66 and the lower point to a redshift of 0.8, both given by Luppino & Gioia (1995). The solid and dashed lines show the corresponding model predictions for [FORMULA] and [FORMULA], respectively.
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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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