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

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6. The X-ray background and the X-ray counts

Two interesting probes of cluster evolution are the X-ray source counts and the contribution of clusters to the X-ray background.

In order to compute the contribution of clusters to the X-ray counts, we must assign a luminosity to each mass in the PS mass function. According to Oukbir & Blanchard (1996), we use the locally observed [FORMULA] correlation and we assume that it evolves such as to best fit the EMSS cluster redshift distribution (Gioia & Luppino 1994). As we mentioned in the previous section, in the case of the [FORMULA] universe, a non-evolving [FORMULA] relation is in acceptable agreement with the observations, although a slight positive evolution [FORMULA] better fits the data. In the case of an open universe, a strong negative evolution is needed to reproduce the same data, and [FORMULA]. These latter relations are the one we will use in the following.

As the models are forced to match the Einstein redshift distribution as well as the local data, we do not expect a significant difference in the predicted quantities between the two models.

In Fig. 4, we show the expected [FORMULA] in the energy band 0.5-2 keV. The triangle at [FORMULA] comes from the ROSAT cluster number counts in the northern sky (Burg et al. 1994), and the arrow at [FORMULA] is a lower limit inferred by Rosati et al. (1995) from deep ROSAT PSPC observations. The solid and the dashed lines are the predicted cluster counts from our models in the case of the [FORMULA] and [FORMULA] models respectively. The thick lines are computed assuming the evolution of the [FORMULA] correlation which best fits the EMSS redshift distribution, whereas the thin lines correspond to a non-evolving [FORMULA] relation. Although the models are slightly above the observed number counts at low fluxes, our self-consistent modeling leads to predicted number counts which are in agreement with the data, and as expected, the flat and the open case are then almost identical. The strong negative evolution that is necessary in open models is again emphasized: if one assumes a non-evolving [FORMULA] correlation at high redshifts in the [FORMULA] universe, then one overproduces the number of expected clusters at low fluxes by a factor close to five. Although the counts at [FORMULA] could constitute a lower limit, it is unlikely that they were underestimated by such a large factor.

[FIGURE] Fig. 4. The galaxy cluster number counts in the 0.5 -2 keV energy band. The triangle comes from the ROSAT cluster number counts in the northern sky (Burg et al. 1994), and the arrow is a lower limit inferred by Rosati et al. (1995) from deep ROSAT PSPC observations. The solid and the dashed lines are the predicted cluster counts from our models in the case of the [FORMULA] and [FORMULA] models respectively. The thick lines are computed assuming that [FORMULA] in the case [FORMULA] and [FORMULA] in the case [FORMULA]. The thin lines correpond to a non-evolving [FORMULA] relation.

With our approach we can also estimate the contribution of clusters to the X-ray background.

The contribution of X-ray clusters to the XRB has already been discussed at length in the literature. From the X-ray luminosity function of Abell clusters, McKee et al. (1980) have put an upper limit of [FORMULA] to this contribution in the 2-10 keV band. Piccinotti et al. (1982) have used a complete X-ray survey of the HEAO experiment to derive a similar result for the same energy band. At energies less than 1 keV, Schaeffer & Silk (1988) derived a contribution as high as [FORMULA] coming from small objects with large redshifts. However, this was based on the self-similar model. Blanchard et al. (1992b) investigated the contribution of X-ray clusters to the XRB within the framework of different cosmological models. Using parameters in the luminosity-mass relation which reproduce the local luminosity function, they found a contribution of approximately [FORMULA] in the 2-10 keV band. Burg et al. (1993) have also estimated this contribution, but do not attempt to reproduce the locally observed quantities. Fig. 5 shows our calculation of the cluster contribution to the X-ray background in the energy range 0.07-10 keV. The two crossing, thin, solid lines correspond to the region where the ROSAT background lies (Hasinger 1992). The two parallel, solid lines are power laws with energy index of -0.4 and two different normalizations at [FORMULA]: [FORMULA], as determined from the HEAO spectrum by Marshall et al. (1980), and [FORMULA] from the Wisconsin results of McCammon et al. (1983). The triangles are the values inferred by Wu et al. (1991). The solid and the dashed lines are the predicted cluster counts from our models in the case of the [FORMULA] and [FORMULA] models, respectively. As in Fig. 4, the thick lines are computed assuming the evolution of the [FORMULA] correlation which best fits the EMSS redshift distribution, whereas the thin lines correspond to the case of the non-evolving [FORMULA] correlation. As for the contribution of clusters to the X-ray counts, if the self-consistent modeling is used, then the contribution of clusters to the X-ray background is very similar in the case of the critical and open models. In the 1 - 2 keV band, this contribution is about 10%. If one considers the hypothesis of a non-evolving [FORMULA] correlation in the case of the [FORMULA] model (recall that this model does not fit the redshift distribution of the EMSS data), the contribution in the same band reaches 30%, which is still lower than the boundary which is allowed by considering that approximately 50% of the background in the 1 - 2 keV band is already resolved by point sources (Hasinger 1992). Nevertheless, Barcons et al. (1994) showed from fluctuation analysis that the extrapolated counts of the present known point sources could explain 90% of the background, but there still remains an unidentified component. In this context, a contribution of 10% is far from negligible. This is especially true since clusters are extended objects and they probably escape detection by the point source detection algorithms routinely employed (Blanchard et al. 1992b).

[FIGURE] Fig. 5. Contribution of galaxy clusters to the XRB in the case of the critical model (solid lines) and in the case of the open model (dashed lines). As in Fig. 4, the thick lines are computed assuming that [FORMULA] in the case [FORMULA] and [FORMULA] in the case [FORMULA]. The thin solid lines in the range 0.5 - 2 keV represent the ROSAT background (Hasinger 1992) and the thin solid lines in the range 2 to 10 keV are the HEAO 1 background (Marshall et al. 1980) and the Wisconsin data (McCammon et al. 1983) with same power law index and different normalisations (see text). The triangles are the values inferred by Wu et al. (1991).

We conclude that the self-consistent modeling of galaxy clusters is in agreement with the observed X-ray cluster counts, and, contrary to other claims (Evrard & Henry 1991, Burg et al. 1993), that the X-ray background does not provide us with stringent constraints on the power spectrum or the evolution of X-ray properties of galaxy clusters.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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