The contribution of galaxy clusters to the soft X-ray background

We examine models for the expected contribution to the X-ray background (XRB) from clusters of galaxies in a flat universe with a spectrum of fluctuations corresponding to the standard cold dark matter picture and for a power-law spectrum P(k) is-proportional-to k(n) with n = -2. We consider a self-similar scaling model for clusters proposed by Kaiser, along with several variants. The self-similar model produces an appreciable fraction of the soft X-ray background. However, the predicted luminosity function overproduces low-luminosity clusters and expected number counts exceed observations. Incompleteness due to spatial extension of the sources is unlikely to account for these discrepancies. Photon statistics from synthesized maps of deep Einstein fields show a granularity similar to that deduced by Hamilton and Helfand from the Einstein data but overproduces by a large factor the number of discrete sources observed as clusters, and the fluctuation limit derived from the recent correlation analyses of the background. This occurs even though a large fraction of cluster sources may be missed by detection algorithms geared toward detection of point sources. Two alternative models are designed to be consistent with the local luminosity function data. For these, we generate expected deep images for the ROSAT satellite. We predict that a substantial fraction of extragalactic component of the soft (0.1-2.4 keV) XRB might be due to clusters. Clusters of galaxies should be a significant source of background at energies around 2 keV and are likely to contribute up to 30% of the unresolved component. They should produce fluctuations at a level close to present limits. These sources are extended and might easily be missed by use of a point source algorithm for detection. Furthermore, we find that the clusters' number counts as well as their contribution in the soft ROSAT energy ranges are higher in the n = -2 model than in CDM models. ROSAT observations might therefore help in differentiating between these models.