Expectations for X-ray cluster observations by the ROSAT satellite

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Abstract
We present predictions for characteristics of the X-ray cluster population expected to be observed by the ROSAT satellite. The theoretical modeling requires an assumed fluctuation spectrum and relations describing the behavior of cluster X-ray luminosity and core radius with cluster binding mass and redshift. The most natural model, which assumes self-similar scaling L(x) is-proportional-to M4/3 in a cold dark matter (CDM) universe, fails to reproduce the shape of the local X-ray cluster luminosity function. For CDM to be successful, the bolometric X-ray luminosity L(x) must scale with binding mass M as L(x) is-proportional-to M3, perhaps indicative of a strong dependence of intracluster gas fraction with mass. An alternative model motivated by recent evidence for more large-scale power, uses an n = -2 initial fluctuation spectrum and fits local cluster abundances with an intermediate scaling L(x) is-proportional-to M11/6. This scaling law may imply a fixed minimum entropy for the gas in the cores of rich clusters, perhaps a signature of activity from an earlier galaxy formation era. For the north ecliptic pole region of the ROSAT all-sky survey, which will cover a 10-degrees radius field to a limiting flux of roughly 9 x 10(-14) ergs s-1 cm-2, the successful models predict approximately 330 cluster X-ray sources visible above the flux limit if a square detect cell of side 4'8 is employed. The clusters would have a median redshift of 0.2, and 10% of them should have z > 0.4 but essentially none should be seen at z > 1. Roughly 2500 clusters are expected with this detect geometry in the all-sky survey above the limiting flux of 7 x 10(-13) ergs s-1 cm-2. Cluster sources would be expected to contribute approximately 10% of the observed soft X-ray background. The sensitivity of cluster detectability to treatment of the core emission and detect cell geometry is the principal source of uncertainty in these predictions

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