Expectations for X-ray cluster observations by the ROSAT satellite

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 Lₓ_ 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 Lₓ_ must scale with binding mass M as Lₓ_ 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 Lₓ_ 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 10ᵈeg^ radius field to a limiting flux of roughly 9 x 10^-14^ ergs s^-1^ cm ^-2^, the successful models predict ~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 ~10% of the observed soft X-ray back-ground. The sensitivity of cluster detectability to treatment of the core emission and detect cell geometry is the principal source of uncertainty in these predictions.