Deep X-ray source counts from a fluctuation analysis of ROSAT PSPC images

We present deep, soft X-ray source counts of the high-Galactic-latitude sky down to a flux level of 7 × 10^-16 erg cm^-2 s^-1, obtained from fluctuation analyses of six medium-exposure fields (exposure times from 13 to 21 ks) and one deep field (73 ks) observed with the ROSAT Position Sensitive Proportional Counter. Using a P(D) analysis of the medium fields, we confirm a flattening of the source counts below ∼2.2 × 10^-14 erg cm^-2 s^-1, as previously found with data from the Einstein Observatory. The source counts inferred in this way are in good agreement with direct source counts both from our deep field and from counts in the Lockman hole survey by Hasinger and others. A subsequent fluctuation analysis of our deep field shows that the differential source counts (sources per unit flux and per unit solid angle) follow n(S) ∝ S^-γ, with $$\gamma=1.8_{+0.2}^{-0.1}$$ down to a flux of at least 7 × 10^-16 erg cm^-2 s^-1, which is much flatter than the counts above ∼2.2 × 10^-14 erg cm^-2 s^-1. We find no evidence for any new source population at low flux levels following steeper, Euclidean source counts, much as might be expected from low-luminosity active galaxies or starbursts. The total surface density of sources detected down to a flux level of 7 × 10^-16 erg cm^-2 s^-1 from the fluctuations is the highest ever reported at X-ray wavelengths (900 to 1800 source deg^-2). The integrated emission of the detected sources is only about 70 per cent of the 0.5-2 keV extragalactic X-ray background, implying that the source counts must steepen at lower fluxes (or that there is some other source for the remaining background).