Deep hard X-ray source counts from a fluctuation analysis of ASCA SIS images

An analysis of the spatial fluctuations in 15 deep ASCA SIS0 images has been conducted in order to probe the 2–10 keV X-ray source counts down to a flux limit ～ 2 × 10^?14 erg cm^?2 s^?1. Special care has been taken in modelling the fluctuations in terms of the sensitivity maps of every one of the 16 regions (5.6 × 5.6 arcmin² each) into which the SIS0 has been divided, by means of ray-tracing simulations with improved optical constants in the X-ray telescope. The very extended 'sidelobes' (extending up to a couple of degrees) exhibited by these sensitivity maps make our analysis sensitive to both faint on-axis sources and brighter off-axis ones, the former being dominant. The source counts in the range (2?12) × 10^?14 erg cm^?2 s^?1 are found to be close to a Euclidean form which extrapolates well to previous results from higher fluxes and are in reasonable agreement with some recent ASCA surveys. However, our results disagree with the deep survey counts by Georgantopoulos et al. The possibility that the source counts flatten to a sub-Euclidean form, as is observed at soft energies in ROSAT data, is only weakly constrained to happen at a flux < 1.8 × 10^?12 erg cm^?2 s^?1 (90 per cent confidence). Down to the sensitivity limit of our analysis, the integrated contribution of the sources the imprint of which is seen in the fluctuations amounts to ～ 35 ± 13 per cent of the extragalactic 2–10 keV X-ray background.