Detailed Analysis of the Cross-Correlation Function between the X-Ray Background and Foreground Galaxies

摘要

Recent ROSAT surveys suggest that galaxies can constitute the new class of faint sources required to explain the full phenomenology of the cosmic X-ray background (XRB). To test this hypothesis without resorting to optical identifications, we compute the two-point cross-correlation function (CCF) estimator Wxg(θ) between 62 Einstein IPC fields (0.81-3.5 keV) and the APM Northern Galaxy Catalog (13.5 E 19.0). At zero lag (θ = 0), we detect a 3.5 σ correlation signal with an amplitude of Wxg(0) = 0.045 ± 0.013. This signal passes a series of control tests. At non-zero lag (θ 0), the angular dependence of Wxg has two main features: the main signal for θ 4', and an almost flat plateau with an amplitude of Wxg(θ 4') 0.015. When fields with galaxy clusters as Einstein targets are removed, the plateau virtually disappears, and the zero-lag amplitude becomes Wxg(0) = 0.029 ± 0.013. We develop a simple, two-dimensional formalism to interpret the CCF that takes into account the point-spread function of the imaging X-ray detector. Three distinct effects can produce a correlation signal: the X-ray emission from galaxies themselves, the clustering of galaxies with discrete X-ray sources, and the clustering of galaxies with diffuse X-ray emission. It is likely that the plateau at large angles is due to the last effect through the residual diffuse X-ray emission from clusters of galaxies. We do not detect any significant clustering between discrete X-ray sources and galaxies. Using only the fields with noncluster targets, we find that the mean X-ray intensity of APM galaxies in the 0.81-3.5 keV band is (2.2 ± 1.1) × 10-6 counts s-1 arcmin-2, corresponding to 1.5% ± 0.8% of the XRB intensity. The mean X-ray flux of galaxies with E = 17.5 ± 0.3 is then (8.1 ± 4.7) × 10-16 ergs s-1 cm-2. This agrees within 1 σ with the X-ray flux expected from earlier direct studies of brighter, nearby galaxies, which were shown to result in a total integrated galaxy contribution to the XRB of about 13%. We discuss how this powerful cross-correlation method can be used to measure the flux of X-ray sources well below the detection limit of X-ray instruments and, perhaps, to probe otherwise undetectable faint diffuse X-ray emission.