Detailed Analysis of the Cross-Correlation Function between the X-Ray   Background and Foreground Galaxies
  Recent ROSAT surveys suggest that galaxies constitute the new class of X-ray sources required to explain the full phenomenology of the cosmic X-Ray Background (XRB). To test this hypothesis, we compute the two-point cross-correlation function Wxg(theta) between 62 Einstein-IPC fields (.81-3.5 keV) and the APM Northern galaxy catalog (13.5<E<19.0). At zero-lag (theta=0), we detect a 3.5sigma correlation signal with an amplitude of Wxg(0)=.045+/-.013. At non-zero lag (theta>0), the angular dependence of Wxg has two main features: the main signal for theta<4', and an almost flat plateau with an amplitude of Wxg(theta>4')=.015, likely to result from the diffuse X-ray emission by clusters of galaxies. Taking the point-spread function of the X-ray instrument into account, we find that the mean X-ray flux of galaxies with <E>=17.5+/-.3 is (8.1+/-4.7) 10^(-16) ergs/cm^2/s. This agrees with the X-ray flux expected from earlier direct studies of brighter galaxies, which were shown to result in a total 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. 
A. Refregier (1), D.J. Helfand (1), and R.G. McMahon (2) ((1) Columbia   University, (2) Cambridge University)