Cross-correlation of the 2-10 keV XRB with radio sources: constraining the large-scale structure of the x-ray background

We present cross-correlation analyses of the HEAO 2È10 keV di†use X-ray map with both the combined GB6/Parkes-MIT-NRAO (GB6-PMN) 5 GHz and the FIRST 1.4 GHz radio surveys. The crosscorrelation functions (CCFs) of both radio surveys with the unresolved X-ray background were detected at the 5 p level. While the large angular resolution (3¡) of the X-ray map makes it difficult to separate the contributions of clustering from those of Poisson Ñuctuations, the amplitude of the CCF provides important constraints on the X-ray emissivity of the radio sources, as well as on the clustering properties of radio and X-ray sources. These constraints are subject to a number of modeling parameters, e.g., X-ray luminosity evolution, clustering evolution, the radio luminosity function, cosmological model, etc. For reasonable choices of parameters the X-ray/FIRST CCF is consistent with a correlation scale length of 6 h~1 Mpc. This is somewhat smaller than the scale length inferred from the autocorrelation function of the FIRST survey and implies that X-ray sources are less strongly clustered than strong radio sources, a result that is consistent with previous constraints on X-ray clustering. The X-ray/GB6-PMN CCF is several times larger and is likely to be dominated by Poisson Ñuctuations. This implies that D2% of the di†use X-ray background arises from the GB6-PMN sources. Subject headings : di†use radiation È galaxies : statistics È large-scale structure of universe È radio continuum: galaxies È X-rays : galaxies È X-rays : general