Cross Correlation of the 2-10 keV X-Ray Background with Radio Sources: Constraining the Large Scale Structure of the X-Ray Background

We present cross-correlation analyses of the HEAO 2-10 keV diffuse X-ray map with both the combined GB6/Parkes-MIT-NRAO (GB6-PMN) 5 GHz and the FIRST 1.4 GHz radio surveys. The cross-correlation functions (CCFs) of both radio surveys with the unresolved X-ray background were detected at the 5 u level. While the large angular resolution (3 deg) of the X-ray map makes it difficult to separate the contributions of clustering from those of Poisson fluctuations, 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 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 fluctuations. This implies that approx. 2% of the diffuse X-ray background arises from the GB6-PMN sources.