Cross-correlation between X-ray and optical/near-infrared background intensity fluctuations

Angular power spectra of optical and infrared background anisotropies at wavelengths between 0.5 to 5 $\mu$m are a useful probe of faint sources present during reionization, in addition to faint galaxies and diffuse signals at low redshift. The cross-correlation of these fluctuations with backgrounds at other wavelengths can be used to separate some of these signals. A previous study on the cross-correlation between X-ray and $Spitzer$ fluctuations at 3.6 $\mu$m and 4.5 $\mu$m has been interpreted as evidence for direct collapse blackholes (DCBHs) present at $z > 12$. Here we return to this cross-correlation and study its wavelength dependence from 0.5 to 4.5 $\mu$m using $Hubble$ and $Spitzer$ data in combination with a subset of the 4 Ms $Chandra$ observations in GOODS-S/ECDFS. Our study involves five $Hubble$ bands at 0.6, 0.7, 0.85, 1.25 and 1.6 $\mu$m, and two $Spitzer$-IRAC bands at 3.6 $\mu$m and 4.5 $\mu$m. We confirm the previously seen cross-correlation between 3.6 $\mu$m (4.5 $\mu$m) and X-rays with 3.7$\sigma$ (4.2$\sigma$) and 2.7$\sigma$ (3.7$\sigma$) detections in the soft [0.5-2] keV and hard [2-8] keV X-ray bands, respectively, at angular scales above 20 arcseconds. The cross-correlation of X-rays with $Hubble$ is largely anticorrelated, ranging between the levels of 1.4$-$3.5$\sigma$ for all the $Hubble$ and X-ray bands. This lack of correlation in the shorter optical/NIR bands implies the sources responsible for the cosmic infrared background at 3.6 and 4.5~$\mu$m are at least partly dissimilar to those at 1.6 $\mu$m and shorter.