We study the coherence of the near-infrared and X-ray background fluctuations and the X-ray spectral properties of the sources producing it. We use data from multiple Spitzer and Chandra surveys, including the UDS/SXDF surveys, the Hubble Deep Field North, the EGS/AEGIS field, the Chandra Deep Field South and the COSMOS surveys, comprising $sim$2275 Spitzer/IRAC hours and $sim$~16 Ms of Chandra data collected over a total area of $sim$~1~deg$^2$. We report an overall $sim$5$sigma$ detection of a cross-power signal on large angular scales $>$ 20$$ between the 3.6 and 4.5mum and the X-ray bands, with the IR vs [1-2] keV signal detected at 5.2$sigma$. The [0.5-1] and [2-4] keV bands are correlated with the infrared wavelengths at a $sim$1$-$3$sigma$ significance level. The hardest X-ray band ([4-7] keV) alone is not significantly correlated with any infrared wavelengths due to poor photon and sampling statistics. We study the X-ray SED of the cross-power signal. We find that its shape is consistent with a variety of source populations of accreting compact objects, such as local unabsorbed AGNs or high-z absorbed sources. We cannot exclude that the excess fluctuations are produced by more than one population. Because of poor statistics, the current relatively broad photometric bands employed here do not allow distinguishing the exact nature of these compact objects or if a fraction of the fluctuations have instead a local origin.
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