tokens: panels. In the labels we show the average cross-power above 20′′. Figure 2. Stacked CIB–CXB cross-power spectra: between 3.6 μ m and [0.5–1], [1–2], [2–4], and [4–7] keV (top panels); between 4.5 μ m and CXB (bottom panels). Open circles with dashed error bars denote the absolute values of negative results. Note that the shown spectra are subtracted by the cross-power between IR and the stowed X-ray map, that is, the potential contamination from the X-ray particle background is removed from our final results. The final mean powers (used for further SED analysis) are summarized in Table 1 . As demonstrated in Cappelluti et al. ( 2013 , 2017 ), Mitchell-Wynne et al. ( 2016 ), and Li et al. ( 2018 ) the CIB versus CXB cross-power is in excess over shot noise at angular scales larger than 20′′. Since at those scales known foregrounds are significantly weaker than our signal (Helgason et al. 2014 ; Cappelluti et al. 2017 ; Kashlinsky et al. 2018 ), we therefore calculate the weighted mean cross-power above 20′′ asbetween each IR and X-ray band, for each field and for the stacked cross-power spectrum. As shown in Table 2 , the [1–2] keV band is significantly correlated with all IR wavelengths at ∼5 σ significance level, while the [0.5–1] and [2–4] keV bands are correlated with the IR wavelengths at ∼1–3 σ levels. There is no significant cross-power signal between the [4–7] keV band and any IR wavelengths so we cannot exclude an intrinsic correlation. By including the COSMOS field with a larger area, our new analysis extends the CIB–CXB cross-power analysis to ∼3000′′, doubling the largest scale reached in Cappelluti et al. ( 2017 ). The reason the highest significance is in the [1–2] keV band is due the higher S/N due to the peak in effective area of the Chandra mirror in that spectral region. Stacked results in the hard X-ray band (i.e., [2–4] keV + [4+7] keV) are not as significant as in Li et al. ( 2018 ) since deep fields add data affected by strong cosmic variance on very large scales. In the hard band most of the events are particles, so the low astrophysical hard X-ray photon statistics is another source of noise. As a cross-check we compared the significance of our stacks with those shown in Figure 17 of Li et al. ( 2018 ) for the [2–7] keV band versus 3.6 and 4.5 μ m and found consistent results. Table 2 Cross-power Spectrum Amplitude (>20′′), Calculated as a Note. a In units of 10 −11 photon s −1 cm −2 nW m −2 sr −1 . 4.2. Cross-power Hardness Ratios Similar to the X-ray color–color diagram, we look into three hardness ratios for the mean cross -power, which are the equivalent of photometric color indices, following the typical definition (Brunner et al. 2008 ) The statistical 1 σ hardness ratio errors are calculated from the mean power (Table 2 ) by error propagation. The mean 1 σ errors for the hardness ratios are ∼0.3 for HR1 and HR2 and ∼0.8 for HR3. Due to the larger errors in HR3, resulting from the uncertainties from harder
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