Observations and theoretical simulations suggest that a significant fraction of merger-triggered accretion onto supermassive black holes is highly obscured, particularly in late-stage galaxy mergers, when the black hole is expected to grow most rapidly. Starting with the Wide-Field Infrared Survey Explorer all-sky survey, we identified a population of galaxies whose morphologies suggest ongoing interaction and which exhibit red mid-infrared colors often associated with powerful active galactic nuclei (AGNs). In a follow-up to our pilot study, we now present Chandra/ACIS and XMM-Newton X-ray observations for the full sample of the brightest 15 IR-preselected mergers. All mergers reveal at least one nuclear X-ray source, with 8 out of 15 systems exhibiting dual nuclear X-ray sources, highly suggestive of single and dual AGNs. Combining these X-ray results with optical line ratios and with near-IR coronal emission line diagnostics, obtained with the near-IR spectrographs on the Large Binocular Telescope, we confirm that 13 out of the 15 mergers host AGNs, two of which host dual AGNs. Several of these AGNs are not detected in the optical. All X-ray sources appear X-ray weak relative to their mid-infrared continuum, and of the nine X-ray sources with sufficient counts for spectral analysis, eight reveal strong evidence of high absorption with column densities of $N_mathrm{H} gtrsim 10^{23}$~cm$^{-2}$. These observations demonstrate that a significant population of single and dual AGNs are missed by optical studies, due to high absorption, adding to the growing body of evidence that the epoch of peak black hole growth in mergers occurs in a highly obscured phase.
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