We perform a systematic X-ray spectroscopic analysis of 57 local ultra/luminous infrared galaxy systems (containing 84 individual galaxies) observed with Nuclear Spectroscopic Telescope Array and/or Swift/BAT. Combining soft X-ray data obtained with Chandra, XMM-Newton, Suzaku and/or Swift/XRT, we identify 40 hard ($>$10 keV) X-ray detected active galactic nuclei (AGNs) and constrain their torus parameters with the X-ray clumpy torus model XCLUMPY (Tanimoto et al. 2019). Among the AGNs at $z < 0.03$, for which sample biases are minimized, the fraction of Compton-thick ($N_{rm H} geq 10^{24}$ cm$^{-2}$) AGNs reaches 64$^{+14}_{-15}$% (6/9 sources) in late mergers, while 24$^{+12}_{-10}$% (3/14 sources) in early mergers, consistent with the tendency reported by Ricci et al. (2017). We find that the bolometric AGN luminosities derived from the infrared data increase, but the X-ray to bolometric luminosity ratios decrease, with merger stage. The X-ray weak AGNs in late mergers ubiquitously show massive outflows at sub-pc to kpc scales. Among them, the most luminous AGNs ($L_{rm bol,AGN} sim 10^{46}$ erg s$^{-1}$) have relatively small column densities of $lesssim$10$^{23}$ cm$^{-2}$ and almost super-Eddington ratios ($lambda_{rm Edd} sim$ 1.0). Their torus covering factors ($C_{rm T}^{rm (22)} sim 0.6$) are larger than those of Swift/BAT selected AGNs with similarly high Eddington ratios. These results suggest a scenario that, in the final stage of mergers, multiphase strong outflows are produced due to chaotic quasi-spherical inflows and the AGN becomes extremely X-ray weak and deeply buried due to obscuration by inflowing and/or outflowing material.
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