By using a large highly obscured ($N_{rm H} > 10^{23} rm cm^{-2}$) AGN sample (294 sources at $z sim 0-5$) selected from detailed X-ray spectral analyses in the deepest Chandra surveys, we explore distributions of these X-ray sources in various optical/IR/X-ray color-color diagrams and their host-galaxy properties, aiming at characterizing the nuclear obscuration environment and the triggering mechanism of highly obscured AGNs. We find that the refined IRAC color-color diagram fails to identify the majority of X-ray selected highly obscured AGNs, even for the most luminous sources with ${rm log},L_{rm X}, rm (erg s^{-1}) > 44$. Over 80% of our sources will not be selected as heavily obscured candidates using the flux ratio of $f_{rm 24 mu m}, /,f_R > 1000$ and $R - K > 4.5$ criteria, implying complex origins and conditions for the obscuring materials that are responsible for the heavy X-ray obscuration. The average star formation rate of highly obscured AGNs is similar to that of stellar mass- ($M_*$-) and $z$-controlled normal galaxies, while the lack of quiescent hosts is observed for the former. Partial correlation analyses imply that highly obscured AGN activity (traced by $L_{rm X}$) appears to be more fundamentally related to $M_*$, and no dependence of $N_{rm H}$ on either $M_*$ or SFR is detected. Morphology analyses reveal that 61% of our sources have a significant disk component, while only 27% of them exhibit irregular morphological signatures. These findings together point toward a scenario where secular processes (e.g., galactic-disk instabilities), instead of mergers, are most probable to be the leading mechanism that triggers accretion activities of X-ray-selected highly obscured AGNs.
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