Obscuration in active galactic nuclei (AGN) provides insights into the material surrounding the central engine. Compton-thick AGN (CTAGN), c
Obscuration in active galactic nuclei (AGN) provides insights into the material surrounding the central engine. Compton-thick AGN (CTAGN), characterized by a column density of $N_{\mathrm{H}} \geq 1.5 \times 10^{24} \ \mathrm{cm}^{-2}$, are heavily obscured by dust and gas. While X-ray observations primarily determine this column density, the sub-mm obscuration properties of CTAGN remain less explored. We analyze archival ALMA CO(3-2) data for CTAGN and non-CTAGN from the 70-month $\textit{Swift}$/BAT catalog and other X-ray surveys. Integrated intensity maps (moment 0) reveal dense gas concentrated around the nucleus. Assuming a constant CO-to-$\mathrm{H_2}$ conversion factor, $X_{\mathrm{CO}} = 2.2 \times 10^{20} \ \mathrm{cm}^{-2} \ (\mathrm{K\ km\ s}^{-1})^{-1}$, we find that molecular hydrogen column densities ($N_{\mathrm{H_2}}$) are generally lower than X-ray-derived total hydrogen column densities ($N_{\mathrm{H}}$). However, $N_{\mathrm{H_2}}$ values in this work are slightly higher than in previous studies due to the adopted conversion factor. The discrepancy between $N_{\mathrm{H}}$ and $N_{\mathrm{H_2}}$ aligns with prior findings that X-ray-derived values tend to be higher, except for non-CTAGN, where $N_{\mathrm{H_2}}$ can exceed $N_{\mathrm{H}}$. Kendall and Spearman tests indicate a positive monotonic correlation, though not statistically significant, suggesting a complex interplay of factors. The optically thick nature of CO in dense regions may contribute to the observed differences. Our results highlight the need for an accurate CO-to-$\mathrm{H_2}$ conversion factor in deriving column densities, potentially offering an alternative method for identifying CTAGN. Future studies with larger datasets and refined methodologies are essential for a deeper understanding of sub-mm and X-ray properties in AGN. Comment: This paper has been accepted for publication in PASA
