Velocity Structure and Molecular Formation in Polaris Molecular Cloud

Abstract: We present a wide-field $(60\arcmin \times 30\arcmin)$ study of a dense region within the Polaris Flare, hereafter referred to as the `Polaris molecular cloud', using $^{12}$CO, $^{13}$CO, and C$^{18}$O ($J=1-0$) observations at $20\arcsec$ resolution, obtained with the Nobeyama 45 m Radio Telescope. The analysis reveals molecular gas formation occurring at column densities up to $\sim10^{21}$ cm$^{-2}$, evidenced by an anti-correlation between $\textsc{Hi}$ and CO distributions, indicating active atomic-to-molecular gas conversion. We found a threshold column density for molecular formation at $\sim5\times10^{20}$ cm$^{-2}$, which is common among more evolved molecular clouds. The CO-to-H$2$ conversion factor, $X{\rm CO}$, was found to be $0.7 \times 10^{20}$ H$2$ cm$^{-2}$ (K km s$^{-1})^{-1}$, lower than the solar neighborhood average. Our chemical models estimate the cloud's age to be $\sim10^{5}-10^{6}$ years, suggesting an early stage of molecular cloud evolution. This interpretation is consistent with the observed low $X{\rm CO}$ factor. While virial analysis suggests that the entire cloud is gravitationally unbound, we identified several filamentary structures extending from the main cloud body. These filaments show systematic velocity gradients of $0.5-1.5$ km s$^{-1}$ pc$^{-1}$, and analysis of the velocities shows that the molecular gas within them is falling toward the main cloud body, following a free-fall model. This suggests ongoing mass accumulation processes through the filaments, demonstrating that gravitational processes can be important even at column densities of $\sim10^{21}$ cm$^{-2}$.