Morphology of molecular clouds at kiloparsec scale in the Milky Way: Shear-induced alignment and vertical confinement

The shape of the cold interstellar molecular gas is determined by several processes, including self-gravity, tidal force, turbulence, magnetic field, and galactic shear. Based on the 3D dust extinction map derived by Vergely et al., we identify a sample of 550 molecular clouds (MCs) within $3\hspace{0.2em}\rm kpc$ of the solar vicinity in the Galactic disk. Our sample contains clouds whose size ranges from pc to kiloparsec, which enables us to study the effect of Galactic-scale processes, such as shear, on cloud evolution. We find that our sample clouds follow a power-law mass-size relation of $M\propto 32.00\hspace{0.2em}{R_{\rm{max}}}^{1.77}$, $M\propto 20.59\hspace{0.2em}{R_S}^{2.04}$ and $M\propto 14.41\hspace{0.2em}{R_V}^{2.29}$, where $R_{\rm{max}}$ is the major axis-based cloud radius, $R_S$ is the area-based radius, and $R_V$ is the volume-based radius, respectively. These clouds have a mean constant surface density of $\sim 7 \hspace{0.2em} \rm {M_{\odot}pc^{-2}}$, and follow a volume density-size relation of $\rho \propto 2.60\hspace{0.2em}{R_{\rm{max}}}^{-0.55}$. As cloud size increases, their shapes gradually transition from ellipsoidal to disk-like to bar-like structures. Large clouds tend to have a pitch angle of $28^{\circ} - 45^{\circ}$, where the angle is measured concerning the Galactic tangential direction. These giant clouds also tend to stay parallel to the Galactic disk plane and are confined within the Galactic molecular gas disk. Our results show that large molecular clouds in the Milky Way can be shaped by Galactic shear and confined in the vertical direction by gravity.