Relative velocities between $^{13}$CO structures within $^{12}$CO Molecular clouds

Abstract

Velocity fields of molecular clouds (MCs) can provide crucial information on the merger and split between clouds, as well as their internal kinematics and maintenance, energy injection and redistribution, even star formation within clouds. Using the CO spectral lines data from the Milky Way Imaging Scroll Painting (MWISP) survey, we measure the relative velocities along the line of sight ($\Delta$V$_{\rm LOS}$) between $^{13}$CO structures within $^{12}$CO MCs. Emphasizing MCs with double and triple $^{13}$CO structures, we find that approximately 70$\%$ of $\Delta$V$_{\rm LOS}$ values are less than $\sim$ 1 km s$^{-1}$, and roughly 10$\%$ of values exceed 2 km s$^{-1}$, with a maximum of $\sim$ 5 km s$^{-1}$. Additionally, we compare $\Delta$V$_{\rm LOS}$ with the internal velocity dispersion of $^{13}$CO structures ($\sigma_{\rm ^{13}CO,in}$) and find that about 40$\%$ of samples in either double or triple regime display distinct velocity discontinuities, i.e. the relative velocities between $^{13}$CO structures are larger than the internal linewidths of $^{13}$CO structures. Among these 40$\%$ samples in the triple regime, 33$\%$ exhibit signatures of combinations through the two-body motion, whereas the remaining 7$\%$ show features of configurations through the multiple-body motion. The $\Delta$V$_{\rm LOS}$ distributions for MCs with double and triple $^{13}$CO structures are similar, as well as their $\Delta$V$_{\rm LOS}$/$\sigma_{\rm ^{13}CO,in}$ distributions. This suggests that relative motions of $^{13}$CO structures within MCs are random and independent of cloud complexities and scales.