Cloud Scale Star Formation and Gas Scaling Relations in the Milky Way
We investigate cloud-scale star formation in the Milky Way using a sample of 45 molecular clouds (sizes of $5-240$ pc) in the inner Galactic plane, spanning heliocentric distances of $1.1-14.4$ kpc. Masses of these clouds are derived from $^{12}$CO and $^{13}$CO emission, while stellar masses are estimated using the young stellar object (YSO) population. The studied molecular clouds have masses ranging from $\sim10^{3}$ to $2.3\times10^{6}$ $\rm M_\odot$, with star formation efficiencies (SFE) up to 0.33. We find a tight, nearly linear scaling of the star formation rate (SFR) with the cloud mass, indicating that more massive clouds form proportionally more stars. The SFE, however, shows a declining trend with cloud mass. The relation between the star formation rate surface density ($\Sigma_{\rm SFR}$) and gas surface density ($\Sigma_{\rm gas}$) exhibits substantial cloud-to-cloud scatter, indicating that the canonical Kennicutt--Schmidt law is not strongly recovered at the scale of individual molecular clouds. Incorporating the cloud free-fall time ($\rm t_{ff}$) into the star formation scaling relation highlights its important role in regulating star formation, although the observed relations suggest that the star formation efficiency per free-fall time is not universal. In particular, the SFE decreases with increasing gas mass available per free-fall time. We discuss the implications of our results in the context of recent theoretical models of molecular cloud evolution and star formation.