Cloud Scale Star Formation and Gas Scaling Relations in the Milky Way

Abstract

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 $\sim 10^3$ to $2.3\times 10^6$ ${\mathrm{M}}_{\odot }$, 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 (${\Sigma }_{\mathrm{SFR}}$) and gas surface density (${\Sigma }_{\mathrm{gas}}$) 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 (${\mathrm{t}}_{\mathrm{ff}}$) 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.

15 pages, 10 figures, Accepted for publication in ApJ