2025ApJ...985...14L

We compare measurements of star formation efficiency to cloud-scale gas properties across the PHANGS- ALMA sample. Dividing 67 galaxies into 1.5 kpc scale regions, we calculate the molecular gas depletion time ${\tau }_{{\rm{dep}}}^{{\rm{mol}}}={{\rm{\Sigma }}}_{{\rm{mol}}}/{{\rm{\Sigma }}}_{{\rm{SFR}}}$ and the star formation efficiency per freefall time ${\epsilon }_{{\rm{ff}}}^{{\rm{mol}}}={\tau }_{{\rm{ff}}}/{\tau }_{{\rm{dep}}}^{{\rm{mol}}}$ for each region. Then we test how ${\tau }_{{\rm{dep}}}^{{\rm{mol}}}$ and ${\epsilon }_{{\rm{ff}}}^{{\rm{mol}}}$ vary as functions of the regional mass-weighted mean molecular gas properties on cloud scales (60-150 pc): gas surface density, $\langle {{\rm{\Sigma }}}_{{\rm{mol}}}^{{\rm{cloud}}}\rangle $, velocity dispersion, $\langle {\sigma }_{{\rm{mol}}}^{{\rm{cloud}}}\rangle $, virial parameter, $\langle {\alpha }_{{\rm{vir}}}^{{\rm{cloud}}}\rangle $, and gravitational freefall time, $\langle {\tau }_{{\rm{ff}}}^{{\rm{cloud}}}\rangle $. $\langle {\tau }_{{\rm{ff}}}^{{\rm{cloud}}}\rangle $ and ${\tau }_{{\rm{dep}}}^{{\rm{mol}}}$ correlate positively, consistent with the expectation that gas density plays a key role in setting the rate of star formation. Our fiducial measurements suggest ${\tau }_{{\rm{dep}}}^{{\rm{mol}}}\propto {\langle {\tau }_{{\rm{ff}}}^{{\rm{cloud}}}\rangle }^{0.5}$ and ${\epsilon }_{{\rm{ff}}}^{{\rm{mol}}}\approx 0.34 \% $, though the exact numbers depend on the adopted fitting methods. We also observe anticorrelations between ${\tau }_{{\rm{dep}}}^{{\rm{mol}}}$ and $\langle {{\rm{\Sigma }}}_{{\rm{mol}}}^{{\rm{cloud}}}\rangle $ and between ${\tau }_{{\rm{dep}}}^{{\rm{mol}}}$ and $\langle {\sigma }_{{\rm{mol}}}^{{\rm{cloud}}}\rangle $. All three correlations may reflect the same underlying link between density and star formation efficiency combined with systematic variations in the degree to which self-gravity binds molecular gas in galaxies. We highlight the ${\tau }_{{\rm{dep}}}^{{\rm{mol}}}$-$\langle {\sigma }_{{\rm{mol}}}^{{\rm{cloud}}}\rangle $ relation because of the lower degree of correlation between the axes. Contrary to theoretical expectations, we observe an anticorrelation between ${\tau }_{{\rm{dep}}}^{{\rm{mol}}}$ and $\langle {\alpha }_{{\rm{vir}}}^{{\rm{cloud}}}\rangle $ and no significant correlation between ${\epsilon }_{{\rm{ff}}}^{{\rm{mol}}}$ and $\langle {\alpha }_{{\rm{vir}}}^{{\rm{cloud}}}\rangle $. Our results depend sensitively on the adopted CO-to-H₂ conversion factor, with corrections for excitation and emissivity effects in inner galaxies playing an important role. We emphasize that our simple methodology and clean selection allow for easy comparison to numerical simulations and highlight this as a logical next direction.