Cloud-scale gas properties, depletion times, and star formation efficiency per free-fall time in PHANGS--ALMA

We compare measurements of star formation efficiency to cloud-scale gas properties across PHANGS-ALMA. Dividing 67 galaxies into 1.5 kpc scale regions, we calculate the molecular gas depletion time, tau_dep= Sigma_mol/Sigma_SFR, and the star formation efficiency per free-fall time, eff=tau_ff/tau_dep, for each region. Then we test how tau_dep and eff vary as functions of the regional mass-weighted mean molecular gas properties on cloud scales (60-150pc): gas surface density, <Sigma_mol^cloud>, velocity dispersion, <sigma_mol^cloud>, virial parameter, <alpha_vir^cloud>, and gravitational free-fall time, <tau_ff^cloud>. <tau_ff^cloud> and tau_dep 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_dep \propto <tau_ff^cloud>^0.5 and eff \approx 0.39%, though the exact numbers depend on the adopted fitting methods. We also observe anti-correlations between tau_dep and <Sigma_mol^cloud> and between tau_dep^mol and <sigma_mol^cloud> . 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_dep-<sigma_mol^cloud> relation because of the lower degree of correlation between the axes. Contrary to theoretical expectations, we observe an anti-correlation between tau_dep^mol and <alpha_vir^cloud> and no significant correlation between eff and <alpha_vir^cloud>. 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 easy comparison to numerical simulations and highlight this as a logical next direction.