The Star Formation Efficiency per Free Fall Time in Nearby Galaxies
  We estimate the star formation efficiency per gravitational free fall time,
$\epsilon_{\rm ff}$, from observations of nearby galaxies with resolution
matched to the typical size of a Giant Molecular Cloud. This quantity,
$\epsilon_{\rm ff}$, is theoretically important but so far has only been
measured for Milky Way clouds or inferred indirectly in a few other galaxies.
Using new, high resolution CO imaging from the PHANGS-ALMA survey, we estimate
the gravitational free-fall time at 60 to 120 pc resolution, and contrast this
with the local molecular gas depletion time to estimate $\epsilon_{\rm ff}$.
Assuming a constant thickness of the molecular gas layer ($H = 100$ pc) across
the whole sample, the median value of $\epsilon_{\rm ff}$ in our sample is
$0.7\%$. We find a mild scale-dependence, with higher $\epsilon_{\rm ff}$
measured at coarser resolution. Individual galaxies show different values of
$\epsilon_{\rm ff}$, with the median $\epsilon_{\rm ff}$ ranging from $0.3\%$
to $2.6\%$. We find the highest $\epsilon_{\rm ff}$ in our lowest mass targets,
reflecting both long free-fall times and short depletion times, though we
caution that both measurements are subject to biases in low mass galaxies. We
estimate the key systematic uncertainties, and show the dominant uncertainty to
be the estimated line-of-sight depth through the molecular gas layer and the
choice of star formation tracers.
