  Using a suite of isolated $L_\star$ galaxy simulations, we show that global
depletion times and star-forming gas mass fractions in simulated galaxies
exhibit systematic and well-defined trends as a function of the local star
formation efficiency per freefall time, $\epsilon_{\rm ff}$, strength of
stellar feedback, and star formation threshold. We demonstrate that these
trends can be reproduced and explained by a simple physical model of global
star formation in galaxies. Our model is based on mass conservation and the
idea of gas cycling between star-forming and non-star-forming states on certain
characteristic time scales under the influence of dynamical and feedback
processes. Both the simulation results and our model predictions exhibit two
limiting regimes with rather different dependencies of global galactic
properties on the local parameters. When $\epsilon_{\rm ff}$ is small and
feedback is inefficient, the total star-forming mass fraction, $f_{\rm sf}$, is
independent of $\epsilon_{\rm ff}$ and the global depletion time, $\tau_{\rm
dep}$, scales inversely with $\epsilon_{\rm ff}$. When $\epsilon_{\rm ff}$ is
large or feedback is very efficient, these trends are reversed: $f_{\rm sf}
\propto \epsilon_{\rm ff}^{-1}$ and $\tau_{\rm dep}$ is independent of
$\epsilon_{\rm ff}$ but scales linearly with the feedback strength. We also
compare our results with the observed depletion times and mass fractions of
star-forming and molecular gas and show that they provide complementary
constraints on $\epsilon_{\rm ff}$ and the feedback strength. We show that
useful constraints on $\epsilon_{\rm ff}$ can also be obtained using
measurements of the depletion time and its scatter on different spatial scales.

Astrophysics of Galaxies