An uncertainty principle for star formation - II. A new method for
  characterising the cloud-scale physics of star formation and feedback across
  cosmic history
  The cloud-scale physics of star formation and feedback represent the main
uncertainty in galaxy formation studies. Progress is hampered by the limited
empirical constraints outside the restricted environment of the Local Group. In
particular, the poorly-quantified time evolution of the molecular cloud
lifecycle, star formation, and feedback obstructs robust predictions on the
scales smaller than the disc scale height that are resolved in modern galaxy
formation simulations. We present a new statistical method to derive the
evolutionary timeline of molecular clouds and star-forming regions. By
quantifying the excess or deficit of the gas-to-stellar flux ratio around peaks
of gas or star formation tracer emission, we directly measure the relative
rarity of these peaks, which allows us to derive their lifetimes. We present a
step-by-step, quantitative description of the method and demonstrate its
practical application. The method's accuracy is tested in nearly 300
experiments using simulated galaxy maps, showing that it is capable of
constraining the molecular cloud lifetime and feedback time-scale to $<0.1$ dex
precision. Access to the evolutionary timeline provides a variety of additional
physical quantities, such as the cloud-scale star formation efficiency, the
feedback outflow velocity, the mass loading factor, and the feedback energy or
momentum coupling efficiencies to the ambient medium. We show that the results
are robust for a wide variety of gas and star formation tracers, spatial
resolutions, galaxy inclinations, and galaxy sizes. Finally, we demonstrate
that our method can be applied out to high redshift ($z\lesssim4$) with a
feasible time investment on current large-scale observatories. This is a major
shift from previous studies that constrained the physics of star formation and
feedback in the immediate vicinity of the Sun.
