An uncertainty principle for star formation II. A new method for characterizing 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.