A scaling relation for the molecular cloud lifetime in Milky Way-like galaxies

We study the time evolution of molecular clouds across three Milky Way-like isolated disc galaxy simulations at a temporal resolution of 1 Myr, and at a range of spatial resolutions spanning two orders of magnitude in spatial scale from ~10 pc up to ~1 kpc. The cloud evolution networks generated at the highest spatial resolution contain a cumulative total of ~80,000 separate molecular clouds in different galactic-dynamical environments. We find that clouds undergo mergers at a rate proportional to the crossing time between their centroids, but that their physical properties are largely insensitive to these interactions. Below the gas disc scale-height, the cloud lifetime obeys a scaling relation of the form $\tau_{\rm life} \propto \ell^{-0.3}$ with the cloud size $\ell$, consistent with over-densities that collapse, form stars, and are dispersed by stellar feedback. Above the disc scale-height, these self-gravitating regions are no longer resolved, so the scaling relation flattens to a constant value of ~13 Myr, consistent with the turbulent crossing time of the gas disc, as observed in nearby disc galaxies.