The Molecular Cloud Lifecycle II: Formation and Destruction of Molecular Clouds Diagnosed via H$_2$ Fluorescent Emission Emission

Molecular hydrogen (H$_2$) formation and dissociation are key processes that drive the gas lifecycle in galaxies. Using the SImulating the LifeCycle of Molecular Clouds (SILCC) zoom-in simulation suite, we explore the utility of future observations of H$_2$ dissociation and formation for tracking the lifecycle of molecular clouds. The simulations used in this work include non-equilibrium H$_2$ formation, stellar radiation, sink particles, and turbulence. We find that, at early times in the cloud evolution, H$_2$ formation rapidly outpaces dissociation and molecular clouds build their mass from the atomic reservoir in their environment. Rapid H$_2$ formation is also associated with a higher early star formation rate. For the clouds studied here, H$_2$ is strongly out of chemical equilibrium during the early stages of cloud formation but settles into a bursty chemical steady-state about 2 Myrs after the first stars form. At the latest stage of cloud evolution, dissociation outweighs formation and the clouds enter a dispersal phase. We discuss how theories for the molecular cloud lifecycle and the star formation efficiency may be distinguished with observational measurements of H$_2$ fluorescence with a space-based high-resolution FUV spectrometer, such as the proposed Hyperion and Eos NASA Explorer missions. Such missions would enable measurements of the H$_2$ dissociation and formation rates, which we demonstrate can be connected to different phases in a molecular cloud's star-forming life, including cloud building, rapidly star-forming, H$_2$ chemical equilibrium, and cloud destruction.