The Molecular Cloud Lifecycle I: Constraining H2 formation and dissociation rates with observations

Molecular clouds (MCs) are the birthplaces of new stars in galaxies. A key component of MCs are photodissociation regions (PDRs), where far-ultraviolet radiation plays a crucial role in determining the gas's physical and chemical state. Traditional PDR models assume chemical steady state (CSS), where the rates of H$_2$ formation and photodissociation are balanced. However, real MCs are dynamic and can be out of CSS. In this study, we demonstrate that combining H$_2$ emission lines observed in the far-ultraviolet or infrared with column density observations can be used to derive the rates of H$_2$ formation and photodissociation. We derive analytical formulae that relate these rates to observable quantities, which we validate using synthetic H$_2$ line emission maps derived from the SILCC-Zoom hydrodynamical simulation. Our method estimates integrated H$_2$ formation and dissociation rates with an accuracy $\approx 30$ % (on top of uncertainties in observed H$_2$ emission maps and column densities). Our simulations, valid for column densities $N \leq 2 \times 10^{22}$ cm$^{-2}$, cover a wide dynamic range in H$_2$ formation and photodissociation rates, showing significant deviations from CSS, with 74 % of the MC's mass deviating from CSS by a factor greater than 2. Our analytical formulae can effectively distinguish between regions in and out of CSS. When applied to actual H$_2$ line observations, our method can assess the chemical state of MCs, providing insights into their evolutionary stages and lifetimes. A NASA Small Explorer mission concept, Eos, will be proposed in 2025 and is specifically designed to conduct the types of observations outlined in this study.