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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 H₂ formation and photodissociation are balanced. However, real MCs are dynamic and can be out of CSS. In this study, we demonstrate that combining H₂ emission lines observed in the far-ultraviolet or infrared with column density observations can be used to derive the rates of H₂ formation and photodissociation. We derive analytical formulae that relate these rates to observable quantities, which we validate using synthetic H₂ line emission maps derived from the SILCC-Zoom hydrodynamical simulation. Our method estimates integrated H₂ formation and dissociation rates to within 29\% accuracy. Our simulations cover a wide dynamic range in H₂ 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 H₂ line observations, our method can assess the chemical state of MCs, providing insights into their evolutionary stages and lifetimes.
Bialy et al. (Mon,) studied this question.