Abstract
The latest ALMA and JWST observations provide new information on the birth and evolution of galaxies in the early Universe at the epoch of reionization. Measurements at redshift $ z > 5$ of their cold-gas budget are particularly important because this budget is known to be the main fuel for star formation. A powerful tool for probing the physics characterising galaxies at high redshift is the m$ emission line. Due to its low excitation potential emission can be produced in photodissociation regions, neutral atomic gas, and molecular clouds. To properly capture the cold-gas processes taking place in these environments (molecule formation, self-shielding, dust grain catalysis, and photoelectric and cosmic-ray heating), we made use of a new set of dedicated hydrodynamic simulations ( including time-dependent non-equilibrium chemistry, star formation, stellar evolution, metal spreading, and feedback mechanisms. We were able to accurately track the evolution of and H$_2$ in a cosmological context and predict the contribution of each gas phase to luminosity. We provide formulas that can be used to estimate the mass of molecular and atomic gas from detections. Furthermore, we analysed the evolution of conversion factors with galactic properties, such as stellar metallicity, star formation rate, and stellar mass. We demonstrate that emission is dominated by gas and that most of the luminosity is generated in warm, dense, star-forming regions. We conclude that although predominantly traces atomic rather than molecular gas, the luminosity remains a robust indicator of the H$_2$ mass.
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