Determining the efficiency with which gas is converted into stars in galaxies requires an accurate determination of the total reservoir of molecular gas mass. However, despite being the most abundant molecule in the Universe, H$_2$ is challenging to detect through direct observations and indirect methods have to be used to estimate the total molecular gas reservoir. These are often based on scaling relations from tracers such as CO or dust, and are generally calibrated in the Milky Way. Yet, evidence that these scaling relations are environmentally dependent is growing. In particular, the commonly used CO-to-H$_2$ conversion factor (X$_{rm CO}$) is expected to be higher in metal-poor and/or strongly UV-irradiated environments. We use new SOFIA/FIFI-LS observations of far-infrared fine structure lines from the ionised and neutral gas and the Meudon photodissociation region model to constrain the physical properties and the structure of the gas in the massive star-forming region of 30 Doradus in the Large Magellanic Cloud, and determine the spatially resolved distribution of the total reservoir of molecular gas in the proximity of the young massive cluster R136. We compare this value with the molecular gas mass inferred from ground-based CO observations and dust-based estimates to quantify the impact of this extreme environment on commonly used tracers of the molecular gas. We find that the strong radiation field combined with the half-solar metallicity of the surrounding gas are responsible for a large reservoir of CO-dark molecular gas, leaving a large fraction of the total H$_2$ gas (> 75%) undetected when adopting a standard X$_{rm CO}$ factor in this massive star-forming region.
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