Metallicity dependence of the CO-to-H₂ and the [CI]-to-H₂ conversion factors in galaxies

Understanding the molecular gas content in the interstellar medium (ISM) is crucial for studying star formation and galaxy evolution. The CO-to-H₂ (X_CO) and the [CI]-to-H₂ (X_CI) conversion factors are widely used to estimate the molecular mass content in galaxies. However, these factors depend on many environmental parameters in the ISM, such as metallicity, cosmic-ray ionization rate, and far-ultraviolet (FUV) radiation field, in particular, in the low-metallicity ISM that is found at large galactocentric radii and in early-type galaxies. This work investigates the dependence of X_CO and X_CI on the environmental parameters of the ISM, with a focus on the low-metallicity α-enhanced ISM ([C/O] < 0), to provide improved tracers of molecular gas under diverse conditions. We used the statistical algorithm PDFCHEM, coupled with a database of photodissociation region (PDR) models generated with the 3D-PDR astrochemical code. The models account for a wide range of metallicities, dust-to-gas mass ratios, FUV intensities, and cosmic-ray ionization rates. The conversion factors were computed by integrating the PDR properties over log-normal column density distributions (A_V-PDFs) that represent various cloud types. The X_CO factor increases significantly with decreasing metallicity. It exceeds ∼1000 times the Galactic value at [O/H] = -1.0 under α-enhanced conditions, as opposed to ∼300 times under non-α-enhanced conditions ([C/O] = 0). In contrast, X_CI varies more gradually with metallicity, which makes it a more reliable tracer of molecular gas in metal-poor environments under most conditions. The fraction of CO-dark molecular gas increases dramatically in low-metallicity regions, where it exceeds 90% at [O/H] = -1.0, in particular, in diffuse clouds and environments with strong FUV radiation fields. The results highlight the limitations of CO as a molecular gas tracer in the metal-poor ISM and demonstrate the potential of [CI] (1-0) as a complementary tracer. The use of metallicity-dependent X_CO and X_CI factors as provided by this study is recommended for accurately estimating molecular gas masses in diverse environments. We recommend the use of the log₁₀ X_CO ≃ -2.41 Z + 41.3 relation for the CO-to-H₂ conversion factor and the log₁₀ X_CI ≃ -0.99 Z + 29.7 relation for the [CI]-to-H₂ conversion factor, where Z = 12 + log₁₀(O/H).