Metallicity dependence of the CO-to-H${}_2$ and the [CI]-to-H${}_2$ conversion factors in galaxies

Abstract

Understanding the molecular gas content in the interstellar medium (ISM) is crucial for studying star formation and galaxy evolution. The CO-to-H${}_2$ ($X_{\mathrm{CO}}$) and the [CI]-to-H${}_2$ ($X_{\mathrm{CI}}$) conversion factors are widely used to estimate the molecular mass content in galaxies. However, these factors depend on many ISM environmental parameters. This work investigates the dependence of $X_{\mathrm{CO}}$ and $X_{\mathrm{CI}}$ on these parameters, with a focus on the low-metallicity $\alpha$-enhanced ISM ($[C/O]<0$), to provide improved tracers of molecular gas in diverse conditions. We used the PDFchem algorithm, coupled with a database of 3D-PDR models. These 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 ($A_{\mathrm{V}}$-PDFs) representing various cloud types. The $X_{\mathrm{CO}}$ factor increases significantly with decreasing metallicity, exceeding $\sim 1000$ times the Galactic value at $[O/H]=-1.0$ under $\alpha$-enhanced conditions, as opposed to $\sim 300$ times under non-$\alpha$-enhanced conditions ($[C/O]=0$). In contrast, $X_{\mathrm{CI}}$ shows a more gradual variation with metallicity, making 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, exceeding 90\% at $[O/H]=-1.0$, particularly in diffuse clouds and environments with strong FUV radiation fields. We recommend the use of the ${\log }_{10}{X}_{\mathrm{CO}}\simeq -2.41Z+41.3$ relation for the CO-to-H${}_2$ conversion factor, and the ${\log }_{10}{X}_{\mathrm{CI}}\simeq -0.99Z+29.7$ relation for the [CI]-to-H${}_2$, where $Z=12+{\log }_{10}(O/H)$.

16 pages, 10 figures, A&A accepted, comments welcome!

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