A high-redshift calibration of the [OI]-to-HI conversion factor in star-forming galaxies

The assembly and build-up of neutral atomic hydrogen (HI) in galaxies is one of the most fundamental processes in galaxy formation and evolution. Studying this process directly in the early universe is hindered by the weakness of the hyperfine 21-cm HI line transition, impeding direct detections and measurements of the HI gas masses ($M_{\rm HI}$). Here we present a new method to infer $M_{\rm HI}$ of high-redshift galaxies using neutral, atomic oxygen as a proxy. Specifically, we derive metallicity-dependent conversion factors relating the far-infrared [OI]-$63\mu$m and [OI]-$145\mu$m emission line luminosities and $M_{\rm HI}$ in star-forming galaxies at $z\approx 2-6$ using gamma-ray bursts (GRBs) as probes. We substantiate these results by observations of galaxies at $z\approx 0$ with direct measurements of $M_{\rm HI}$ and [OI]-$63\mu$m and [OI]-$145\mu$m in addition to hydrodynamical simulations at similar epochs. We find that the [OI]$_{\rm 63\mu m}$-to-HI and [OI]$_{\rm 145\mu m}$-to-HI conversion factors universally appears to be anti-correlated with the gas-phase metallicity. The high-redshift GRB measurements further predict a mean ratio of $L_{\rm [OI]-63\mu m} / L_{\rm [OI]-145\mu m}=1.55\pm 0.12$ and reveal generally less excited [CII]. The $z \approx 0$ galaxy sample also shows systematically higher $\beta_{\rm [OI]-63\mu m}$ and $\beta_{\rm [OI]-145\mu m}$ conversion factors than the GRB sample, indicating either suppressed [OI] emission in local galaxies or more extended, diffuse HI gas reservoirs traced by the HI 21-cm. Finally, we apply these empirical calibrations to the few high-redshift detections of [OI]-$63\mu$m and [OI]-$145\mu$m line transitions from the literature and further discuss the applicability of these conversion factors to probe the HI gas content in the dense, star-forming ISM of galaxies at $z\gtrsim 6$, well into the epoch of reionization.