Constraints on the evolution of the relationship between H I mass and halo mass in the last 12 Gyr

The neutral hydrogen (H I) content of dark matter haloes forms an intermediate state in the baryon cycle that connects the hot shock-heated gas and cold star-forming gas in haloes. Measurement of the relationship between H I mass and halo mass therefore puts important constraints on galaxy formation models. We combine radio observations of H I in emission at low redshift (z ∼ 0) with optical/UV observations of H I in absorption at high redshift (1 < z < 4) to derive constraints on the evolution of the H I-mass-halo-mass (HIHM) relation from redshift z = 4 to 0. We find that one can model the HIHM relation similar to the stellar-mass-halo-mass (SHM) relation at z ∼ 0. At z = 0, haloes with mass 10^11.7 M_⊙ have the highest H I mass fraction (∼1 per cent), which is about four times smaller than their stellar-mass fraction. We model the evolution of the HIHM relation in a manner similar to that of the SHM relation. Combining this parametrization with a redshift- and mass-dependent modified Navarro-Frenk-White profile for the H I density within a halo, we draw constraints on the evolution of the HIHM relation from the observed H I column density, incidence rate and clustering bias at high redshift. We compare these findings with results from hydrodynamical simulations and other approaches in the literature and find the models to be consistent with each other at the 68 per cent confidence level.