The neutral hydrogen ( HI ) 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 HI mass and halo mass therefore puts important constraints on galaxy formation models .
We combine radio observations of HI in emission at low redshift ( z \sim 0 ) with optical/UV observations of HI in absorption at high redshift ( 1 < z < 4 ) to derive constraints on the evolution of the HI-mass halo-mass ( HIHM ) relation from redshift z = 4 to z = 0 .
We find that one can model the HIHM relation similar to the stellar-mass halo-mass ( SHM ) relation at z \sim 0 .
At z = 0 , haloes with mass 10 ^ { 11.7 } M _ { \odot } have the highest HI mass fraction ( \sim 1 \% ) , 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 parameterisation with a redshift- and mass-dependent modified Navarro-Frenk-White ( NFW ) profile for the HI density within a halo , we draw constraints on the evolution of the HIHM relation from the observed HI 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 % confidence level .