Semi-empirical constraints on the HI mass function of star-forming galaxies and $\Omega_{\rm HI}$ at $z\sim 0.37$ from interferometric surveys

The HI mass function is a crucial tool to understand the evolution of the HI content in galaxies over cosmic times and to constrain both the baryon cycle in galaxy evolution and the reionization history of the Universe. We aim to derive semi-empirical constraints at $z\sim 0.37$ by combining literature results on the stellar mass function from optical surveys with recent findings on the $M_{\rm HI}-M_\star$ scaling relation derived via spectral stacking analysis applied to 21-cm line interferometric data from the MIGHTEE and CHILES surveys, conducted with MeerKAT and the VLA, respectively. We draw synthetic stellar mass samples directly from the publicly-available results underlying the analysis of the COSMOS2020 galaxy photometric sample. Afterwards, we convert $M_\star$ into $M_{\rm HI}$ using analytical fitting functions to the data points from HI stacking. We then fit a Schechter function to the median HIMF from all the samples via MCMC. We finally derive the posterior distribution for $\Omega_{\rm HI}$ by integrating the models for the HIMF built from the posteriors samples of the Schechter parameters. We find evolution of the HIMF at $z\sim 0.37$ with respect to results at $z\sim 0$ from the ALFALFA survey and at $z\sim 1$ from uGMRT data. Our results for $\Omega_{\rm HI}$ are in broad agreement with other literature results, and follow the trend on $\Omega_{\rm HI}$ as a function of redshift. The derived value $\Omega_{\rm HI}=\left(7.02^{+0.59}_{-0.52}\right)\times10^{-4}$ at $z\sim 0.37$ from the combined analysis deviates at $ \sim 2.9\sigma$ from the ALFALFA result at $z\sim 0$. We conclude that the HIMF and $\Omega_{\rm HI}$ constraints that we derive from state-of-the-art deep interferometric surveys suggest an evolution of the HIMF and of the cosmic HI density, supporting a picture of smooth transition of the HI content of galaxies from $z\sim 0$ to $z\sim 1$.