Semi-empirical constraints on the HI mass function of star-forming galaxies and ΩHI at z~ 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. We aim to derive semi-empirical constraints at z~ 0.37 by combining literature results on the M_ function from optical surveys with recent findings on the MHI-M_ scaling relation derived via spectral stacking analysis applied to 21-cm line interferometric data from the MIGHTEE and CHILES surveys, conducted with the MeerKAT and VLA radio telescopes, respectively. We draw synthetic M_ samples directly from the publicly-available results underlying the analysis of the COSMOS2020 galaxy photometric sample. Afterwards, we convert M_ into MHI 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 ΩHI by integrating the models for the HIMF built from the posteriors samples of the Schechter parameters. We find a deviation of the HIMF at z~ 0.37 from the results at z~ 0 from the ALFALFA survey and at z~ 1 from uGMRT data. Our results for ΩHI are in broad agreement with other literature results, and follow the overall trend on ΩHI as a function of redshift. The derived value ΩHI=(7.02+0.59-0.52)×10⁻⁴ at z~ 0.37 from the combined analysis deviates at ~ 2.9σ from the ALFALFA result at z~ 0. Our findings about the HIMF and ΩHI differ from previous literature results at z~0 and z~1, although we are unable to confirm at this stage whether these differences are due to cosmic evolution consistent with a smooth transition of the HI content of galaxies over the last 8 Gyr or due to selection biases and systematics.