Semiempirical constraints on the HI mass function of star-forming galaxies and Ω $_HI$ at $z$ ∼ 0.37 from interferometric surveys

Context. The H I mass function (HIMF) is a crucial tool for understanding the evolution of the H I content in galaxies over cosmic time and, hence, to constraining both the baryon cycle in galaxy evolution and the reionization history of the Universe. Aims. We aim to derive semiempirical constraints at z ∼ 0.37 by combining literature results on the stellar mass function from optical surveys with recent findings on the M $_{HI}$ − 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. Methods. We drew synthetic stellar mass samples directly from the publicly available results underlying the analysis of the COSMOS2020 galaxy photometric sample. We then converted M $_{⋆}$ into M $_{HI}$ using analytical fitting functions to the data points from H I stacking. We next fit a Schechter function to the median HIMF from all the samples via Monte Carlo Markov chains. We finally derived the posterior distribution for Ω $_{HI}$ by integrating the models for the HIMF built from the posteriors samples of the Schechter parameters. Results. 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 Ω $_{HI}$ are in broad agreement with other literature results and follow the overall trend on Ω $_{HI}$ as a function of redshift. The derived value Ω $_{HI}$ = (7.02 $^{+0.59}$ $_{−0.52}$ ) × 10 $^{−4}$ at z ∼ 0.37 from the combined analysis deviates by ∼2.9 σ from the ALFALFA result at z ∼ 0. Conclusions. Our findings regarding the HIMF and Ω $_{HI}$ derived from deep, state-of-the-art interferometric surveys differ from previous literature results at z ∼ 0 and z ∼ 1. We are unable to confirm at this stage whether these differences are due to cosmic evolution consistent with a smooth transition of the H I content of galaxies over the last 8 Gyr or due to selection biases and systematics.