MIGHTEE-H I: the M_Hi - M_* relation of massive galaxies and the H I mass function at 0.25 < z < 0.5 

The relationship between the already formed stellar mass in a galaxy and the gas reservoir of neutral atomic hydrogen, is a key element in our understanding of how gas is turned into stars in galaxy haloes. In this paper, we measure the M_HI − M_* relation based on a stellar-mass selected sample at 0.25 < z < 0.5 and the MeerKAT International GHz Tiered Extragalactic Exploration-H I Data Release 1 spectral data. Using a powerful Bayesian stacking technique, for the first time we are also able to measure the underlying bivariate distribution of H I mass and stellar mass of galaxies with M_* > 10_9.5 M, finding that an asymmetric underlying H I distribution is strongly preferred by our complete samples. We define the concepts of the average of the logarithmic H I mass, ⟨log10(MH I)⟩, and the logarithmic average of the H I mass, log10(⟨M_{H I}⟩), and find that the difference between ⟨log10(MH I)⟩ and log10(⟨M_{H I}⟩) can be as large as ∼0.5 dex for the preferred asymmetric H I distribution. We observe shallow slopes in the underlying M_{H I} − M_* scaling relations, suggesting the presence of an upper H I mass limit beyond which a galaxy can no longer retain further H I gas. From our bivariate distribution we also infer the H I mass function at this redshift and find tentative evidence for a decrease of 2–10 times in the comoving space density of the most H I massive galaxies up to z ∼ 0.5.K