MIGHTEE-H  I : The M _{H i} – 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 MIGHTEE-H I DR1 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_★ > 109.5 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 (𝑀_HI)⟩, and the logarithmic average of the H i mass, log₁₀ (⟨𝑀_HI⟩), and find that the difference between ⟨log₁₀ (𝑀_HI)⟩ and log10 (⟨𝑀_HI⟩) can be as large as ∼0.5 dex for the preferred asymmetric H i distribution. We observe shallow slopes in the underlying 𝑀_HI − 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 co-moving space density of the most Hi massive galaxies up to 𝑧 ∼ 0.5.