The HI mass function of star-forming galaxies at $\mathbf{z \sim 0.35}$

The neutral atomic hydrogen (HI) mass function (HIMF) describes the distribution of the HI content of galaxies at any epoch; its evolution provides an important probe of models of galaxy formation and evolution. Here, we report Giant Metrewave Radio Telescope HI 21cm spectroscopy of blue star-forming galaxies at $z\approx0.20-0.42$ in the Extended Groth Strip, which has allowed us to determine the scaling relation between the average HI mass ($\rm{M_{HI}}$) and the absolute B-band magnitude ($\rm{M_B}$) of such galaxies at $z \approx 0.35$, by stacking the HI 21cm emission signals of galaxy subsamples in different $\rm{M_B}$ ranges. We combine this $\rm{M_{HI}-M_B}$ scaling relation (with a scatter assumed to be equal to that in the local Universe) with the known B-band luminosity function of star-forming galaxies at these redshifts to determine the HIMF at $z\approx0.35$. We show that the use of the correct scatter in the $\rm{M_{HI}-M_B}$ scaling relation is critical for an accurate estimate of the HIMF. We find that the HIMF has evolved significantly from $z\approx0.35$ to $z\approx0$, i.e. over the last four Gyr, especially at the high-mass end. High-mass galaxies, with $\rm{M_{HI}\gtrsim10^{10}\ M_\odot}$, are a factor of $\approx3.4$ less prevalent at $z\approx0.35$ than at $z \approx 0$. Conversely, there are more low-mass galaxies, with $\rm{M_{HI} \approx10^9\ {M}_\odot}$, at $z\approx0.35$ than in the local Universe. While our results may be affected by cosmic variance, we find that massive star-forming galaxies have acquired a significant amount of HI through merger events or accretion from the circumgalactic medium over the past four Gyr.