Constraining the $z \approx 1$ neutral hydrogen (HI) distribution
We constrain the $z \approx 1$ HI distribution by jointly modeling two independent, existing observations of the 21-cm signal, the HI density parameter $\Omega_{\rm HI}$ measured using uGMRT by stacking the 21-cm emission from blue, star-forming galaxies, and the 21-cm autocorrelation power spectrum (PS) measured using CHIME. We assign HI to the dark matter halos in a cosmological simulation using an HI mass-halo mass (HIHM) relation with three free parameters whose values we estimate by performing a joint Bayesian inference comparing the simulated $\Omega_{\rm HI}$ and 21-cm PS with the measurements. We use the inferred HIHM posterior to simulate the HI distribution and predict the $z \approx 1$ HI mass function (HIMF). We find that the HIMF remains nearly constant at low HI masses $( \lesssim 3.6 \times 10^9 M_\odot)$, and it declines rapidly for larger HI masses. Around $\sim 90$ percent of the total HI gas is contained in the mass range $M_{\rm HI} \in [2 \times 10^9, \, 4 \times 10^{11}] \, M_\odot$. Our estimates predict a larger abundance of high mass HI galaxies than predicted by earlier observations and hydrodynamical simulations. We expect these results to be useful in understanding galaxy evolution and star formation.