Looking At the Distant Universe with the MeerKAT Array: the HI Mass Function in the Local Universe

We present measurements of the neutral atomic hydrogen (HI) mass function (HIMF) and cosmic HI density ($\Omega_{\rm HI}$) at $0 \leq z \leq 0.088$ from the Looking at the Distant Universe with MeerKAT Array (LADUMA) survey. Using LADUMA Data Release 1 (DR1), we analyze the HIMF via a new "recovery matrix" (RM) method that we benchmark against a more traditional Modified Maximum Likelihood (MML) method. Our analysis, which implements a forward modeling approach, corrects for survey incompleteness and uses extensive synthetic source injections to ensure robust estimates of the HIMF parameters and their associated uncertainties. This new method tracks the recovery of sources in mass bins different from those in which they were injected and incorporates a Poisson likelihood in the forward modeling process, allowing it to correctly handle uncertainties in bins with few or no detections. The application of our analysis to a high-purity subsample of the LADUMA DR1 spectral line catalog in turn mitigates any possible biases that could result from the inconsistent treatment of synthetic and real sources. For the surveyed redshift range, the recovered Schechter function normalization, low-mass slope, and "knee" mass are $\phi_\ast = 3.56_{-1.92}^{+0.97} \times 10^{-3}$ Mpc$^{-3}$ dex$^{-1}$, $\alpha = -1.18_{-0.19}^{+0.08}$, and $\log(M_\ast/M_\odot) = 10.01_{-0.12}^{+0.31}$, respectively, which together imply a comoving cosmic HI density of $\Omega_{\rm HI}=3.09_{-0.47}^{+0.65}\times 10^{-4}$. Our results show consistency between RM and MML methods and with previous low-redshift studies, giving confidence that the cosmic volume probed by LADUMA, even at low redshifts, is not an outlier in terms of its HI content.