Optimizing spectral stacking for 21-cm observations of galaxies: accuracy assessment and symmetrized stacking

We present an assessment of the accuracy of common operations performed in $21$-cm spectral line stacking experiments. To this end, we generate mock interferometric data surveying the 21-cm emission at frequency $1310<\nu<1420$ MHz ($0.005<z<0.084$) and covering an area $\sim 6$ deg$^2$ of the sky, mimicking the observational characteristics of real MeerKAT observations. We find that the primary beam correction accounts for just few per cent ($\sim8\%$ at 0 primary beam power, $\sim 3\%$ at 0.6 primary beam power) deviations from the true $M_{\rm HI}$ signal, and that weighting schemes based on noise properties provide unbiased results. On the contrary, weighting schemes based on distance can account for significant systematic mass differences when applied to a flux-limited sample ($\Delta M_{\rm HI}\sim 40-50\%$ in the studied case). We find no significant difference in the final $\braket{M_{\rm HI}}$ obtained when spectroscopic redshift uncertainties are accounted for in the stacking procedure ($\Delta z\sim 0.00035$, i.e. $\Delta v \sim 100\,{\rm km\, s}^{-1}$). We also present a novel technique to increase the effective size of the galaxy sample by exploiting the geometric symmetries of galaxy cubelets, potentially enhancing the SNR by a factor $\sim\sqrt{2}$ when analyzing the final stacked spectrum (a factor 4 in a cubelet). This procedure is found to be robustly unbiased, while efficiently increasing the SNR, as expected. We argue that an appropriate framework employing detailed and realistic simulations is required to exploit upcoming datasets from SKA pathfinders in an accurate and reliable manner.