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 < v < 1420 MHz (0.005 < z < 0.084) and covering an area similar to 6 deg(2) of the sky, mimicking the observational characteristics of real MeerKAT observations. We find that the primary beam (PB) correction accounts for just few per cent (similar to 8 per cent at 0 PB power, similar to 3 per cent at 0.6 PB power) deviations from the true M-HI signal, and that weighting schemes are 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-HI similar to 40-50 per cent in the studied case). We find no significant difference in the final (M-HI) obtained when spectroscopic redshift uncertainties are accounted for in the stacking procedure (Delta z similar to 0.00035, i.e. Delta v similar to 100km 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 S/N by a factor of similar to root 2 when analyzing the final stacked spectrum (a factor of 4 in a cubelet). This procedure is found to be robustly unbiased, while efficiently increasing the S/N, as expected. We argue that an appropriate framework employing detailed and realistic simulations is required to exploit upcoming data sets from SKA pathfinders in an accurate and reliable manner.