Interferometric Cubelet Stacking to Recover H\,\textsc{i} Emission from Distant Galaxies.

In this paper we introduce a method for stacking data cubelets extracted from interferometric surveys of galaxies in the redshifted 21-cm H\,\textsc{i} line. Unlike the traditional spectral stacking technique, which stacks one-dimensional spectra extracted from data cubes, we examine a method based on image domain stacks which makes deconvolution possible. To test the validity of this assumption, we mock a sample of 3622 equatorial galaxies extracted from the GAMA survey, recently imaged as part of a DINGO-VLA project. We first examine the accuracy of the method using a noise-free simulation and note that the stacked image and flux estimation are dramatically improved compared to traditional stacking. The extracted H\,\textsc{i} mass from the deconvolved image agrees with the average input mass to within 3\%. However, with traditional spectral stacking, the derived H\,\textsc{i} is incorrect by greater than a factor of 2. For a more realistic case of a stack with finite S/N, we also produced 20 different noise realisations to closely mimic the properties of the DINGO-VLA interferometric survey. We recovered the predicted average H\,\textsc{i} mass to within $\sim$4\%. Compared with traditional spectral stacking, this technique extends the range of science applications where stacking can be used, and is especially useful for characterizing the emission from extended sources with interferometers.