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.
