When is Stacking Confusing?: The Impact of Confusion on Stacking in Deep
  HI Galaxy Surveys
  We present an analytic model to predict the HI mass contributed by confused
sources to a stacked spectrum in a generic HI survey. Based on the ALFALFA
correlation function, this model is in agreement with the estimates of
confusion present in stacked Parkes telescope data, and was used to predict how
confusion will limit stacking in the deepest SKA-precursor HI surveys. Stacking
with LADUMA and DINGO UDEEP data will only be mildly impacted by confusion if
their target synthesised beam size of 10 arcsec can be achieved. Any beam size
significantly above this will result in stacks that contain a mass in confused
sources that is comparable to (or greater than) that which is detectable via
stacking, at all redshifts. CHILES' 5 arcsec resolution is more than adequate
to prevent confusion influencing stacking of its data, throughout its bandpass
range. FAST will be the most impeded by confusion, with HI surveys likely
becoming heavily confused much beyond z = 0.1. The largest uncertainties in our
model are the redshift evolution of the HI density of the Universe and the HI
correlation function. However, we argue that the two idealised cases we adopt
should bracket the true evolution, and the qualitative conclusions are
unchanged regardless of the model choice. The profile shape of the signal due
to confusion (in the absence of any detection) was also modelled, revealing
that it can take the form of a double Gaussian with a narrow and wide
component.
