EDGE: What shapes the relationship between HI and stellar observables in
  faint dwarf galaxies?
  We show how the interplay between feedback and mass-growth histories
introduces scatter in the relationship between stellar and neutral gas
properties of field faint dwarf galaxies ($M_{\star} \lessapprox 10^{6}
M_{\odot}$). Across a suite of cosmological, high-resolution zoomed
simulations, we find that dwarf galaxies of stellar masses $10^5 \leq M_{\star}
\leq 10^{6} M_{\odot}$ are bimodal in their cold gas content, being either
HI-rich or HI-deficient. This bimodality is generated through the coupling
between (i) the modulation of HI contents by the background of ultraviolet
radiation (UVB) at late times and (ii) the significant scatter in the
stellar-mass-halo-mass relationship induced by reionization. Furthermore, our
HI-rich dwarfs exhibit disturbed and time-variable neutral gas distributions
primarily due to stellar feedback. Over the last four billion years, we observe
order-of-magnitude changes around the median $M_{HI}$, factor-of-a-few
variations in HI spatial extents, and spatial offsets between HI and stellar
components regularly exceeding the galaxies' optical sizes. Time variability
introduces further scatter in the $M_{\star}-M_{HI}$ relation and affects a
galaxy's detectability in HI at any given time. These effects will need to be
accounted for when interpreting observations of the population of faint,
HI-bearing dwarfs by the combination of optical and radio wide, deep surveys.
