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.