EDGE: What shapes the relationship between H I 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 ($M_{\star }\lessapprox 10^{6} \, \mbox{M}_\mathrm{\odot }$). Across a suite of cosmological, high-resolution zoomed simulations, we find that dwarf galaxies of stellar masses $10^5 \le M_{\star }\le 10^{6} \, \mbox{M}_\mathrm{\odot }$ are bimodal in their cold gas content, being either H I-rich or H I-deficient. This bimodality is generated through the coupling between (i) the modulation of H I contents by the background of ultraviolet radiation (UVB) at late times and (ii) the significant scatter in the stellar-to-halo mass relationship induced by reionization. Furthermore, our H I-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 $M_{\mathrm{H\,\small {I} }}$, factor-of-a-few variations in H I spatial extents, and spatial offsets between H I and stellar components regularly exceeding the galaxies' optical sizes. Time variability introduces further scatter in the $M_{\star }\!-\! M_{\mathrm{H\,\small {I} }}$ relation and affects a galaxy's detectability in H I at any given time. These effects will need to be accounted for when interpreting observations of the population of faint, H I-bearing dwarfs by the combination of optical and radio wide, deep surveys.