EDGE: Predictable Scatter in the Stellar Mass--Halo Mass Relation of Dwarf Galaxies

The stellar-mass--halo-mass (SMHM) relation is central to our understanding of galaxy formation and the nature of dark matter. However, its normalisation, slope, and scatter are highly uncertain at dwarf galaxy scales. In this paper, we present DarkLight, a new semi-empirical dwarf galaxy formation model designed to robustly predict the SMHM relation for the smallest galaxies. DarkLight harnesses a correlation between the mean star formation rate of dwarfs and their peak rotation speed -- the $\langle$SFR$\rangle$-$v_{\rm max}$ relation -- that we derive from simulations and observations. Given the sparsity of data for isolated dwarfs with $v_{\rm max} \lesssim 20$ km/s, we fit the $\langle$SFR$\rangle$-$v_{\rm max}$ relation to observational data for dwarfs above this velocity scale and to the high-resolution EDGE cosmological simulations below. Reionisation quenching is implemented via distinct $\langle$SFR$\rangle$-$v_{\rm max}$ relations before and after reionisation. We find that the SMHM scatter is small at reionisation, $\sim$0.2 dex, but rises to $\sim$0.5 dex ($1\sigma$) at a halo mass of $\sim$10$^9$ M$_\odot$ as star formation is quenched by reionisation but dark matter halo masses continue to grow. While we do not find a significant break in the slope of the SMHM relation, one can be introduced if reionisation occurs early ($z_{\rm quench} \gtrsim 5$). Finally, we find that dwarfs can be star forming today down to a halo mass of $\sim$2 $\times 10^9$ M$_\odot$. We predict that the lowest mass star forming dwarf irregulars in the nearby universe are the tip of the iceberg of a much larger population of quiescent isolated dwarfs.