EDGE: The sensitivity of ultra-faint dwarfs to a metallicity-dependent initial mass function

We study how an observationally-motivated, metallicity-dependent initial mass function (IMF) affects the feedback budget and observables of an ultra-faint dwarf galaxy. We model the evolution of a low-mass ($\approx 8 \, \times \, 10^{8} \, \rm M_{\odot}$) dark matter halo with cosmological, zoomed hydrodynamical simulations capable of resolving individual supernovae explosions. We complement the EDGE galaxy formation model from Agertz et al. (2020) with a new prescription for IMF variations according to Geha et al. (2013). At the low metallicities typical of faint dwarf galaxies, the IMF becomes top-heavy, increasing the efficiency of supernova and photo-ionization feedback in regulating star formation. This results in a 100-fold reduction of the final stellar mass of the dwarf compared to a canonical IMF, at fixed dynamical mass. The increase in the feedback budget is nonetheless met by increased metal production from more numerous massive stars, leading to nearly constant iron content at $z=0$. A metallicity-dependent IMF therefore provides a mechanism to produce low-mass ($\rm M_{\star}\sim 10^3 \rm M_{\odot}$), yet enriched ($\rm [Fe/H]\approx -2$) field dwarf galaxies, thus opening a self-consistent avenue to populate the plateau in $\rm [Fe/H]$ at the faintest end of the mass-metallicity relation.