ABSTRACT Low-mass dwarf galaxies are expected to reside within dark matter haloes that have a pristine, ‘cuspy’ density profile within their stellar half-light radii. This is because they form too few stars to significantly drive dark matter heating through supernova-driven outflows. Here, we study such simulated faint systems ($10^4 \le M_{\star }\le 2 \times 10^6 \, \mbox{M}_\mathrm{\odot }$) drawn from high-resolution (3 pc) cosmological simulations from the ‘Engineering Dwarf Galaxies at the Edge of galaxy formation’ (EDGE) project. We confirm that these objects have steep and rising inner dark matter density profiles at z = 0, little affected by galaxy formation effects. But five dwarf galaxies from the suite also showcase a detectable H i reservoir ($M_{\mathrm{H\, {\small I} }}\approx 10^{5}-10^{6} \, \mbox{M}_\mathrm{\odot }$), analogous to the observed population of faint, H i-bearing dwarf galaxies. These reservoirs exhibit episodes of ordered rotation, opening windows for rotation curve analysis. Within actively star-forming dwarfs, stellar feedback easily disrupts the tenuous H i discs ($v_{\phi , g}\approx 10\, \mathrm{km} \, \mathrm{s}^{-1}$), making rotation short-lived ($\ll 150 \, \mathrm{Myr}$) and more challenging to interpret for dark matter inferences. In contrast, we highlight a long-lived ($\ge 500 \, \mathrm{Myr}$) and easy-to-interpret H i rotation curve extending to $\approx 2\, r_{1/2, \text{3D}}$ in a quiescent dwarf, that has not formed new stars since z = 4. This stable gas disc is supported by an oblate dark matter halo shape that drives high-angular momentum gas flows. Our results strongly motivate further searches for H i in rotation curves in the observed population of H i-bearing low-mass dwarfs, that provide a key regime to disentangle the respective roles of dark matter microphysics and galaxy formation effects in driving dark matter heating.
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