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ABSTRACT A standard prediction of galaxy formation theory is that the ionizing background suppresses galaxy formation in haloes with peak circular velocities smaller than $V_{\rm peak}\simeq 20 \, \rm km \, s^{-1}$, rendering the majority of haloes below this scale completely dark. We use a suite of cosmological zoom simulations of Milky Way-like haloes that include central Milky Way disc galaxy potentials to investigate the relationship between subhaloes and ultrafaint galaxies. We find that there are far too few subhaloes within 50 kpc of the Milky Way that had $V_{\rm peak}\gtrsim 20\, \rm km \, s^{-1}$ to account for the number of ultrafaint galaxies already known within that volume today. In order to match the observed count, we must populate subhaloes down to $V_{\rm peak}\simeq 6\, \rm km \, s^{-1}$ with ultrafaint dwarfs. The required haloes have peak virial temperatures as low as 1500 K, well below the atomic hydrogen cooling limit of 104 K. Allowing for the possibility that the Large Magellanic Cloud contributes several of the satellites within 50 kpc could potentially raise this threshold to $10\, \rm km \, s^{-1}$ (4000 K), still below the atomic cooling limit and far below the nominal reionization threshold. 

We perform high-resolution simulations of an MW-like galaxy in a self-interacting cold dark matter model with elastic cross-section over mass of $1~\rm cm^2\, g^{-1}$ (SIDM) and compare to a model without self-interactions (CDM). We run our simulations with and without a time-dependent embedded potential to capture effects of the baryonic disc and bulge contributions. The CDM and SIDM simulations with the embedded baryonic potential exhibit remarkably similar host halo profiles, subhalo abundances, and radial distributions within the virial radius. The SIDM host halo is denser in the centre than the CDM host and has no discernible core, in sharp contrast to the case without the baryonic potential (core size ${\sim}7 \, \rm kpc$). The most massive subhaloes (with $V_{\mathrm{peak}}\gt 20 \, \rm km\, s^{-1}$) in our SIDM simulations, expected to host the classical satellite galaxies, have density profiles that are less dense than their CDM analogues at radii less than 500 pc but the deviation diminishes for less massive subhaloes. With the baryonic potential included in the CDM and SIDM simulations, the most massive subhaloes do not display the too-big-to-fail problem. However, the least dense among the massive subhaloes in both these simulations tend to have the smallest pericenter values, a trend that is not apparent among the bright MW satellite galaxies.