The upper bound on the lowest mass halo

Abstract: We explore the connection between galaxies and dark matter halos in the Milky Way (MW) and quantify the implications on properties of the dark matter particle and the phenomenology of low-mass galaxy formation. This is done through a probabilistic comparison of the luminosity function of MW dwarf satellite galaxies to models based on two suites of zoom-in simulations. One suite is dark-matter-only while the other includes a disk component, therefore we can quantify the effect of the MW's baryonic disk on our results. We apply numerous Stellar-Mass-Halo-Mass (SMHM) relations allowing for multiple complexities: scatter, a characteristic break scale, and subhalos which host no galaxy. In contrast to previous works we push the model/data comparison to the faintest dwarfs by modeling observational incompleteness, allowing us to draw three new conclusions. Firstly, we constrain the SMHM relation for $10^2<M_*/M_\odot<10^8$ galaxies, allowing us to bound the peak halo mass of the faintest MW satellite to $M_\mathrm{vir}>2.4\times10^8M_\odot$ ($1\sigma$). Secondly, by translating to a Warm Dark Matter (WDM) cosmology, we bound the thermal relic mass $m_\mathrm{WDM}>2.9$ keV at 95\% confidence, on a par with recent constraints from the Lyman-$\alpha$ forest. Lastly, we find that the observed number of ultra-faint MW dwarfs is in tension with the theoretical prediction that reionisation prevents galaxy formation in almost all $10^8M_\odot$ halos. This can be tested with the next generation of deep imaging surveys. To this end, we predict the likely number of detectable satellite galaxies in the Subaru/HSC survey and the LSST. Confronting these predictions with future observations will be amongst our strongest tests of WDM and the effect reionisation on low-mass systems.