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
$10^2<M_*/M_ødot<10^8$ galaxies, allowing us to bound the peak halo mass of
the faintest MW satellite to $M_vir<2.4\times10^8M_ødot$ ($1\sigma$).
Secondly, by translating to a Warm Dark Matter (WDM) cosmology, we bound the
thermal relic mass $m_WDM>2.9$ 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
$10^8M_ødot$ 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.
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