The case for a cold dark matter cusp in Draco
  We use a new mass modelling method, GravSphere, to measure the central dark
matter density profile of the Draco dwarf spheroidal galaxy. Draco's star
formation shut down long ago, making it a prime candidate for hosting a
'pristine' dark matter cusp, unaffected by stellar feedback during galaxy
formation. We first test GravSphere on a suite of tidally stripped mock
'Draco'-like dwarfs. We show that we are able to correctly infer the dark
matter density profile of both cusped and cored mocks within our 95% confidence
intervals. While we obtain only a weak inference on the logarithmic slope of
these density profiles, we are able to obtain a robust inference of the
amplitude of the inner dark matter density at 150pc, $\rho_{\rm DM}(150\,{\rm
pc})$. We show that, combined with constraints on the density profile at larger
radii, this is sufficient to distinguish a $\Lambda$ Cold Dark Matter
($\Lambda$CDM) cusp $-$ that has $\rho_{\rm DM}(150\,{\rm pc}) > 1.8 \times
10^8\,{\rm M}_\odot \,{\rm kpc}^{-3}$ $-$ from alternative dark matter models
that have lower inner densities. We then apply GravSphere to the real Draco
data. We find that Draco has an inner dark matter density of $\rho_{\rm
DM}(150\,{\rm pc}) = 2.4_{-0.6}^{+0.5} \times 10^8\,{\rm M}_\odot \,{\rm
kpc}^{-3}$, consistent with a $\Lambda$CDM cusp. Using a velocity independent
SIDM model, calibrated on $\Lambda$SIDM cosmological simulations, we show that
Draco's high central density gives an upper bound on the SIDM cross section of
$\sigma/m < 0.57\,{\rm cm}^2\,{\rm g}^{-1}$ at 99% confidence. We conclude that
the inner density of nearby dwarf galaxies like Draco provides a new and
competitive probe of dark matter models.
