Abstract
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 per cent 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 150 pc, ρ _DM(150 pc). We show that, combined with constraints on the density profile at larger radii, this is sufficient to distinguish a Λ Cold Dark Matter (ΛCDM) cusp - that has ρ _DM(150 pc) ≳ 1.8 × 10^8 M_☉ 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 ρ _DM(150 pc) = 2.4_{-0.6}^{+0.5} × 10^8 M_☉ kpc^{-3}, consistent with a ΛCDM cusp. Using a velocity-independent SIDM model, calibrated on ΛSIDM cosmological simulations, we show that Draco's high central density gives an upper bound on the SIDM cross-section of σ/m < 0.57 cm2 g-1 at 99 per cent confidence. We conclude that the inner density of nearby dwarf galaxies like Draco provides a new and competitive probe of dark matter models.