tokens: a low self-interaction cross section). However, it seems unlikely that this same model could then be responsible also for the much larger dark matter core reported in Fornax (e.g. Goerdt et al. 2006 ; Walker Peñarrubia 2011 ; Cole et al. 2012 ; Pascale et al. 2018 ) and the similarly large cores reported in nearby gas-rich isolated dwarf irregulars (e.g. Moore 1994 ; Flores Primack 1994 ; Read et al. 2017 ). By contrast, models in which dark matter is heated by bursty stellar feedback could naturally account for such a diversity of central dark matter densities, at least in principle. Recall that whether or not a dark matter core can form from such ‘heating’ depends on: (i) the pre-infall dark matter halo mass, M 200 ; (ii) the halo concentration parameter, c 200 ; (iii) the total stellar mass, M * ; and (iv) the size of the dark matter core (e.g. Di Cintio et al. 2014 ; Read et al. 2016a ; Contenta et al. 2018 ; Bermejo-Climent et al. 2018 ). (Smaller cores require less energy to form and form more rapidly.) Dark matter cores are also easier to form at high redshift when the star formation rates are high and the halo masses are smaller (Madau, Shen Governato 2014 ). This suggests that small (pc) dark matter cores may indeed form very early in the Universe even in ultra-faint dwarfs. This effect could be ubiquitous, or it could be stochastic, depending on the merger history, spin and/or concentration of any given dwarf (e.g. Laporte Peñarrubia 2015 ). We will return to this issue in more detail in a forthcoming paper where we present GravSphere models for all of the Milky Way classical dwarfs. 8 CONCLUSIONS We have used a new mass modelling method, GravSphere , to measure the central dark matter density profile of the Draco dwarf spheroidal galaxy. Our key findings are as follows: Using mock data with sampling, binary star population, and foreground contamination similar to that for the real Draco dwarf, we showed that GravSphere is able to successfully recover the dark matter density profile of a tidally stripped Draco-like dwarf within its 95 per cent confidence intervals (Fig. 4 ). However, while we were able to distinguish the amplitude of the central density, , of our cored and cusped mocks at 95 per cent confidence, the logarithmic slope of the density profile, , depended on our choice of priors. This sensitivity to the prior diminishes with improved spectroscopic sampling (Appendix B ). We then applied GravSphere to the real Draco data. We inferred a high central density of with logarithmic slope at 95 per cent confidence, consistent with expectations from pure-dark matter structure formation simulations in ΛCDM (Fig. 7 ). We tested the robustness of this result, showing that even using a rather extreme prior on γ DM that biases us towards cored models, our GravSphere models still favour a logarithmic slope of at 95 per cent confidence, steeper than that of a uniform-density core. Dark matter models with a high central density and a
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