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ABSTRACT It has been proposed that gravothermal collapse due to dark matter self-interactions (i.e. self-interacting dark matter, SIDM) can explain the observed diversity of the Milky Way (MW) satellites’ central dynamical masses. We investigate the process behind this hypothesis using an N-body simulation of a MW-analogue halo with velocity-dependent SIDM (vdSIDM) in which the low-velocity self-scattering cross-section, $\sigma _{\rm T}/m_{\rm x}$, reaches 100 cm2 g−1; we dub this model the vd100 model. We compare the results of this simulation to simulations of the same halo that employ different dark models, including cold dark matter (CDM) and other, less extreme SIDM models. The masses of the vd100 haloes are very similar to their CDM counterparts, but the values of their maximum circular velocities, Vmax, are significantly higher. We determine that these high Vmax subhaloes were objects in the mass range [5 × 106, 1 × 108] M⊙ at z = 1 that undergo gravothermal core collapse. These collapsed haloes have density profiles that are described by single power laws down to the resolution limit of the simulation, and the inner slope of this density profile is approximately −3. Resolving the ever decreasing collapsed region is challenging, and tailored simulations will be required to model the runaway instability accurately at scales <1 kpc. 

ABSTRACT We derive joint constraints on the warm dark matter (WDM) half-mode scale by combining the analyses of a selection of astrophysical probes: strong gravitational lensing with extended sources, the Ly α forest, and the number of luminous satellites in the Milky Way. We derive an upper limit of λhm = 0.089 Mpc h−1 at the 95 per cent confidence level, which we show to be stable for a broad range of prior choices. Assuming a Planck cosmology and that WDM particles are thermal relics, this corresponds to an upper limit on the half-mode mass of Mhm < 3 × 107 M⊙ h−1, and a lower limit on the particle mass of mth > 6.048 keV, both at the 95 per cent confidence level. We find that models with λhm > 0.223 Mpc h−1 (corresponding to mth > 2.552 keV and Mhm < 4.8 × 108 M⊙ h−1) are ruled out with respect to the maximum likelihood model by a factor ≤1/20. For lepton asymmetries L6 > 10, we rule out the 7.1 keV sterile neutrino dark matter model, which presents a possible explanation to the unidentified 3.55 keV line in the Milky Way and clusters of galaxies. The inferred 95 percentiles suggest that we further rule out the ETHOS-4 model of self-interacting DM. Our results highlight the importance of extending the current constraints to lower half-mode scales. We address important sources of systematic errors and provide prospects for how the constraints of these probes can be improved upon in the future.