We present N‐body simulations of a new class of self‐interacting dark matter models, which do not violate any astrophysical constraints due to a non‐power‐law velocity dependence of the transfer cross‐section which is motivated by a Yukawa‐like new gauge boson interaction. Specifically, we focus on the formation of a Milky‐Way‐like dark matter halo taken from the Aquarius project and resimulate it for a couple of representative cases in the allowed parameter space of this new model. We find that for these cases, the main halo only develops a small core (∼1 kpc) followed by a density profile identical to that of the standard cold dark matter scenario outside of that radius. Neither the subhalo mass function nor the radial number density of subhaloes is altered in these models but there is a significant change in the inner density structure of subhaloes resulting in the formation of a large density core. As a consequence, the inner circular velocity profiles of the most massive subhaloes differ significantly from the cold dark matter predictions and we demonstrate that they are compatible with the observational data of the brightest Milky Way dwarf spheroidals (dSphs) in such a velocity‐dependent self‐interacting dark matter scenario. Specifically, and contrary to the cold dark matter case, there are no subhaloes that are more concentrated than what is inferred from the kinematics of the Milky Way dSphs. We conclude that these models offer an interesting alternative to the cold dark matter model that can reduce the recently reported tension between the brightest Milky Way satellites and the dense subhaloes found in cold dark matter simulations.

Self-Interacting Dark Matter is an attractive alternative to the Cold Dark Matter paradigm only if it is able to substantially reduce the central densities of dwarf-size haloes while keeping the densities and shapes of cluster-size haloes within current constraints. Given the seemingly stringent nature of the latter, it was thought for nearly a decade that Self-Interacting Dark Matter would be viable only if the cross section for self-scattering was strongly velocitydependent. However, it has recently been suggested that a constant cross section per unit mass of σ T /m ∼ 0.1 cm 2 g −1 is sufficient to accomplish the desired effect. We explicitly investigate this claim using high resolution cosmological simulations of a Milky-Way size halo and find that, similarly to the Cold Dark Matter case, such cross section produces a population of massive subhaloes that is inconsistent with the kinematics of the classical dwarf spheroidals, in particular with the inferred slopes of the mass profiles of Fornax and Sculptor. This problem is resolved if σ T /m ∼ 1 cm 2 g −1 at the dwarf spheroidal scales. Since this value is likely inconsistent with the halo shapes of several clusters, our results leave only a small window open for a velocity-independent Self-Interacting Dark Matter model to work as a distinct alternative to Cold Dark Matter.

We present a theoretical analysis of some unexplored aspects of relaxed Bose-Einstein condensate dark matter (BECDM) haloes. This type of ultralight bosonic scalar field dark matter is a viable alternative to the standard cold dark matter (CDM) paradigm, as it makes the same large-scale predictions as CDM and potentially overcomes CDM's small-scale problems via a galaxy-scale de Broglie wavelength. We simulate BECDM halo formation through mergers, evolved under the Schrödinger-Poisson equations. The formed haloes consist of a soliton core supported against gravitational collapse by the quantum pressure tensor and an asymptotic r −3 NFW-like profile. We find a fundamental relation of the core=to-halo mass with the dimensionless invariant Ξ ≡ |E|/M 3 /(Gm/ ) 2 or M c /M 2.6Ξ 1/3 , linking the soliton to global halo properties. For r ≥ 3.5 r c core radii, we find equipartition between potential, classical kinetic, and quantum gradient energies. The haloes also exhibit a conspicuous turbulent behavior driven by the continuous reconnection of vortex lines due to wave interference. We analyse the turbulence 1D velocity power spectrum and find a k −1.1 power-law. This suggests the vorticity in BECDM haloes is homogeneous, similar to thermally-driven counterflow BEC systems from condensed matter physics, in contrast to a k −5/3 Kolmogorov power-law seen in mechanically-driven quantum systems. The mode where the power spectrum peaks is approximately the soliton width, implying the soliton-sized granules carry most of the turbulent energy in BECDM haloes.