The phase-space density of fermionic dark matter haloes

We have performed a series of numerical experiments to investigate how the primordial thermal velocities of fermionic dark matter particles affect the physical and phase-space density profiles of the dark matter haloes into which they collect. The initial particle velocities induce central cores in both profiles, which can be understood in the framework of phase-space density theory. We find that the maximum coarse-grained phase-space density of the simulated haloes (computed in six-dimensional phase space using the ENBID code is very close to the theoretical fine-grained upper bound, while the pseudo-phase-space density, Q similar to rho/sigma(3), overestimates the maximum phase-space density by up to an order of magnitude. The density in the inner regions of the simulated haloes is well described by a 'pseudo-isothermal' profile with a core. We have developed a simple model based on this profile which, given the observed surface brightness profile of a galaxy and its central velocity dispersion, accurately predicts its central phase-space density. Applying this model to the dwarf spheroidal satellites of the Milky Way yields values close to 0.5 keV for the mass of a hypothetical thermal warm dark matter particle, assuming that the satellite haloes have cores produced by warm dark matter free streaming. Such a small value is in conflict with the lower limit of 1.2 keV set by the observations of the Lyman alpha forest. Thus, if the Milky Way dwarf spheroidal satellites have cores, these are likely due to baryonic processes associated with the forming galaxy, perhaps of the kind proposed by Navarro, Eke and Frenk and seen in the recent simulations of galaxy formation in the cold dark matter model.