The phase space density of fermionic dark matter haloes

TL;DR

This study investigates how primordial thermal velocities of fermionic dark matter influence halo density profiles, revealing that phase space density constraints challenge warm dark matter models based on dwarf galaxy observations.

Contribution

It introduces a numerical analysis linking primordial velocities to core formation and develops a model predicting phase space density from observable galaxy properties.

Findings

Maximum phase space density approaches theoretical limit

Pseudo phase space density overestimates true density

Dwarf galaxy cores imply warm dark matter particle mass below 1.2 keV

Abstract

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 6 dimensional phase space using the EnBid code) is very close to the theoretical fine-grained upper bound, while the pseudo phase space density, Q ~ {\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 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 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 recent simulations of galaxy formation in the cold dark matter model.