Dark matter phase space densities

Abstract

The low velocity part of a kinetic equilibrium dark matter distribution has higher phase space density and is more easily incorporated in formation of a low mass galaxy than the high velocity part. For relativistically decoupling fermions (bosons), this explains one (two) orders of magnitude of the observed trend, that phase space densities in dark matter halo cores are highest in the smallest systems, and loosens constraints on particle masses significantly. For non-relativistic decoupling and/or finite chemical potentials even larger effects may occur. It is therefore premature to dismiss dissipationless particle distributions as dark matter on the basis of phase space arguments.

Figures (2)

• Figure 1: Phase space density of dark matter particles in units of the mean density as a function of fraction of particles, $F$. Upper (lower) solid curves are fermions with $(m-\mu_D) /T_D=0$ and $m/T_D\rightarrow 0$ ($\infty$). Lower (upper) dotted curves are for bosons in the same limits. Dashed curves are for fermions and bosons alike in the limits $(m-\mu_D)/T_D\rightarrow \infty$ for $m/T_D\rightarrow 0$ (upper) and $m/T_D\rightarrow\infty$ (lower). Fully degenerate fermions ($(m-\mu_D)/T_D\rightarrow -\infty$) have no amplification factor, i.e. $q/q_X\equiv 1$.
• Figure 2: As Figure 1, but as function of the dimensionless momentum, $x$.