Conserved actions, maximum entropy and dark matter haloes

We use maximum entropy arguments to derive the phase-space distribution of a virialized dark matter halo. Our distribution function gives an improved representation of the end product of violent relaxation. This is achieved by incorporating physically motivated dynamical constraints (specifically on orbital actions) which prevent arbitrary redistribution of energy.

We compare the predictions with three high-resolution dark matter simulations of widely varying mass. The numerical distribution function is accurately predicted by our argument, producing an excellent match for the vast majority of particles.

The remaining particles constitute the central cusp of the halo (≲4 per cent of the dark matter). They can be accounted for within the presented framework once the short dynamical time-scales of the centre are taken into account.