Conserved actions, maximum entropy and dark matter haloes
ABSTRACT We use maximum entropy arguments to derive the phase space distribution of a virializeddark matter halo. Our distribution function gives an improved representation of the end prod-uct of violent relaxation. This is achieved by incorporating physically motivated dynamicalconstraints (speciﬁcally on orbital actions) which prevent arbitrary redistribution of energy.We compare the predictions with three high-resolution dark matter simulations of widelyvarying 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% of the dark mat-ter). They can be accounted for within the presented framework once the short dynamicaltimescales of the centre are taken into account. 1 INTRODUCTIONFor over two decades it has been possible to use numerical meth-ods to model systems of cold, collisionless dark matter particlescollapsing under gravity to form stable, virialized ‘halos’ (Frenket al. 1985; Dubinski & Carlberg 1991; for a review see Frenk &White 2012). The density of these halos declines with radius fol-lowing a slowly changing power law dependence, roughly r ˘r