Abstract
We introduce a new method to calculate dark matter halo density profiles from
simulations. Each particle is 'smeared' over its orbit to obtain a dynamical
profile that is averaged over a dynamical time, in contrast to the traditional
approach of binning particles based on their instantaneous positions. The
dynamical and binned profiles are in good agreement, with the dynamical
approach showing a significant reduction in Poisson noise in the innermost
regions. We find that the inner cusps of the new dynamical profiles continue
inward all the way to the softening radius, reproducing the central density
profile of higher resolution simulations within the 95$\%$ confidence
intervals, for haloes in virial equilibrium. Folding in dynamical information
thus provides a new approach to improve the precision of dark matter density
profiles at small radii, for minimal computational cost. Our technique makes
two key assumptions: that the halo is in equilibrium (phase mixed), and that
the potential is spherically symmetric. We discuss why the method is successful
despite strong violations of spherical symmetry in the centres of haloes, and
explore how substructures disturb equilibrium at large radii.