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The density profiles of dark matter haloes can potentially probe dynamics,fundamental physics, and cosmology, but some of the most promising signalsreside near or beyond the virial radius. While these scales have recentlybecome observable, the profiles at large radii are still poorly understoodtheoretically, chiefly because the distribution of orbiting matter (theone-halo term) is partially concealed by particles falling into halos for thefirst time. We present an algorithm to dynamically disentangle the orbiting andinfalling contributions by counting the pericentric passages of billions ofsimulation particles. We analyse dynamically split profiles out to 10 R200macross a wide range of halo mass, redshift, and cosmology. We show that theorbiting term experiences a sharp truncation at the edge of the orbitdistribution. Its sharpness and position are mostly determined by the massaccretion rate, confirming that the entire profile shape primarily depends onhalo dynamics and secondarily on mass, redshift, and cosmology. The infallingterm also depends on the accretion rate for fast-accreting haloes but is mostlyset by the environment for slowly accreting haloes, leading to a diverse arrayof shapes that does not conform to simple theoretical models. While theresulting scatter in the infalling term reaches 1 dex, the scatter in theorbiting term is only between 0.1 and 0.4 dex and almost independent of radius.We demonstrate a tight correspondence between the redshift evolution in LCDMand the slope of the matter power spectrum. Our code and data are publiclyavailable.

A dynamics-based density profile for dark haloes. I. Algorithm and basic results