A dynamics-based density profile for dark haloes -- II. Fitting function
  The density profiles of dark matter haloes are commonly described by fitting
functions such as the NFW or Einasto models, but these approximations break
down in the transition region where halos become dominated by newly accreting
matter. In Paper I we dynamically split simulation particles into orbiting and
infalling components and analysed their separate profiles. Here we propose
simple, accurate fitting functions designed to capture the asymptotic shapes of
the two terms at large and small radii. The orbiting term is described as a
truncated Einasto profile, $\rho_{\rm orb} \propto \exp \left[-2/\alpha\ (r /
r_{\rm s})^\alpha - 1/\beta\ (r / r_{\rm t})^\beta \right]$, with a
five-parameter space of normalization, physically distinct scale and truncation
radii, and $\alpha$ and $\beta$, which control how rapidly the profiles
steepen. The infalling profile is modelled as a power law in overdensity that
smoothly transitions to a constant at the halo centre. We show that these
formulae fit the averaged, total profiles in simulations to about 5% accuracy
across almost all of an expansive parameter space in halo mass, redshift,
cosmology, and accretion rate. When fixing $\alpha = 0.18$ and $\beta = 3$, the
formula becomes a three-parameter model for the orbiting term that fits
individual halos better than the Einasto profile on average.
