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. Here we present a simple, accurate new fitting function that is inspired by the asymptotic shapes of the separate orbiting and infalling halo components. 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 that fits individual halos better than the Einasto profile on average. By analogy with King profiles, we show that the sharp truncation resembles a cut-off in binding energy.