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 transition region where halos become dominated newly accreting matter. Here we present a simple, accurate new function that is inspired asymptotic shapes separate orbiting and infalling halo components. term truncated profile, $\rho_{\rm orb} \propto \exp \left[-2/\alpha\ (r / r_{\rm s})^\alpha - 1/\beta\ t})^\beta \right]$, with five-parameter space normalization, physically distinct scale truncation radii, $\alpha$ $\beta$, which control how rapidly steepen. profile modelled power law overdensity smoothly transitions to constant at centre. We show formulae fit averaged, total simulations about 5% accuracy across almost all an expansive parameter mass, redshift, cosmology, accretion rate. When fixing $\alpha = 0.18$ $\beta 3$, formula becomes three-parameter model fits individual better than on average. By analogy King profiles, sharp resembles cut-off binding energy.