The Dekel-Zhao profile: A mass-dependent dark-matter density profile
  with flexible inner slope and analytic potential, velocity dispersion, and
  lensing properties
  We explore a function with two shape parameters for the dark-matter halo
density profile subject to baryonic effects, which is a special case of the
general Zhao family of models applied to simulated dark matter haloes by Dekel
et al. This profile has variable inner slope and concentration parameter, and
analytic expressions for the gravitational potential, velocity dispersion, and
lensing properties. Using the NIHAO cosmological simulations, we find that it
provides better fits than the Einasto profile and the generalized NFW profile
with variable inner slope, in particular towards the halo centers. We show that
the profile parameters are correlated with the stellar-to-halo mass ratio
$M_{\rm star}/M_{\rm vir}$. This defines a mass-dependent density profile
describing the average dark matter profiles in all galaxies, which can be
directly applied to observed rotation curves of galaxies, gravitational lenses,
and semi-analytic models of galaxy formation or satellite-galaxy evolution. The
effect of baryons manifests itself by a significant flattening of the inner
density slope and a 20\% decrease of the concentration parameter for $M_{\rm
star}/M_{\rm vir} = 10^{-3.5}$ to $10^{-2}$, corresponding to $M_{\rm star}
\sim 10^{7-10} M_\odot$. The accuracy by which this profile fits simulated
galaxies is similar to certain multi-parameter, mass-dependent profiles, but
its fewer parameters and analytic nature make it most desirable for many
purposes.
