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

monthly notices of the royal astronomical society

The Dekel-Zhao profile: A mass-dependent dark-matter density profile  with flexible inner slope and analytic potential, velocity dispersion, and  lensing properties