Testing phenomenological and theoretical models of dark matter density profiles with galaxy clusters

We use the stacked gravitational lensing mass profile of four high-mass ($M \gtrsim 10^15M_odot$) galaxy clusters around $z≈ 0.3$ from (Umetsu 2011) to fit density profiles of phenomenological (NFW, Einasto, Sérsic, Stadel and Hernquist) and theoretical (non-singular Isothermal Sphere, DARKexp and Kang & He) models of the dark matter distribution. We account for large-scale structure effects, including a 2-halo term in the analysis. We find that the Stadel model provides the best fit to the data as measured by the reduced $χ^2$. It is followed by the generalized NFW profile with a free inner slope and by the Einasto profile. The NFW model provides the best fit if we neglect the 2-halo term, in agreement with results from (Umetsu 2011). Among the theoretical profiles, the DARKexp model with a single form parameter has the best performance, almost identical to that of the Stadel profile. This may indicate a connection between this theoretical model and the phenomenology of dark matter halos, shedding light on the dynamical basis of empirical profiles which emerge from numerical simulations.