Surface mass density of the Einasto family of dark matter haloes: Are they Sersic-like?

Recent advances in N-body simulations of dark matter haloes have shown that three-parameter models, in particular the Einasto profile characterized by d ln ρ(r)/d ln r ∝ r^α with a shape parameter α ≲ 0.3, are able to produce better fits to the 3D spatial density profiles than two-parameter models like the Navarro, Frenk and White and Moore et al. profiles.In this paper, we present for the first time an analytically motivated form for the 2D surface mass density of the Einasto family of dark matter haloes, in terms of the 3D spatial density parameters for a wide range of the shape parameter 0.1 ≤ α ≤ 1. Our model describes a projected (2D) Einasto remarkably well between 0 and (3-5) r₂₀₀, with errors less than 0.3 per cent for α ≤ 0.3 and less than 2 per cent for α as large as 1. This model (in 2D) can thus be used to fit strong and weak lensing observations of galaxies and clusters whose total spatial (3D) density distributions are believed to be Einasto-like. Further, given the dependence of our model on the 3D parameters, one can reliably estimate structural parameters of the spatial (3D) density from 2D observations.We also consider a Sersic-like parametrization for the above family of projected Einasto and observe that fits with a Sersic model are sensitive to whether one fits the projected density in linear scale or logarithmic scale and yield widely varying results. Structural parameters of Einasto-like systems, inferred from fits with a Sersic model, should be used with caution.