Empirical Models for Dark Matter Halos. I. Nonparametric Construction of Density Profiles and Comparison with Parametric Models

Abstract

We use techniques from nonparametric function estimation theory to extract the density profiles, and their derivatives, from a set of N -body dark matter halos. We consider halos generated from ΛCDM simulations of gravitational clustering, as well as isolated, spherical collapses. The logarithmic density slopes γ ≡ d log ρ/d log r of the ΛCDM halos are found to vary as power-laws in radius, reaching values of γ ≈ −1 at the innermost resolved radii, ∼ 10 −2 r vir . This behavior is significantly different from that of broken power-law models like the NFW profile, but similar to that of models like de Vaucouleurs'. Accordingly, we compare the N -body density profiles with various parametric models to find which provide the best fit. We consider an NFW-like model with arbitrary inner slope; Dehnen & McLaughlin's anisotropic model; Einasto's model (identical in functional form to Sérsic's model but fit to the space density); and the density model of Prugniel & Simien that was designed to match the deprojected form of Sérsic's R 1/n law. Overall, the best-fitting model to the ΛCDM halos is Einasto's, although the Prugniel-Simien and Dehnen-McLaughlin models also perform well. With regard to the spherical collapse halos, both the Prugniel-Simien and Einasto models describe the density profiles well, with an rms scatter some four times smaller than that obtained with either the NFW-like model or the 3-parameter Dehnen-McLaughlin model. Finally, we confirm recent claims of a systematic variation in profile shape with halo mass.

The global mass-to-light ratio of SLACS lenses

“…Although somewhat extreme, such a shape in the outer regions is not unrealistic. Indeed, recent high resolution N-body simulations (Navarro et al 2004;Merritt et al 2006) show that the global mass profile is well approximated by an Einasto model (Einasto 1965;Einasto & Haud 1989;Cardone et al 2005) which indeed predicts such an exponential decay 2 . It is worth stressing that the same results are obtained also for other values of n as we have checked numerically (for n ≥ 2) so that the constraint on α can be used in the following analysis.…”

Density profile of dark matter haloes and galaxies in the horizon–agn simulation: the impact of AGN feedback

“…Moore et al 1998;Jing & Suto 2000). Later numerical works favour the Einasto profile with a finite central density though this profile is still cuspy and close to the NFW one (Merritt et al 2006;Stadel et al 2009;Navarro et al 2010).…”

The variation of rotation curve shapes as a signature of the effects of baryons on dark matter density profiles

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