An analytic surface density profile for $\Lambda$CDM halos and gravitational lensing studies

Abstract

We introduce an analytic surface density profile for dark matter halos that accurately reproduces the structure of simulated halos of mass $M_{\mathrm{vir}}=10^{7-11}{M}_{\odot }$, making it useful for modeling line-of-sight perturbers in strong gravitational lensing models. The two-parameter function has an analytic deflection potential and is more accurate than the projected Navarro, Frenk & White (NFW) profile commonly adopted at this mass scale for perturbers, especially at the small radii of most relevant for lensing perturbations. Using a characteristic radius, $R_{-1}$, where the log slope of surface density is equal to $-1$, and an associated surface density, ${\Sigma }_{-1}$, we can represent the expected lensing signal from line-of-sight halos statistically, for an ensemble of halo orientations, using a distribution of {\em projected concentration} parameters, ${\mathcal{C}}_{\mathrm{vir}}:=r_{\mathrm{vir}}/R_{-1}$. Though an individual halo can have a projected concentration that varies with orientation with respect to the observer, the range of projected concentrations correlates with the usual three-dimensional halo concentration in a way that enables ease of use.

15 pages, 13 figures, Accepted to MNRAS