An analytic surface density profile for ΛCDM halos and gravitational lensing studies

We introduce an analytic surface density profile for dark matter halos that accurately reproduces the structure of simulated halos of mass M_ vir = 10^7-11 M_⊙, 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, Σ_-1, we can represent the expected lensing signal from line-of-sight halos statistically, for an ensemble of halo orientations, using a distribution of projected concentration parameters, 𝒞_ vir := r_ 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.