Gravitational Lensing by NFW Halos

We investigate the gravitational lensing properties of dark matter halos with Navarro, Frenk & White (NFW) density profiles and derive an analytic expression for the radial dependence of the shear, γ(x), due to these objects. In addition, we derive an expression for the mean shear interior to a given radius, (x), and use this to quantify systematic errors that will arise in weak-lensing mass estimates of astronomical objects in cases where the mass estimate is based on an a priori assumption that the underlying potential is that of a singular isothermal sphere when in fact the potential is that of an NFW-type object. On mass scales of 1011 M☉ ≲ M200 ≲ 1015 M☉, the assumption of an isothermal sphere potential results in an overestimate of the halo mass, and the amount by which the mass is overestimated increases linearly with the value of the NFW concentration parameter. Considerable overestimates of the mass (~60%) can occur for galaxy-sized halos, but for rich clusters the mass overestimate is small. The degree to which the mass is systematically in error depends on the cosmology adopted, with a COBE-normalized standard cold dark matter (CDM) model yielding the largest systematic errors for a given true value of the halo mass.