Gravitational lensing by NFW halos

We investigate the gravitational lensing properties of dark matter halos wi th Navarro, Frenk & White (NFW) density profiles and derive an analytic exp ression for the radial dependence of the shear, gamma(x), due to these obje cts. In addition, we derive an expression for the mean shear interior to a given radius, <(gamma)over bar>(x), and use this to quantify systematic err ors 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 th e 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 10(11) M. l ess than or similar to M-200 less than or similar to 10(15) M., the assumpt ion of an isothermal sphere potential results in an overestimate of the hal o mass, and the amount by which the mass is overestimated increases linearl y with the value of the NFW concentration parameter. Considerable overestim ates of the mass (similar to 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-n ormalized standard cold dark matter (CDM) model yielding the largest system atic errors for a given true value of the halo mass.