We investigate the gravitational lensing properties of dark matter halos with Navarro, Frenk & White (NFW) density proÐles and derive an analytic expression for the radial dependence of the shear, c(x), due to these objects. In addition, we derive an expression for the mean shear interior to a given radius, c(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 the assumption of an isothermal sphere potential results in[ 1015 M _ , 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 (D60%) 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.

The Tycho-2 Catalogue contains positions, proper motions, and B T and V T magnitudes for approximately 2.5 million stars. We have obtained spectral types for 351,864 of the Tycho-2 stars by cross-referencing Tycho-2 to several catalogs containing spectral types, using the VizieR astronomical database. The positional matching requirements were stringent (97.5% of the matches were within 1 00 ), and the validity of the positional matches is further supported by the distribution of magnitude differences for matched pairs, which is symmetric about the median value (dV ) med = 0.043 and has a small standard deviation, dV = 0.40 mag.

High-resolution N-body simulations are used to investigate systematic trends in the mass profiles and total masses of clusters as derived from 3 simple estimators: (1) the weak gravitational lensing shear field under the assumption of an isothermal cluster potential, (2) the dynamical mass obtained from the measured velocity dispersion under the assumption of an isothermal cluster potential, and (3) the classical virial estimator. The clusters consist of order 2.5e+05 particles of mass $m_p \simeq 10^{10} \Msun$, have triaxial mass distributions, and significant substructure exists within their virial radii. Not surprisingly, the level of agreement between the mass profiles obtained from the various estimators and the actual mass profiles is found to be scale-dependent. The virial estimator yields a good measurement of the total cluster mass, though it is systematically underestimated by of order 10%. This result suggests that, at least in the limit of ideal data, the virial estimator is quite robust to deviations from pure spherical symmetry and the presence of substructure. The dynamical mass estimate based upon a measurement of the cluster velocity dispersion and an assumption of an isothermal potential yields a poor measurement of the total mass. The weak lensing estimate yields a very good measurement of the total mass, provided the mean shear used to determine the equivalent cluster velocity dispersion is computed from an average of the lensing signal over the entire cluster (i.e. the mean shear is computed interior to the virial radius). [abridged]Comment: Accepted for publication in The Astrophysical Journal. Complete paper, including 3 large colour figures can also be obtained from http://bu-ast.bu.edu/~brainerd/preprints

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