The Effects of Physically Unrelated Near Neighbors on the Galaxy-Galaxy   Lensing Signal
  The effects of near neighbors on the galaxy-galaxy lensing signal are investigated using a suite of Monte Carlo simulations. The redshifts, luminosities, and relative coordinates for the simulated lenses were obtained from a set of galaxies with known spectroscopic redshifts and known luminosities. As expected, when all lenses are assigned a single, fixed redshift, the mean tangential shear is identically equal to the excess surface mass density, scaled by the critical surface mass density: $\gamma_T = \Delta\Sigma \times \Sigma_c^{-1}$. When the lenses are assigned their observed redshifts and $\Sigma_c$ is taken to be the critical surface mass density of the central lens, the relationship $\gamma_T = \Delta\Sigma \times \Sigma_c^{-1}$ is violated because $\gtrsim 90$% of the near neighbors are located at redshifts significantly different from the central lenses. For a given central lens, physically unrelated near neighbors give rise to a ratio of $\gamma_T$ to $\Delta\Sigma \times \Sigma_c^{-1}$ that spans a wide range of $\sim 0.5$ to $\sim 1.5$ at projected distances $r_p \sim 1$ Mpc. The magnitude and sense of the discrepancy between $\gamma_T$ and $\Delta\Sigma \times \Sigma_c^{-1}$ are functions of both $r_p$ and the velocity dispersions of the central lenses, $\sigma_v$. At large $r_p$, the difference between $\gamma_T$ and $\Delta\Sigma \times \Sigma_c^{-1}$ is, on average, much greater for low-$\sigma_v$ central lenses than it is for high-$\sigma_v$ central lenses. 
Tereasa G. Brainerd
astro-ph.CO