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.
