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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: $γ_T = ΔΣ\times Σ_c^{-1}$. When the lenses are assigned their observed redshifts and $Σ_c$ is taken to be the critical surface mass density of the central lens, the relationship $γ_T = ΔΣ\times Σ_c^{-1}$ 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 $γ_T$ to $ΔΣ\times Σ_c^{-1}$ 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 $γ_T$ and $ΔΣ\times Σ_c^{-1}$ are functions of both $r_p$ and the velocity dispersions of the central lenses, $σ_v$. At large $r_p$, the difference between $γ_T$ and $ΔΣ\times Σ_c^{-1}$ is, on average, much greater for low-$σ_v$ central lenses than it is for high-$σ_v$ central lenses.