The importance of magnification effects in galaxy-galaxy lensing

Magnification changes the observed number counts of galaxies on the sky. This biases the observed tangential shear profiles around galaxies, the so-called galaxy-galaxy lensing (GGL) signal, and the related excess mass profile. Correspondingly, inference of physical quantities, such as the mean mass profile of halos around galaxies, are affected by magnification effects. We use simulated shear and galaxy data of the Millennium Simulation to quantify the effect on shear and mass estimates from magnified lens and source number counts. The former are due to the large-scale matter distribution in the foreground of the lenses, the latter are caused by magnification of the source population by the matter associated with the lenses. The GGL signal is calculated from the simulations by an efficient fast-Fourier transform that can also be applied to real data. The numerical treatment is complemented by a leading-order analytical description of the magnification effects, which is shown to fit the numerical shear data well. We find the magnification effect is strongest for steep galaxy luminosity functions and high redshifts. For a lens redshift of $z_\mathrm{d}=0.83$, a limiting magnitude of $22\,\mathrm{mag}$ in the $r$-band and a source redshift of $z_\mathrm{s}=0.99$, we find that a magnification correction changes the shear profile up to $45\%$ and the mass is biased by up to $55 \%$. For medium-redshift galaxies the relative change in shear and mass is typically a few percent. As expected, the sign of the bias depends on the local slope of the lens luminosity function $\alpha_\mathrm{d}$, where the mass is biased low for $\alpha_\mathrm{d}<1$ and biased high for $\alpha_\mathrm{d}>1$. Whereas the magnification effect of sources is rarely than more $1\%$, the statistical power of future weak lensing surveys warrants correction for this effect.