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.
