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 .