The importance of magnification effects in galaxy-galaxy lensing

¹ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
e-mail: sandra@astro.uni-bonn.de
² Exzellenzcluster Universe, Boltzmannstr. 2, 85748 Garching, Germany
³ Ludwig-Maximilians-Universität, Universitäts-Sternwarte, Scheinerstr. 1, 81679 München, Germany
⁴ Physik-Department, Technische Universität München, 85748 Garching, Germany

Received: 14 October 2019
Accepted: 16 April 2020

Abstract

Magnification changes the observed local number density of galaxies on the sky. This biases the observed tangential shear profiles around galaxies: the so-called galaxy-galaxy lensing (GGL) signal. Inference of physical quantities, such as the mean mass profile of halos around galaxies, are correspondingly affected by magnification effects. We used simulated shear and galaxy data from the Millennium Simulation to quantify the effect on shear and mass estimates from the magnified lens and source number counts. The former is due to the large-scale matter distribution in the foreground of the lenses; the latter is 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, which 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 KiDS+VIKING+GAMA-like survey with lens galaxies at redshift z_d = 0.36 and source galaxies in the last three redshift bins with a mean redshift of _¯z_s = 0.79, the magnification correction changes the shear profile up to 2%, and the mass is biased by up to 8%. We further considered an even higher redshift fiducial lens sample at z_d = 0.83, with a limited magnitude of 22 mag in the r-band and a source redshift of z_s = 0.99. Through this, we find that a magnification correction changes the shear profile up to 45% and that the mass is biased by up to 55%. As expected, the sign of the bias depends on the local slope of the lens luminosity function α_d, where the mass is biased low for α_d <  1 and biased high for α_d >  1. While the magnification effect of sources is rarely more than 1% of the measured GGL signal, the statistical power of future weak lensing surveys warrants correction for this effect.