Abstract
Galaxy-galaxy or galaxy-quasar lensing can provide important information on the mass distribution in the Universe. It consists of correlating the lensing signal (either shear or magnification) of a background galaxy/quasar sample with the number density of a foreground galaxy sample. However, the foreground galaxy density is inevitably altered by the magnification bias due to the mass between the foreground and the observer, leading to a correction to the observed galaxy-lensing signal. The aim of this paper is to quantify this correction. The single most important determining factor is the foreground redshift : the correction is small if the foreground galaxies are at low redshifts but can become non-negligible for sufficiently high redshifts. For instance, we find that for the multipole , the correction is above for , and above for , where is the number count slope of the foreground sample and its galaxy bias. These considerations are particularly important for geometrical measures, such as the Jain and Taylor ratio or its generalization by Zhang et al. Assuming , we find that the foreground redshift should be limited to in order to avoid biasing the inferred dark energy equation of state by more than 5%, and that even for a low foreground redshift (), the background samples must be well separated from the foreground to avoid incurring a bias of similar magnitude. Lastly, we briefly comment on the possibility of obtaining these geometrical measures without using galaxy shapes, using instead magnification bias itself.
- Received 19 September 2008
DOI:https://doi.org/10.1103/PhysRevD.78.123517
©2008 American Physical Society