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 $z_f$: 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 $\ell =1000$, the correction is above $1\%\times (5s_f-2)/b_f$ for $z_f\gtrsim 0.37$, and above $5\%\times (5s_f-2)/b_f$ for $z_f\gtrsim 0.67$, where $s_f$ is the number count slope of the foreground sample and $b_f$ 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 $(5s_f-2)/b_f=1$, we find that the foreground redshift should be limited to $z_f\lesssim 0.45$ in order to avoid biasing the inferred dark energy equation of state $w$ by more than 5%, and that even for a low foreground redshift ($<0.45$), 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