Magnification bias corrections to galaxy-lensing cross-correlations

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 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 ℓ = 1000, the correction is above 1% × (5s f − 2)/b f for z f 0.37, and above 5% × (5s f − 2)/b f for z f 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 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.PACS numbers: 98.80.Es; 98.65.Dx; 95.35.+d

Ray-tracing through the Millennium Simulation: Born corrections and lens-lens coupling in cosmic shear and galaxy-galaxy lensing

“…We became aware recently that Ziour & Hui (2008) discuss the impact of magnification bias on galaxygalaxy lensing power spectra.…”

Weak lensing in the Horizon-AGN simulation lightcone

“…For z l 0.6, the lens population starts being lensed by yet nearer structures. This can lead to a magnification bias, which was studied by Ziour & Hui (2008).…”

Large-scale imprint of relativistic effects in the cosmic magnification

“…the background flux per unit solid angle per redshift bin is proportional to the associated observed magnification density, it follows that ∂ lnF = ∂ lnM; consequently δF/F = δM/M. The quantity Q is the magnification bias [3,6,7,[9][10][11][12][13][14][15][16]65], given by…”