Galaxy Number Counts and Implications for Strong Lensing

We compare galaxy number counts in Advanced Camera for Surveys (ACS) fields containing moderate-redshift (0.2 < z < 1.0) strong gravitational lenses with those in two comparison samples: (1) the first square degree of the COSMOS survey, comprising 259 ACS fields and (2) 20 “pure parallel” fields randomly located on the sky. Through a Bayesian analysis we determine the expectation values (μ0) and confidence levels of the underlying number counts for a range of apertures and magnitude bins. Our analysis has produced the following results: (i) We infer that our control samples are not consistent at the >10–σ level, with the number counts in the COSMOS sample being higher than in the pure parallel sample. This result matches those found in previous analyses of COSMOS data using different techniques. (ii) We find that small-size apertures, centered on strong lenses, are overdense around the 2–σ level compared with randomly placed apertures in the control samples, even compared to the COSMOS sample. Correcting for the local clustering of elliptical galaxies, based on the average two-point correlation function, this over density reduces to the < ∼ 1–σ level. Thus, the overdensity of galaxies seen along a typical line of sight to a lens can be explained by the natural clustering of galaxies, rather than being due to lenses lying along otherwise biased lines of sight. (iii) Despite the considerable scatter in the lines of sight to individual lens systems, we find that quantities that are linearly dependent on the external convergence (e.g. H0) should become unbiased if the few extra galaxies that cause the bias (i.e. ∆μ0 ∼ 2.0 galaxies with 19 ≤ m ≤ 24 for aperture sizes ≤ 45 radius) can be accounted for in the lens models.