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Galaxy Number Counts and Implications for Strong Lensing

We compare galaxy number counts in HST/ACS fields containing moderate-redshift (0.2<z<1.0) strong gravitational lenses with those in two control 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 (mu_0) 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, with the number counts in the COSMOS sample being significantly higher than in the pure parallel sample for 21 <= F814W <= 23. 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 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 reduces this overdensity to the 1-2 sigma level. Thus, the overdensity of galaxies seen along a typical line of sight to a lens can be explained mostly by the natural clustering of galaxies, rather than being due to lenses lying along otherwise biased lines of sight. However, a larger sample of lenses is needed to see if the remaining bias persists when the lens-field uncertainties are smaller. (iii) There is considerable scatter in the lines of sight to _individual_ lens systems, but quantities that are linearly dependent on the external convergence (e.g., H_0) should become unbiased if the extra galaxies that cause the bias can be accounted for in the lens models either through direct modeling or via an informed prior on the external convergence. The number counts can used to set such an informed prior.