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.
