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 ( \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 at the > 10– \sigma 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– \sigma 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 \la 1– \sigma 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 . H _ { 0 } ) should become unbiased if the few extra galaxies that cause the bias ( i.e . \Delta \mu _ { 0 } \la 2.0 galaxies with 19 \leq m \leq 24 for aperture sizes \leq 45 ^ { \prime \prime } radius ) can be accounted for in the lens models .