The E/SO sequence of a cluster defines a boundary redward of which a reliable weak lensing signal can be obtained from background galaxies , uncontaminated by cluster members .
For bluer colors , both background and cluster galaxies are present , reducing the average distortion signal by the proportion of unlensed cluster members .
In deep Subaru and HST/ACS images of A1689 , we show that the tangential distortion of galaxies with bluer colors falls rapidly toward the cluster center relative to the background reference level provided by the red background .
We use this dilution effect to derive the cluster light profile and luminosity function to large radius , with the advantage that no subtraction of far-field background counts is required .
The light profile of A1689 is found to decline steadily to the limit of the data , r < 2 ~ { } h ^ { -1 } Mpc , with a constant slope , d \log ( L ) / d \log ( r ) = -1.12 \pm 0.06 , unlike the lensing mass profile which steepens continuously with radius , so that M / L peaks at an intermediate radius , \simeq 100 ~ { } h ^ { -1 } kpc .
A flatter behaviour is found for the more physically meaningful ratio of dark-matter to stellar-matter , when account is made of the color-mass relation of cluster members .
We derive a cluster luminosity function with a flat faint-end slope of \alpha = -1.05 \pm 0.07 , nearly independent of radius and with no faint upturn to M _ { i ^ { \prime } } < { -12 } .
We establish that the very bluest objects are negligibly contaminated by the cluster ( [ V - i ^ { \prime } ] _ { AB } < 0.2 ) , because their distortion profile rises continuously towards the center following the red background ( [ V - i ^ { \prime } ] _ { AB } > 1.2 ) , but is offset higher by \simeq 20 \% .
This larger amplitude is consistent with the greater estimated depth of the faint blue galaxies \langle z \rangle \sim 2 compared to \langle z \rangle \sim 0.85 for the red background , a purely geometric effect .
With a larger sample of background galaxies behind several clusters we may use this geometric effect to constrain the cosmological parameters in a model independent way , by comparing the weak lensing strength over a wide range of photometrically derived redshifts .
Finally , we improve upon our earlier modeling of the mass profile by combining both the red and blue background populations , and very clearly exclude low concentration profiles predicted for massive CDM dominated haloes .